[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.
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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