Why Two Dimes Data Is Wrong (Continued...)
 

I'm still confused by gergery's original post on the subject.

Let's say the game is $100 buy-in PLO/8. Both the hero and the villain started the hand with exactly $100. On the turn, the pot is heads-up and the board reads:

7[img]/images/graemlins/diamond.gif[/img] 8[img]/images/graemlins/heart.gif[/img] 9[img]/images/graemlins/spade.gif[/img] T[img]/images/graemlins/club.gif[/img]

You are the hero facing an all-in bet of $50 into a $100 pot. That is, to continue you must call your remaining $50 all-in at the chance to win a $150 pot.

Situation 1) You have a draw to the low side of the pot only, giving you exactly 25% pot equity.

Villain: J[img]/images/graemlins/diamond.gif[/img] Q[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/club.gif[/img]
Hero: A[img]/images/graemlins/diamond.gif[/img] 2[img]/images/graemlins/spade.gif[/img] 3[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/spade.gif[/img]

pokenum -o8 jd qs kh kc - ad 2s 3h 4s -- 7d 8h 9s tc
Omaha Hi/Low 8-or-better: 40 enumerated boards containing 9s Tc 7d 8h
cards scoop HIwin HIlos HItie LOwin LOlos LOtie EV
Qs Kc Jd Kh 20 40 0 0 0 0 0 0.750
4s 2s Ad 3h 0 0 40 0 20 0 0 0.250

Situation 2) You have a draw to the high side of the pot only, giving you exactly 25% pot equity.

Villain: J[img]/images/graemlins/diamond.gif[/img] Q[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/club.gif[/img]
Hero: T[img]/images/graemlins/diamond.gif[/img] T[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/spade.gif[/img]

pokenum -o8 jd qs kh kc - td ts ah ks -- 7d 8h 9s tc
Omaha Hi/Low 8-or-better: 40 enumerated boards containing 9s Tc 7d 8h
cards scoop HIwin HIlos HItie LOwin LOlos LOtie EV
Qs Kc Jd Kh 30 30 10 0 0 0 0 0.750
Ks Ts Td Ah 10 10 30 0 0 0 0 0.250

In both situations, twodimes.net says you have the same "EV". Yet if you were to run the two scenarios over and over again, is one situation more profitable than the other?

Re: Why Two Dimes Data Is Wrong (Continued...)
 

In situation 2), there is no possible low.

The same EV is the same EV.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

TGoldman - That's beautiful!

What a well chosen set of cards and money! Did Greg do that, or did you? In any event, very clever!

Hero has either 20/40 outs to take half the pot or 10/40 outs to scoop.

And when the amount in the pot is three times the investment, the odds seem exactly the same. Well done!

But let's make the amount in the pot seven times the investment, as it would be if both players started with $100 each, each had already invested $75 in the pot, and Villain bet $25.

Now when Hero scoops he wins seven times what it costs him to call. But when he wins half the pot, he only wins three times what it costs him to call. He's getting 7 to 1 scoop odds but only 3 to 1 half-pot odds.

Or we could go back to the original example, I suppose. With $150 in the pot, Hero is getting 3 to 1 whole pot odds and only 1 to 1 half pot odds. It's made confusing because of the clever choice of cards and monies involved.

It reminds me of the old bell boy tip puzzle. (Where did the extra dollar go?)

The plain truth is you get better than twice the odds for scooping once than you get for winning half of the pot twice.

The way the simulators tally the results is slighlty misleading. They count two half pot wins the same as one whole pot win. And of course that makes sense.

It's in terms of the odds you're getting when you call the bet that there's the discrepancy. You have to put your chips at risk twice as often to get the same amount back!

Think of it this way: Suppose you were at the race track. Would you rather bet ten dollars once and win seventy dollars, or would you rather bet ten dollars twice and win thirty dollars each time? Either way, when you go to the window to collect, you are awarded a total of eighty dollars.

See it?

Even though you get your own money back, you don't want to be thinking you won eighty dollars. (You either won seventy dollars or sixty dollars).

If you bet ten dollars twice and only win seventy dollars once, that's the same as betting ten dollars twice and winning thirty dollars each time. Looks the same, but it's not.

I think the key to understanding is realizing you have to take twice the risk to get the same money back when you compare half pots to scoops.

And that makes scoops worth more than winning twice as many half pots. But when twodimes.net tallies the results, there's no way to account for that double risk factor.

I've got the much the same problem when I run simulations using Wilson. The low total displayed is the total number of half pots for low times two plus the total number of quarter pots for low times four plus the total number of sixth pots for low times six plus the total number of eighth pots for low times eight. In short,
H*2+Q*4+S*6+E*8 = the total given under "low only pots" in the totals frame of the statistical data to review.

Here are the results of two hands compared (both 10000 runs against eight random hands with random board cards)

hand......high...low....scoop
9JQQs.....471.....0.....815
A333n......77...1071....138

Wilson wisely doesn't total the highs+lows+scoops to get a total. (Twodimes.net does, and records it as "E.V.").

When I total them myself, I get:
hand......high...low....scoop...total
9JQQs.....471.....0.....815.....1286
A333n......77...1071....138.....1286

Neither starting hand is great, but I think
9[img]/images/graemlins/heart.gif[/img], J[img]/images/graemlins/club.gif[/img], Q[img]/images/graemlins/diamond.gif[/img], Q[img]/images/graemlins/heart.gif[/img] is a better starting hand than
A[img]/images/graemlins/heart.gif[/img], 3[img]/images/graemlins/club.gif[/img], 3[img]/images/graemlins/diamond.gif[/img], 3[img]/images/graemlins/spade.gif[/img].
I think that mainly because, although they both have the same winning total, 9JQQs scoops more than A333n.

But how do I quantify that difference?

Anyhow, I don't mean to steal your post with my own problems, and I hope I have made clear to you that scooping is worth more than winning half the pot twice, although the simulator has to show them as the same if the simulator tallies the results (as twodimes.net does).

Buzz

Re: Why Two Dimes Data Is Wrong (Continued...)
 

Buzz, you're forgetting that you get your $25 bet back twice as often in the case where you're drawing to a low as compared to the case where you're drawing to a scoop. Have to include that to get the odds right; when you do, you'll see that the "extra dollar" has been there all along.

TG, the two hands are equivalent equity-wise *and* risk-wise, 2dimes isn't pulling any fast ones.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
Buzz, you're forgetting that you get your $25 bet back twice as often in the case where you're drawing to a low as compared to the case where you're drawing to a scoop. Have to include that to get the odds right; when you do, you'll see that the "extra dollar" has been there all along.

[/ QUOTE ]

FatBallz (Wintermute?) - You have to bet twice as often to get your $25 back twice as often.

When you bet twice as often, you take double the risk.

And in any event, odds are figured on the basis of what you win from someone else divided by what you risk yourself.

