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  #1  
Old 11-17-2005, 05:55 PM
TGoldman TGoldman is offline
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Default 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?
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  #2  
Old 11-17-2005, 08:25 PM
jthegreat jthegreat is offline
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Default Re: Why Two Dimes Data Is Wrong (Continued...)

In situation 2), there is no possible low.

The same EV is the same EV.
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  #3  
Old 11-17-2005, 09:16 PM
Buzz Buzz is offline
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Default 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
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  #4  
Old 11-17-2005, 10:33 PM
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Default 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.
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  #5  
Old 11-17-2005, 10:54 PM
Buzz Buzz is offline
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Default 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
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  #6  
Old 11-17-2005, 10:59 PM
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Default 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.
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  #7  
Old 11-18-2005, 01:22 AM
Buzz Buzz is offline
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Default 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
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  #8  
Old 11-18-2005, 02:22 AM
TGoldman TGoldman is offline
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Default 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?
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  #9  
Old 11-18-2005, 05:08 AM
gergery gergery is offline
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Default 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
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  #10  
Old 11-18-2005, 09:49 AM
Chamonyx Chamonyx is offline
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Default 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.
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