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

Buzz · #11 12-05-2005, 04:38 AM

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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 _my point? Winning half the pot 2X/10000 times is _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 fold 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 & 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