Buzz

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
FatBallz (Wintermute?) - You have to bet twice as often to get your $25 back twice as often.

[/ QUOTE ]

Buzz, this is wrong. (The second part.)

Consider running this example 100 times. In either case, you risk $2500. In either case, you end up with $5,000 on average. The scenarios are equivalent in equity and risk.

Edit: One more thing w.r.t. the needing-to-count-your-$25-twice bit. You might argue that when you scoop, you *also* get your opponents $25, so that cancels out. However, you already counted his $25 in those situations by assigning 7:1 odds. We can't count his $25 twice, otherwise we're creating money out of thin air. We'd all get very rich very quickly doing that, which would be fun, but alas it is impossible. The $25 you're getting back twice as often when you draw at the low is the problem with your analysis.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

FatBallz - I think you are right, which means I was wrong.

I need to do some re-thinking regarding this topic.

Thank you for the correction.

Buzz

Re: Why Two Dimes Data Is Wrong (Continued...)
 

I'm still confused then, what was the point gergery was trying to make in his original post?

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
I'm still confused then, what was the point gergery was trying to make in his original post?

[/ QUOTE ]

You'll note further down in that thread that gergery admitted to making a math error.

The point is that twodimes only tells you how often you win parts of the pot. it doesn't tell you how much you have to pay for that equity.

this doens't matter as much when heads up or on turn, but more comes into play in 3 way pots or when there are several cards yet to come.

Simple example:
You have A234 with a flush redraw, your opponent has A234. Board is 567. So you both have nut low with counterfeit protection and a straight. The pot is small now but you both jam huge stacks in all-in.

your opponent has 40% equity, but can only win a portion of a tiny pot on the flop. So his profit here is miniscule even tho he has decent equity. Twodimes gives you chances to win, but that is not profit.

Omaha Hi/Low 8-or-better: 820 enumerated boards containing 7s 6s 5c
cards scoop HIwin HIlos HItie LOwin LOlos LOtie EV
As 2s 3c 4d 0 324 0 496 0 0 820 0.599
Ac 2d 4h 3h 0 0 324 496 0 0 820 0.401

-g

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
[ QUOTE ]
FatBallz (Wintermute?)

Consider running this example 100 times. In either case, you risk $2500. In either case, you end up with $5,000 on average. The scenarios are equivalent in equity and risk.


[/ QUOTE ]

They may have the same EV, but the variance (risk) will be different.

Example of misusing 2 dimes data.
 

I played this hand recently on Prima, which really irritated me and I ran it on 2 dimes and the percentages only aggravated me further when I analyzed it as a 3 way hand.

** Game ID 579278870 starting - 2005-11-15 19:06:04
** Brave Starr [Omaha H/L] (0.50|1.00 Pot Limit - Cash Game) Real Money

- sliwezia sitting in seat 1 with $114.53
- hazan-stepha sitting in seat 2 with $147.06
- Aifix sitting in seat 3 with $58.31
- lagiro sitting in seat 4 with $94.01
- TOLDYOUSO sitting in seat 5 with $66.99 [Sitting out]
- seminole2005 sitting in seat 6 with $98.97
- carnesio sitting in seat 7 with $19.00
- Mendacious sitting in seat 8 with $105.45 [Dealer]
- open_cobra sitting in seat 9 with $62.65
- udomyex sitting in seat 10 with $96.00

open_cobra posted the small blind - $0.50
udomyex posted the big blind - $1.00
carnesio posted to play - $1.00
** Dealing card to Mendacious: 3[img]/images/graemlins/club.gif[/img] A[img]/images/graemlins/club.gif[/img] 8[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/spade.gif[/img]
sliwezia folded
hazan-stepha called - $1.00
Aifix folded
lagiro called - $1.00
seminole2005 folded
carnesio checked
Mendacious called - $1.00
open_cobra called - $1.00
udomyex bet - $4.00
hazan-stepha called - $4.00
lagiro folded
carnesio called - $4.00
Mendacious called - $4.00
open_cobra called - $4.00

** Dealing the flop: Q[img]/images/graemlins/club.gif[/img] 2[img]/images/graemlins/club.gif[/img] 6[img]/images/graemlins/heart.gif[/img]
open_cobra checked
udomyex bet - $21.00
hazan-stepha folded
carnesio went all-in - $16.00
Mendacious raised - $100.00
open_cobra folded
udomyex went all-in - $72.00
carnesio shows: 2[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img] 6[img]/images/graemlins/spade.gif[/img] 6[img]/images/graemlins/diamond.gif[/img]
udomyex shows: A[img]/images/graemlins/heart.gif[/img] Q[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/spade.gif[/img] 8[img]/images/graemlins/diamond.gif[/img]

** Dealing the turn: 9[img]/images/graemlins/club.gif[/img]

** Dealing the river: 2[img]/images/graemlins/diamond.gif[/img]
carnesio wins $66.00 from the main pot
udomyex wins $154.00 from side pot 1

UDOMYEX called a huge raise all in on a hand where I came over him with was over 57% on the flop against 2 opponents, AND UDO's PE was a paltry .083.

pokenum -o8 ac 3c 8h 4s - 2h 5h 6s 6d - ah qs 2s 8d -- qc 2c 6h
Omaha Hi/Low 8-or-better: 666 enumerated boards containing Qc 2c 6h
cards scoop HIwin HIlos HItie LOwin LOlos LOtie EV
4[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/club.gif[/img] 3[img]/images/graemlins/club.gif[/img] 8[img]/images/graemlins/heart.gif[/img] 251 254 412 0 467 0 9 0.576
6[img]/images/graemlins/spade.gif[/img] 6[img]/images/graemlins/diamond.gif[/img] 5[img]/images/graemlins/heart.gif[/img] 2[img]/images/graemlins/heart.gif[/img] 113 341 325 0 0 77 0 0.341
Q[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/spade.gif[/img] 8[img]/images/graemlins/diamond.gif[/img] A[img]/images/graemlins/heart.gif[/img] 35 71 595 0 0 381 9 0.083


HOWEVER,

If you view the hand as a heads up between UDO and I (which my raise really accomplished because of the short stack, UDO may be a 62/38 dog to me, which isn't nearly so bad, AND his call gets him some equity in a decent sized main pot.

cards scoop HIwin HIlos HItie LOwin LOlos LOtie EV
4[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/club.gif[/img] 3[img]/images/graemlins/club.gif[/img] 8[img]/images/graemlins/heart.gif[/img] 366 369 451 0 558 0 9 0.617
Q[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/spade.gif[/img] 8[img]/images/graemlins/diamond.gif[/img] A[img]/images/graemlins/heart.gif[/img] 173 451 369 0 0 460 9 0.383


So how you do the 2 dimes analysis is obviously very relevant to assessing the true odds the players had relative to various portions of the pot, not just as a whole.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

The EV and odds are the same. The only difference is that the low draw hand will have lower variance. Write out the calculation for mean and standard deviation if you can't see this.

