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

[Buzz]

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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.

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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.

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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, .....

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

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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.

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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.

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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

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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.

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axiomatically fixed

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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.

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

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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.

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It gave me satisfaction to point out your mistake

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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.

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I promise I won't bring this thing up again.

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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

[Buzz]

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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.

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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

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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.

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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.

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(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).

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

[Buzz]

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

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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....

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

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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.

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

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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.

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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

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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.

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Is either superior?

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

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

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

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

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Agreed.

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----------------------------------------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.
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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.

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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.

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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.

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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.
*****
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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).

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Thank you.

Buzz

[Buzz]

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

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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.

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

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High:
.....
Net: $2 per hand.

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

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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.

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

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High:
.....
Net: $2 per hand.

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

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

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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.

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

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

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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

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?

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).

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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.

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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.

[gergery]

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

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*.