Basic HUNLE push/fold Nash question - Poker Theory

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Basic HUNLE push/fold Nash question

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08-30-2015 , 12:17 PM

Pokerlogist

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Join Date: Jul 2005 Posts: 3,302

Should these two simple HUNLE push/fold scenarios have the same Nash Eq. solution as to push/call ranges? I think so, but but some poker software I recently tried may be giving me a different answer. Maybe I'm missing something.

A. Blinds are (.5,1), the pre-blind stacks for (SB,BB) are (3.5,4) so after posting, stacks are (3,3) and pot size is 1.5. This gives a stack size to pot size ratio of 2.

B. Blinds are (1,1), pre-blind stacks are (5,5), so after posting, stacks are (4,4) and pot size is 2. This also gives a stack to pot ratio of 2.

Shouldn't the Nash Eq. GTO ranges for the SB and BB be the same in both scenarios?

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08-30-2015 , 12:57 PM

plexiq

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Join Date: Apr 2007 Posts: 2,554

Version A: The BB has to call 2.5 to play for a pot of 7, he needs >35.71% equity.
Version B: The BB has to call 3.0 to play for a pot of 8, he needs >37.50% equity.

I already gave informal proof that you can't create equivalent scenarios between (0.5, 1) and (1, 1) by simply changing the stack size:

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Originally Posted by plexiq

Informal proof: The stack size (in big blinds) that gives BB the correct pot ratio is not dependent on the small blind structure, this value will stay constant in both versions. Any change to the small blind will require a change of stack size (in big blinds) to give SB the correct risk reward. One of these conditions requires a constant stack size (in terms of big blinds), the other requires a changed stack size if the small blind is changed. You won't be able to satisfy both conditions.

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08-30-2015 , 11:04 PM

Pokerlogist

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Join Date: Jul 2005 Posts: 3,302

Maybe we're defining terms differently. The way I looked at it, in scenario A if the SB shoves 3 units and the BB blind calls with his 3 units, the final pot size is 7.5. Each player has risked 3 units to win 7.5. So by this method each has 40% equity. In Scenario B, each players risks 4 units to win a final pot size of 10 units. So again each has 40% equity. So that's why the two cases seem equivalent to me. I don't see how you got your values for pot size or amount risked.

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08-31-2015 , 03:06 AM

alexrjl

adept

Join Date: Mar 2009 Posts: 1,058

the mistake you're making is that the in the first example the pre blind stack sizes are (3.5,4) but actually they are (3.5, 3.5) because only the smallest stacksize matters. Google "effective stacks" for a longer explanation of this concept.

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08-31-2015 , 01:14 PM

Pokerlogist

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Join Date: Jul 2005 Posts: 3,302

In Case A, they can each make a maximum voluntary wager of exactly 3 units. They "cover" each other exactly. The effective stack size would be 3. Check out the term SPR, stack to pot ratio. If the SB loses a showdown he is left with zero. Same with the BB if he loses a showdown. Why would anyone think that 0.5 unit is not at risk here?

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08-31-2015 , 06:32 PM

plexiq

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Join Date: Apr 2007 Posts: 2,554

The SB can raise to 3.5bb and BB calls 2.5bb on top of the 1.0bb that is already posted as blind. BB can't end the hand with <0.5bb in this scenario.

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09-02-2015 , 05:42 PM

Pokerlogist

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Join Date: Jul 2005 Posts: 3,302

I see what you're doing now. Ok.

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