BTW Buzz since you [censored] this one up so badly, here's another gem from the archives. Is this the same Buzz getting pwned by Ray Zee?

http://www.twoplustwo.com/digests/ot...9_msg.html#532
[ QUOTE ]
Buzz (to Ray Zee): "However, I think you're missing the boat here. When there is an eight or better for low qualifier, I don't think low hands are better than high hands."

[/ QUOTE ]

P.S. Your posts are always great, don't often get a chance to make fun of you [img]/images/graemlins/smile.gif[/img]

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
[ QUOTE ]
FatBallz (Wintermute?)

Consider running this example 100 times. In either case, you risk $2500. In either case, you end up with $5,000 on average. The scenarios are equivalent in equity and risk.


[/ QUOTE ]

They may have the same EV, but the variance (risk) will be different.

[/ QUOTE ]

Variance and risk are definitely not synonyms. The risk is the same in both cases: $2500. The variance is not.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

Are you agreeing that the variance differs for each situation? If so, can you explain why if the EV is the same and the risk is the same that the variance is different?

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
Are you agreeing that the variance differs for each situation? If so, can you explain why if the EV is the same and the risk is the same that the variance is different?

[/ QUOTE ]

The risk and EV are clearly the same, as my example shows (risk = $2500, average return = $5000).

The variances do differ. To get an idea of why this is, start by considering the distributions of outcomes in each scenario.

In the draw-to-a-low scenario, if you hit your low all 100 times, you will end up with $10k. If you hit your low zero times, you will end up with $0. The distribution is symmetric around the $5k mark.

In the draw-to-a-scoop scenario, if you win every time, you will come away with $20k; if you lose every time, you come away with $0. The distribution is asymmetric, with a fatter edge near the lower end in exchange for a long skinny tail to the upper end. It's intuitive to see that these two distributions will have different variances... it may not be intuitive, but the variance of the scoop distribution is actually higher.

To see this mathematically, model each scenario with the binomial distribution (which captures the sum of n random draws of probability p). The variance, by definition, is n*p*(1-p). So, for the low-only situation, the variance is:

1/2*100*0.5*0.5 = 12.5 pots

where we throw in the extra factor of 1/2 because we only get half of the pot with a success, which is our unit of measure.

For the scoop situation, the variance is:

100*.25*.75 = 18.75 pots

So, drawing to a low here is the better option for the risk-averse. On the other hand, if you want to win $20k one in 4^100 times, you should prefer drawing to the scoop.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
The EV and odds are the same. The only difference is that the low draw hand will have lower variance. Write out the calculation for mean and standard deviation if you can't see this.

BTW Buzz since you [censored] this one up so badly, here's another gem from the archives. Is this the same Buzz getting pwned by Ray Zee?

http://www.twoplustwo.com/digests/ot...9_msg.html#532
[ QUOTE ]
Buzz (to Ray Zee): "However, I think you're missing the boat here. When there is an eight or better for low qualifier, I don't think low hands are better than high hands."

[/ QUOTE ]

P.S. Your posts are always great, don't often get a chance to make fun of you [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]

That's a pretty good thread thanks for digging that up.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

O.K. let’s revisit this topic (which is honestly not very well settled in my own mind). Something seems not quite right about equating winning half a pot twice to scooping once.

I agree that winning half a pot twice is equivalent to scooping once and losing once. But.... well, let me try to explain with an example from a passive $4/$8 game.

Let’s say your opponents will contribute a total of $80 to the pot and it will cost you $24 to play a hand all the way to the showdown.
• When you scoop, you will be awarded all $104 in the pot of which $24 is your own investment.
• When you split the pot, you will be awarded $52, of which $24 is your own investment.

Each time you split such a pot, you only actually win $28. When you win half such a pot twice, what you actually win is $56 (and you get your own investment back). If you go home after splitting two such pots and losing none, you’ll be $56 richer.

On the other hand, when you scoop once, you actually win all $80 your opponents have contributed to the pot (and you get your own investment back). If you go home after scooping one such pot and losing none, you’ll be $80 richer.

You have to scoop one pot and also lose another to end up with the same number of dollars as splitting two pots and losing none.

If instead, you scoop one pot and then get out of the next (instead of contributing and losing $24), in that case, scooping the one pot is better than splitting two pots.
*
I realize that winning half the (same sized) pot twice is the same as scooping once and losing once. (You get your own $24 back plus winning a total of $80 invested by your opponents).

But if you scoop once and don’t lose at all, you’ll end up with more money than if you win half the pot twice and don’t lose at all.
*
Let's consider it from the standpoint of odds after the turn.

When you’re looking at your hand and the board after the turn,
• if it will cost you $16 more to continue to see the showdown if you like the river card,
• if there will be $104 in the pot at the showdown if you continue (including the $8 you’ve already invested plus the $16 it will hencefore cost you to see the showdown), and
• if seeing the river will only cost you $8 if you miss (instead of $16 because you will fold if you miss) then at that point in the hand,
• then you are getting 88 to 8 implied pot odds to win the whole pot.

(The pot at that point contains $8 of what was formerly your own money plus at the showdown it will contain $80 of your opponent’s money).

If you only win half the pot, you’ll be awarded $52, of which $16 is what you will henceforth contribute if you call the turn bet.

When you’re only playing for half the pot, if you continue, you’ll be playing to win $36. You’ll be investing $8 to possibly win $36. You’re getting 36 to 8 implied odds for half the pot.

So when you’re playing to win this whole pot, on the third betting round your implied pot odds are 11 to 1, and when you’re playing to win half this pot,
on the third betting round your implied pot odds are 4.5 to 1.

I'm not done thinking this out yet, and I'm not sure I ever will be.

But although I agree that scooping (the same sized pot) 2000 times in 10000 plays to the showdown is the same as winning half the (same sized) pot 4000 times in 10000 plays, there still seems something amiss in equating two half wins to one scoop.

If there is a "blatant" mistake here, I'm oblivious to it (although I'm sure I'm very capable of making a mistake).

It certainly is not my intention to lead anyone astray. I am, as always, looking for the truth. Alas, sometimes I make mistakes. I will continue to correct them if I see them. (In this regard, the record speaks for itself).

Buzz

Re: Why Two Dimes Data Is Wrong (Continued...)
 

Buzz, whenever I said that your mistakes in this thread were blatant, I mispoke. Truth be told, it's really easy for anyone to confuse themself by drawing up complicated examples. But really the best way to go about this problem is to express it as simply & generally as possible and then see that this covers all possibilities. Running example after example will just allow one to make an error in logic somewhere that will lead you to believe you've found a counterexample, when in fact one has honestly just made an error somewhere.

