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:

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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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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. 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:

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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.

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