An anecdote--when I first got into gambling (period) about 5 years ago, I read up on the Martingale system, wrote my own Matlab blackjack simulator, and convinced myself that I could change the EV of blackjack by modifying my bet size, essentially doubling bets when I win repeatedly (in theory to accentuate winning streaks and downplay losing streaks). I even went to lengths to justify this falsehood in my mind by repeating something I heard somewhere about how the players' ability to change their bet size is how they can beat blackjack (not realizing at the time that this referred to card-counting). I mentioned my theory to my brother, and in 2 seconds he told me I was full of it. He explained that no matter what I did with my bet size, I was still going to have the same EV in the game, just the amount wagered would vary.

Well, I got pissed and spent about 3 hours writing down series after series of possible outcomes, trying to demonstrate to myself that my system would yield a winning result in a -EV game. In the end, I realized that I had indeed just made a mistake somewhere, and that when I thought about it my brother's direct, simply way, I saw that this clearly captured all cases, and that I was wrong. (It turns out that modifying bet size affects variance--you can change the shape of the distribution of outcomes, putting greater weight in small wins at the expense of risking an unlikely catastrophe... martingale in a nutshell.)


Now the thing is, when you draw up a very complicated example, it's very difficult to pinpoint each error in logic. I suspect that in your example above, the problem may lie in the statement:

[ QUOTE ]
But if you scoop once and don’t lose at all, you’ll end up with more money than if you win half the pot twice and don’t lose at all.

[/ QUOTE ]

Somehow I get the feeling that this statement implies that you are changing the odds... but I have to admit, I haven't thought about this carefully enough to be sure this is where things have gone awry here. I just know that something in this line of reasoning is out of whack, because a simple, general analysis shows that these two draws have identical EV & risk, just as my brother *knew* with certainty that the EV of blackjack is axiomatically fixed (barring card-counting, etc).


Finally, I apologize for dragging this thing out in the other thread. It gave me satisfaction to point out your mistake then and before because I have been on the other end of it, which is immature. I promise I won't bring this thing up again.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
Let’s say your opponents will contribute a total of $80 to the pot and it will cost you $24 to play a hand all the way to the showdown.
• When you scoop, you will be awarded all $104 in the pot of which $24 is your own investment.
• When you split the pot, you will be awarded $52, of which $24 is your own investment.

Each time you split such a pot, you only actually win $28. When you win half such a pot twice, what you actually win is $56 (and you get your own investment back). If you go home after splitting two such pots and losing none, you’ll be $56 richer.

On the other hand, when you scoop once, you actually win all $80 your opponents have contributed to the pot (and you get your own investment back). If you go home after scooping one such pot and losing none, you’ll be $80 richer.

[/ QUOTE ]

All you've proved in this example is that it's better to have a 1/2 probability of scooping than a 2/3 probability of splitting.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

Someone has to put you out of your misery, might as well be me [img]/images/graemlins/laugh.gif[/img]

As you know, poker is about the long run, and you agree the two are equal in the long run. But in the short run, you think the hi draw is somehow better. So let me ask you this:

You have $100 to gamble. Which of the following do you prefer to do, and why?

- A 1 in 10,000 shot at a million
- A 1 in 2 shot at $200

Is either superior? If the $100 was your food money for the week, which would you take? If you were a millionaire, which would you take?

But you get what I'm saying. So let's look at what you're saying:

[ QUOTE ]
You have to scoop one pot and also lose another to end up with the same number of dollars as splitting two pots and losing none.

[/ QUOTE ]
Correct, so the E.V. is equal in this case.

[ QUOTE ]
If instead, you scoop one pot and then get out of the next (instead of contributing and losing $24), in that case, scooping the one pot is better than splitting two pots.

[/ QUOTE ]
Aha! But that will only happen 1/4 of the time. The other 3/4 of the time, you lose your $24 and there's nothing you can do about it. Your intuition is overlooking this fact. I better write this out to make it clearer:


L = low draw (50%) - L makes $28 or loses $24
H = high draw (25%) - H makes $80 or loses $24

Pretend two concurrent games are running. In one a person has a high draw, in another, a low draw. Pretend only one hand is played. These are the ways it can turn out:

L wins, H wins : H +80, L +28, H nets $52 more (this will happen 1/8 of the time)
L loses, H wins: H +80, L -24, H nets $104 more (this will happen 1/8 of the time)
L wins, H loses: H -24, L +28, L nets $52 more (this will happen 3/8 of the time)
L loses, H loses: H -24, L -24, they both lose $24. (this will happen 3/8 of the time)

So, only 1/8 of the time H will net twice as much as L, but this is balanced out by the fact that L wins $52 more an extra time than H. I think this is where your intuition failed. When H loses and L wins, L actually wins $52 more, not $28 more.

Your next point is about implied odds:

[ QUOTE ]
if seeing the river will only cost you $8 if you miss (instead of $16 because you will fold if you miss) then at that point in the hand, you are getting 88 to 8 implied pot odds to win the whole pot. then you are getting 88 to 8 implied pot odds to win the whole pot.

[/ QUOTE ]

If you still have money to bet on the river, then of course the high draw is favorable and has better EV. No one is debating this (I hope). However, the original question was about being all in and having no more money to bet or make on the river.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
Running example after example will just allow one to make an error in logic somewhere that will lead you to believe you've found a counterexample, when in fact one has honestly just made an error somewhere.

[/ QUOTE ]

Fatballz - I might be making a mistake in logic. I don’t think so, but it’s a possibility. There seem to be a number of posters who are convinced that I am.

I do see very clearly that when you make a 10000 run (or whatever) simulation where all the final pots are the same size, winning half a pot 2000 times or winning a quarter of the pot 4000 times is equivalent to scooping 1000 times.

The simulator I use (Wilson) has the capability of simulating using players who fold along the way under various conditions, and then adding the total amount won by Hero over the 10000 runs. But I don’t see how showing any of that data would clarify the matter.

The simple truth is playing one hand and scooping a pot where your opponents contribute a given amount is worth more to Hero than playing two hands and winning half the same sized pot (where your opponents contribute the same given amount) twice. Period.

[ QUOTE ]
An anecdote--when I first got into gambling (period) about 5 years ago, I read up on the Martingale system, wrote my own Matlab blackjack simulator, .....

[/ QUOTE ]

Interesting anecdote. (I’m not being sarcastic).

[ QUOTE ]
Now the thing is, when you draw up a very complicated example, it's very difficult to pinpoint each error in logic. I suspect that in your example above, the problem may lie in the statement:

But if you scoop once and don’t lose at all, you’ll end up with more money than if you win half the pot twice and don’t lose at all.

[/ QUOTE ]

I didn’t mean to write a complicated example. Try this (not just you WM, anyone): Take a stack of chips of one color. Doesn’t matter how many chips. I just grabbed a stack of ten blue chips. Now let’s suppose they represent your opponents total contribution to the pot. Now take six chips of a different color, say red.

Why six chips? Because in a limit game there are four bets.

Let’s keep it as simple as possible and assume we are playing $1/$2 limit-Omaha-8, that there is a bet on every betting round, and no raises. In that case it will cost Hero $6 to see the showdown.

First, stack the ten chip contribution of Hero’s opponents plus Hero’s six chips together and put it over to your right. There will thus be a 16 chip stack with 10 blue chips and 6 red chips over to your right.

Second, put two identical stacks of chips over to your left. Two stacks, each with 10 blue chips and 6 red chips.

Third, divide each of the stacks over to you left in two, but keeping Hero’s six chips together in each of the half stacks. You will now have four stacks or chips over to your left, two of them with 8 blue chips each and the other two with two blue chips and six red chips each.

Fourth, put one of the stacks with two blue chips and six red chips on top of the other. And put one of the stacks with eight blue chips on top of the other. You will now have two stacks of 16 chips each over to your left, one of the stacks having four blue chips plus twelve red chips.

When you win half the pot twice, you win the stack of chips with twelve red chips and four blue chips.

There’s nothing complicated or tricky here. You simply cannot logically be so obtuse or stubborn to not see that you should rather win eight chips from your opponents than win four chips from your opponents.

Yes, I clearly see that you get awarded the same number of chips when you win half of a given sized pot twice as when you win all of a given sized pot once.

And in terms of counting what you end up with in a simulation, if you scoop a given sized pot 4000 times, and lose your six chips the other 6000 times, that is identical to winning half of the given sized pot 8000 times and losing your six chips the other 2000 times. (You end up with the same number of chips).

Yes, I see that. I do see your point. Winning half the pot 2X/10000 times is identical to winning the whole pot X/10000 times.

Are you unable to comprehend <font color="white">_</font>my point? Winning half the pot 2X/10000 times is <font color="white">_</font>not identical to winning the whole pot X/5000 times.

In a non-folding simulation, such as a twodimes.net simulation, we see how Hero’s hand fares if Hero and opponents play until all five board cards are known. but in a real game, assuming we can play well, we <font color="red">fold</font> some of the time.

To win half the pot twice, you have to play at least twice. To scoop once, you only have to play at least once. A non-folding simulation (such as twodimes.net) has you playing the same number of times, whether you have a chance to possibly scoop after the flop or scooping after the flop is highly unlikely.

[ QUOTE ]
Somehow I get the feeling that this statement implies that you are changing the odds... but I have to admit, I haven't thought about this carefully enough to be sure this is where things have gone awry here. I just know that something in this line of reasoning is out of whack, because a simple, general analysis shows that these two draws have identical EV &amp; risk

[/ QUOTE ]

I’m glad you brought up “risk.” That seems the point. You have to risk some or all of your chips twice to win twice and you only have to risk them once to win once. Therefore, I don’t think the risk is the same.

[ QUOTE ]
axiomatically fixed

[/ QUOTE ]

Interesting phraseology.

Also interesting that you, although seemingly rebellious in some of your posts, seem so sure of an axiomatic idea (regarding ev) I’m challenging.

[ QUOTE ]
Finally, I apologize for dragging this thing out in the other thread.

[/ QUOTE ]

Yeah. I kind of hoped the other thread would go away. Instead Beset re-introduced another thread in which I participated some time ago - a thread I had hoped had gone away. Oh well....

However, it’s good that you did call attention to the other thread. I realize something doesn’t jibe. Maybe someone will be able to make the discrepancy clear.

In terms of your “joke,” I must confess I simply didn’t get it. Didn’t seem right to me that 6789s would beat AA23s, heads-up, but I supposed it was possible a random card generator could randomize such that 6789s would beat AA23s more often than you’d expect. I actually thought of that possibility and also that you had used the simulator incorrectly or mis-read the data, or that there was a typo somewhere.

It didn’t even occur to me that you falsified data to make a joke - not even when I realized how you had falsified the data.

[ QUOTE ]
It gave me satisfaction to point out your mistake

[/ QUOTE ]

Thank you. Whatever your motive, I appreciate you (or anyone) pointing out any mistake I make (or that you think I’ve made). It’s not uncommon for me, while doing something else, to have it pop into my consciousness that I have made an error in a post. And then I feel some kind of obligation, which you may never understand (and which I’m not even sure I understand myself), to make a correction.

[ QUOTE ]
I promise I won't bring this thing up again.

[/ QUOTE ]

As I think about it, I’m actually glad you did bring it up again, because (assuming the total amount contributed to each pot by your opponents is the same) I still think a scoop is better than winning half of two pots. However I do seem to be standing alone on this issue, at least on this forum.

(At the same time, I agree that two half pots equal one scoop in terms of how hands fare in a non-folding simulation, assuming all pots are the same size).

Finally, I apologize to you if I have offended you in my search for the truth.

Buzz

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
All you've proved in this example is that it's better to have a 1/2 probability of scooping than a 2/3 probability of splitting.

[/ QUOTE ]

M.B.E. - First, I don't think I have proven anything. I'm not trying to prove anything. I am trying to get at the truth.

Second, I don't see how the example even indicates (let alone proves) it's better to have a 1/2 probability of scooping than a 2/3 probability of splitting.

But thanks for your reply.

Buzz

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
The simple truth is playing one hand and scooping a pot where your opponents contribute a given amount is worth more to Hero than playing two hands and winning half the same sized pot (where your opponents contribute the same given amount) twice. Period.

[/ QUOTE ]
Buzz, I'm stunned.

Here it is in black and white:

Hero with a 25% high draw to scoop nets $80 or loses $24
Hero with a 50% low draw to split nets $28 or loses $24.

So, ON EACH SINGLE HAND, this is what happens:


High:

25% of the time Hero wins $80, = +$20 per hand
75% of the time Hero loses $24 = -$18 per hand

Net: $2 per hand.

Low

50% of the time Hero wins $28 = $14 per hand
50% of the time Hero loses $24 = $12 per hand

Net: $2 per hand.

Each, individual hand is identical in EV. However, if you wish to lower your variance, the low draw is a better option with the same EV. The variance associated with the high hand is more because you win only half as often.

As I said previously this assumes that all the money goes in on the turn, as stated in the OP.

[ QUOTE ]
(At the same time, I agree that two half pots equal one scoop in terms of how hands fare in a non-folding simulation, assuming all pots are the same size).

[/ QUOTE ]
The two pots concept is unnecessary. One half pot equals one scoop in terms of a single hand.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
However, the original question was about being all in and having no more money to bet or make on the river.

[/ QUOTE ]

Hi Phil - Let me address this part of your post first, because it may make what I am trying to get at clearer.

You're right. The original question was about being all in and having no more money to bet.

But I'm looking at non-folding simulation results (like those of twodimes.net) and trying to show where there seems to be a discrepancy. I'm not picking on twodimes.net. That seems a fine place to run non-folding simulations. But.... well, read on....

[ QUOTE ]
Someone has to put you out of your misery, might as well be me

[/ QUOTE ]

I appreciate your taking the time to write a careful reply. Every time I see a post by you I think of the good times I had in your corner of the world and that delightful kookaburra bird.

[ QUOTE ]
But in the short run, you think the hi draw is somehow better.

[/ QUOTE ]

No. I think scooping once is better than winning half the pot twice, assuming all pots under consideration have equal amounts contributed by your opponents.

[ QUOTE ]
You have $100 to gamble. Which of the following do you prefer to do, and why?

- A 1 in 10,000 shot at a million
- A 1 in 2 shot at $200

[/ QUOTE ]

That's sort of like pot odds, or implied pot odds.

1000000/100 = 10000 to one.
200/2 = only 100 to one.

So naturally I would prefer the one in ten thousand to one shot at a million.

[ QUOTE ]
Is either superior?

[/ QUOTE ]

Yes. the 1 in 10,000 shot at a million is superior.

[ QUOTE ]
If the $100 was your food money for the week, which would you take?

[/ QUOTE ]

At this stage of my life, neither. I think I'd have big problems if I missed eating for a week.

[ QUOTE ]

----------------------------------------You have to scoop one pot and also lose another to end up with the same number of dollars as splitting two pots and losing none.
----------------------------------------

Correct, so the E.V. is equal in this case.

[/ QUOTE ]

Agreed.

[ QUOTE ]

----------------------------------------If instead, you scoop one pot and then get out of the next (instead of contributing and losing $24), in that case, scooping the one pot is better than splitting two pots.
----------------------------------------

Aha! But that will only happen 1/4 of the time. The other 3/4 of the time, you lose your $24 and there's nothing you can do about it.

[/ QUOTE ]

That's how a non-folding simulation works (like the simulations twodimes.net runs for you). However, in a real game you don't necessarily stay for the showdown, or even after the flop or turn.

[ QUOTE ]
So, only 1/8 of the time H will net twice as much as L, but this is balanced out by the fact that L wins $52 more an extra time than H. I think this is where your intuition failed. When H loses and L wins, L actually wins $52 more, not $28 more.

[/ QUOTE ]

It's not exactly intuition. I'm stacking up chips of different colors and making comparisons. I already suggested a way to demonstrate this to WM. Let me copy that part of my response to WM here.
*****
Take a stack of chips of one color. Doesn’t matter how many chips. I just grabbed a stack of ten blue chips. Now let’s suppose they represent your opponents total contribution to the pot. Now take six chips of a different color, say red.

Why six chips? Because in a limit game there are four bets.

Let’s keep it as simple as possible and assume we are playing $1/$2 limit-Omaha-8, that there is a bet on every betting round, and no raises. In that case it will cost Hero $6 to see the showdown.

First, stack the ten chip contribution of Hero’s opponents plus Hero’s six chips together and put it over to your right. There will thus be a 16 chip stack with 10 blue chips and 6 red chips over to your right.

Second, put two identical stacks of chips over to your left. Two stacks, each with 10 blue chips and 6 red chips.

Third, divide each of the stacks over to you left in two, but keeping Hero’s six chips together in each of the half stacks. You will now have four stacks or chips over to your left, two of them with 8 blue chips each and the other two with two blue chips and six red chips each.

Fourth, put one of the stacks with two blue chips and six red chips on top of the other. And put one of the stacks with eight blue chips on top of the other. You will now have two stacks of 16 chips each over to your left, one of the stacks having four blue chips plus twelve red chips.

When you win half the pot twice, you win the stack of chips with twelve red chips and four blue chips.
*****
[ QUOTE ]
If you still have money to bet on the river, then of course the high draw is favorable and has better EV. No one is debating this (I hope).

[/ QUOTE ]

Thank you.

Buzz

Re: Why Two Dimes Data Is Wrong (Continued...)
 

Hi Phil - While I was writing my last response to you, you posted a new one.

[ QUOTE ]
Here it is in black and white:

Hero with a 25% high draw to scoop nets $80 or loses $24
Hero with a 50% low draw to split nets $28 or loses $24.

[/ QUOTE ]

Yes. Change "high" to "scoop" and I agree.

[ QUOTE ]
High:
.....
Net: $2 per hand.

Low
Hi Phil - While I was writing my last response to you, you posted a new one.

[ QUOTE ]
Here it is in black and white:

Hero with a 25% high draw to scoop nets $80 or loses $24
Hero with a 50% low draw to split nets $28 or loses $24.

[/ QUOTE ]

Yes. Change "high" to "scoop" and I agree.

[ QUOTE ]
High:
.....
Net: $2 per hand.

Low
.....
Net: $2 per hand.

[/ QUOTE ]

Yes. Change "high" to "scoop" and I agree.

[ QUOTE ]
Each, individual hand is identical in EV. However, if you wish to lower your variance, the low draw is a better option with the same EV. The variance associated with the high hand is more because you win only half as often.

[/ QUOTE ]

Thank you. I think I understand what you have written. Very clear.

[ QUOTE ]
As I said previously this assumes that all the money goes in on the turn, as stated in the OP.

[/ QUOTE ]

Aye, there's the rub. I'm primarily interested in how to reconcile winning fractional pots with scooping. I understand that in a simulation, with a given number of deals, winning half the pot twice is equivalent to winning a quarter of the pot four times. Similarly, I understand that each is the equivalent of scooping one time.

We're writing about two different things here. I didn't originally make that very clear and that's entirely my fault. I'm sincerely sorry for that.

But in any event, playing a starting hand with the potential to scoop one time in four seems superior to playing a hand with the potential to win half the pot one time in two.

I think it's misleading if you simply add S (the number of scoops in 10000 runs) H/2 (the number of half pot wins in 10000 runs divided by two), Q/4, (the number of quarter pot wins in 10000 runs divided by four), etc. to get a total.

(All pots being equal in terms of what your opponents contribute), I continue to think scooping one time is better than winning half the pot two times.

So I have a dilemma, and I don't know how to resolve it. Wilson doesn't add the sub-totals for high to the sub-totals for low to the sub-totals for scoops. Wilson just gives the data in three columns. It doesn't seem quite correct to me to simply add together the sub totals. That's what I'm doing, but just because I don't know how to do it any better. But doing that doesn't jibe.

Buzz

Re: Why Two Dimes Data Is Wrong (Continued...)
 

From a rollout simulation pont of view, winning two half pots is the same as scooping one.

However, when you actually play with betting post-flop, then scooping of greater value. You are much more likely to drive the betting and win a bigger pot, if you have decent chance to scoop, than if you have a low and are worried about being quarted.

I don't know much about O8, but I didn't find this point in the thread. Is it obvious or wrong?

Re: Why Two Dimes Data Is Wrong (Continued...)
 

It's true, but the originial nature of this post is why two dimes data is wrong. This assumes all-in at the point where you go to 2dimes. Thus, issues of betability, etc, are moot (until the issue has been confused by arbitrary, complicated examples that essentially change the original question).

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]

No. I think scooping once is better than winning half the pot twice, assuming all pots under consideration have equal amounts contributed by your opponents.

[/ QUOTE ]
Buzz, to make this a fair argument, you have to run this situation four times, and allow the scoop to get there once and the low draw to get there twice. That way, the odds are accounted for.

Let me give you an example to make things clearer. Suppose we have the identical situation for the low draw (50% success), but let's let the scoop draw have a single out to get there. Now, your statement still holds: scooping once will net you more profit than winning half twice. However, you'd be insane to argue that this means drawing to the scoop is somehow a better play than drawing to the low, right? This is essentially what you're doing--the difference is that you are allowing yourself to be confused into thinking that because the odds differ by a factor of 2, running one hand once is equivalent to running the other twice, or something. That's just wrong.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

The original post would perhaps have been better titled as “Why twodimes data is misleading”. Twodimes is accurate in that it correctly summarizes how often you win portions (or all) of pots.

But what twodimes does NOT do is translate how much MONEY those portions of pots are worth to you. This is because there is a fixed cost you must pay for the right to earn a portion of the pot.

The key thing here is the point in time at which you are talking about. The less money there is still to go into the pot, the more closely twodimes and actual dollars are to each other. The more money that is still to be put into the pot (on more streets), the less twodimes will reflect actual dollars. Due to the fact that all money put in can be considered a fixed cost for the right to earn part of the pot. Or in other words, you must pay a tax to the guy that wins the other part of the pot.

-g

Re: Why Two Dimes Data Is Wrong (Continued...)
 

Greg,

What you're referring to is what has been called "risk" in this thread. Indeed, if the risk is different between two scenarios, that must be taken into account, and 2dimes has to be used in conjunction with some additional calculation. However, in all the examples that were used in comparing scoop to split draws, the risk was identical, and 2dimes/money/EV/whatever results are *identical*.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
But what twodimes does NOT do is translate how much MONEY those portions of pots are worth to you. This is because there is a fixed cost you must pay for the right to earn a portion of the pot.

[/ QUOTE ]
What you're talking about here is the concept of effective odds, which is applicable to straight high games as well as split games.

There is nothing in the nature of Omaha-8 that makes the twodimes data more "misleading" than it would be for a holdem problem.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

Awesome thread. I finally got it and it shocked me. Somewhere. Thanks all.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
[ QUOTE ]
But what twodimes does NOT do is translate how much MONEY those portions of pots are worth to you. This is because there is a fixed cost you must pay for the right to earn a portion of the pot.

[/ QUOTE ]
What you're talking about here is the concept of effective odds, which is applicable to straight high games as well as split games.

There is nothing in the nature of Omaha-8 that makes the twodimes data more "misleading" than it would be for a holdem problem.

[/ QUOTE ]

No, I'm not referring to effective odds.

I'm referring to the fact that in split pot games you don't get back all the money in put in to call. This is wholly unlike holdem.

ie. let's say its the turn. there are 6 big bets in the pot. you know your opponent has the high side locked up and will check down on the river. you can call 1 big bet for the chance to win low. The holdem, way of thinking would be to say, "I call 1 bet for the chance to win half the pot. the pot is 6, therefore half of 6 is 3. so I'm getting 3:1 pot odds. but that is incorrect. In a split pot game, you'd call that 1 bet making 7 bets in the pot. then you'd get half the pot back or 3.5 bets. then you subtract the 1 bet you put in for 2.5 bets. So you're true odds here are 2.5 to 1, not 3 to 1 as in holdem.

Try this problem out when its heads up on the flop with many bets to come and your opponent is freerolling and you'll see your return is very different than a holdem problem.

the difference is in holdem, if you win you get back the entire amount of money you put in to call. But not so in split pot.

This effect gets larger as more money goes in relative to the existing pot (ie. on earlier streets). This is what i'm referring to.

-g

Re: Why Two Dimes Data Is Wrong (Continued...)
 

Actually, I consider the size of the pot *going into* the action on a given street when considering odds. In this case, there must actually be 5 bets in the pot, then you and villain each put in 1. So the obvious math is "I am getting 2.5 (half of 5) bets to my 1." 2.5:1 odds is correct. I would never be so stupid as to watch the opponent put a bet into a 5-bet pot, and assume that I am getting 3:1 odds on that. I also don't think 2dimes encourages this type of thinking, unless the user is very inexperienced.

Now, I don't disagree that this is a non-trivial aspect of split-pot games. However, it should *definitely* not be used as a reason to favor high draws over low draws when the odds are the same.

Also, I agree with you that in situations where there are many bets to come, you have to think carefully, and 2dimes is not the place to go. I have already stated that in this thread, many times.

But that is not what we were ever talking about in the first place; we were talking about two players, each going all-in, in two situations where risk &amp; EV are identical.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
From a rollout simulation pont of view, winning two half pots is the same as scooping one.

[/ QUOTE ]

Mike - Sort of. Winning two half pots is tabulated separately from scooping. If a hand wins 2000 half pots for high, the number used to combine with the number of scoops to get a total would be 1000. Some simulators tabulate the high wins and then divide them as appropriate before showing a total. Other simulators divide the high wins as appropriate but do not add them to scoops and lows to show a total. And I suppose there are some other possibilities with which I'm unfamiliar.

I'm not a computer or simulation expert. I use twodimes.net and Wilson Turbo Omaha High-Low Split for Windows as tools to aid me in deciding whether I should be playing various hands or hands/boards or not. (And I've seen results from other simulators).

[ QUOTE ]
However, when you actually play with betting post-flop, then scooping of greater value. You are much more likely to drive the betting and win a bigger pot, if you have decent chance to scoop, than if you have a low and are worried about being quarted.

[/ QUOTE ]

Sort of. There are two ways you can scoop.
• win high with nobody winning low and with nobody wharing high with you.
• win high and low with nobody else sharing either high or low with you.

In the simulations, a high hand making a straight is just as likely to be tied as a low hand making a low. In real life there's a difference. You're more likely to get tied for low than for high, and the better your low, the more likely you are to get tied. Don't misunderstand this and start thinking you're better off playing poor low draws since you're less likely to get tied. (You're less likely to get tied with a poor low, but you're more likely to get beaten by a better low).

(In real life, how often a hand will scoop, win half one way or the other, or tie depends on how loosely your opponents are playing. Wilson allows you to use different characters as opponents. The various characters have different propensities to see the flop and then to stay in a hand or fold, and some are more aggressive than others. I mostly just use Painless Potters as opponents in the simulations, opponents who never fold. Twodimes.net is also a non-folding simulator).

Hope the above makes it clearer for you.

I'm currently adding the high, low and scoop sub-totals together. The high sub-totals shown by Wilson are actually halves/2 + quarters/4 + sixths/6 + eighths/8. Similarly, the low sub-totals shown by Wilson are actually halves/2 + quarters/4 + sixths/6 + eighths/8. Wilson doesn't add the sub-totals together. Twodimes.net does, and shows the totals as "ev." Bill Boston in his book added the sub-totals together, divided by 100, and showed them as "%." (I think that's how).

I'm suggesting there's something misleading with adding the sub-totals together, that the sub-total for scoops is worth more in real life than the sub-total for low. However, I agree the scoop sub-total is not worth more in the simulations.

At any rate, although I'm also doing it, it seems misleading to simply add the sub-totals together. Chaos suggested or implied this in response to a post of mine a while back, and I agreed with him. (I don't mean to drag you into this quagmire, Chaos).

Not sure I'm making myself clear. Some other posters evidently think I'm being completely bone-headed about this. (After I get hammered for a while, I start wondering if I'm not doing something wrong or missing something).

But I'm taking the hammering to try to get at the truth.

Buzz

Re: Why Two Dimes Data Is Wrong (Continued...)
 

Buzz, the only reason this thread is a "quagmire" is because of the ridiculously detailed, long posts and convoluted examples. If you could make a brief, concise list of the points you are claiming (which are frankly tough to discern at this point), then it would be easier for folks to either agree with you or point out errors. My list, for example, would be:

1) When you have twice the odds drawing to a split as you do drawing to a scoop, and have to risk the same amount in an equal-sized pot (this is the setup in the OP), then the EV in the two situations is equal.

2) Of these two scenarios, drawing to the split has the lower variance.

3) Using twodimes when there are multiple street of action to come can be misleading, unless you are accounting for potential future action correctly, which is non-trivial.

These three points are incontrovertible fact.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
ie. let's say its the turn. there are 6 big bets in the pot. you know your opponent has the high side locked up and will check down on the river. you can call 1 big bet for the chance to win low. The holdem, way of thinking would be to say, "I call 1 bet for the chance to win half the pot. the pot is 6, therefore half of 6 is 3. so I'm getting 3:1 pot odds. but that is incorrect. In a split pot game, you'd call that 1 bet making 7 bets in the pot. then you'd get half the pot back or 3.5 bets. then you subtract the 1 bet you put in for 2.5 bets. So you're true odds here are 2.5 to 1, not 3 to 1 as in holdem.

[/ QUOTE ]
I agree with you that in this example, drawing to low, you have pot odds of 2.5 to 1. But I don't know what you mean by "the holdem way of thinking". And this example doesn't have anything to do with "why Two Dimes Data is Wrong" (or "misleading" or whatever).

I agree with the idea that in actual play, a chance of scooping is usually worth a bit more than twice the same chance of getting half the pot. But the reason for that is simply the one stated by Mikechops a few posts back: "You are much more likely to drive the betting and win a bigger pot, if you have decent chance to scoop, than if you have a low and are worried about being quartered."

Re: Why Two Dimes Data Is Wrong (Continued...)
 

[ QUOTE ]
Buzz, the only reason this thread is a "quagmire" is because of the ridiculously detailed, long posts and convoluted examples. If you could make a brief, concise list of the points you are claiming (which are frankly tough to discern at this point), then it would be easier for folks to either agree with you or point out errors. My list, for example, would be:

1) When you have twice the odds drawing to a split as you do drawing to a scoop, and have to risk the same amount in an equal-sized pot (this is the setup in the OP), then the EV in the two situations is equal.

2) Of these two scenarios, drawing to the split has the lower variance.

3) Using twodimes when there are multiple street of action to come can be misleading, unless you are accounting for potential future action correctly, which is non-trivial.

These three points are incontrovertible fact.

[/ QUOTE ]

Fatsy-baby,
You’ve been making points 1 and 2 all along. I agree with those and always have. I’m been making point 3 all along. With which you agree. The original example listed here has only 1 further action, therefore twodimes is correct in stating your equity. And yes that was stated in this problem. But people were asking me what the intent of my original post was, and the answer is that

Summary: with more streets to come, and depending on your opponents, the profit you can make in a hand can vary drastically from what the equity that twodimes says you have. The main driver of this variance is the fact that this is a split pot game and that in splitting you will only get half of all money back that goes into the pot from this point forward.

-g

Re: Why Two Dimes Data Is Wrong (Continued...)
 

Yeah, I see we're in agreement. That's why the post you quoted was addressing Buzz...

Mixing apples and oranges by discussing whether there's more action to come or not is just going to confuse things though. Maybe that's what Buzz is doing, I really can't tell anymore.

Re: Why Two Dimes Data Is Wrong (Continued...)
 

I mean that in ‘the holdem way of thinking’, when you win the pot, you win the whole pot. Essentially, you scoop everytime that you win. But in O8 you don’t.

And it has everything to do with twodimes, because depending on how many bets are still to be put in the pot and how many opponent you have scooping is often worth more than twice splitting and can sometimes be worth as much as 7x more in profit (and that has nothing to do with driving the betting, but instead is due to the fact that every bet you put in will at best return half of it to you).

My point is that how you think about pot odds needs to be very different in O8 than in holdem. In holdem you always get the bets you put in back so its straightforward. Not so in split pot, as half the bet you put in goes to the other guy.
Let's take a simple example. You're the button in a pretty tight game. The cutoff seat immediately to your right bets and you call. The small blind calls and the big blind folds. So there are 7 small bets in the pot. On the flop, the cutoff bets, you call, and SB folds, so there are 9 small bets in the pot. On the turn those 9 small bets equal 4.5 big bets, and cutoff bets and you call so there are 6.5 big bets in the pot. On the river, cutoff bets and you call so there are now 8.5 big bets in the pot. So if you scoop, you win 8.5 big bets, and if you get half, you win 4.25 bets.. Now of those 8.5 big bets in the pot, you put in 2 small bets preflop, 1 small bet on the flop, 1 big bet on the turn and 1 more on the river. That's a total of 3.5 big bets.
So, let's recap:
If you scoop, you win 8.5 big bets, minus the 3.5 big bets you put in yourself, for a profit of 5.0 big bets.
If you split, you win 4.25 big bets, minus the 3.5 big bets you put in yourself, for a profit of 0.75 big bets.
That is a HUGE difference! In that example, scooping is 6 to 7 times more profitable than splitting the pot!!!
If this was holdem, you would be putting in 3.5 big bets for the chance to win 5.0 big bets. But if this is O8 and your opponent was freerolling you, then you’re putting in 3.5 big bets for the chance to win 0.75 bets. Even tho in both of these scenario’s your twodimes equity could be 25%.

-g