Difficult HU Game thoery problem

suitedaces84 · by **suitedaces84** » Wed Jan 18, 2006 1:31 pm GMT

**I didn't come up with this. I merely read it and found it interesting and thought I'd share it.**

You're in the SB with xy. You have 10 big blinds left. The blind sturture is 1/2. Your only options are pushing and folding. There is no rake. What do you do with each starting hand? Assume your oppoent plays in an optimum way.

I'll get you started:

Q: Assume you can only push with AA, what would your oppoent be correct to call with?

A: Only AA.

Q: Now assume your oppoent will only call with AA, what would you be correct to push with?

A: Any two cards.

Q: Now assume you push with any two, what will your oppoent be correct to call with?

A: This is where it gets difficult and pokerstove is necessary. Simply determine what hands have 45.2% equity vs a random hand.

If you repeat this process over and over again the range of pushing hands will converge. The range of hands to call with will also converge. Eventually they'll reach an equilibrum. You'll be left with your solution.

Hint: it makes no difference where you start the problem. The final solution will be the same no matter what you assume your initial pushing range to be.

Cyberhwk · by **Cyberhwk** » Wed Jan 25, 2006 4:28 am GMT

Q7? The computer hand?

dstlvb · by **dstlvb** » Thu Feb 16, 2006 8:45 pm GMT

This sounds sorta like the SAGE system i just read about in Cardplayer

HalfSugar · by **HalfSugar** » Thu Feb 16, 2006 8:53 pm GMT

I'm gonna say King to B5, Pawn takes Rook, checkmate.

Jefecaminador · by **Jefecaminador** » Fri Jun 16, 2006 9:17 pm GMT

"A strange game, there is no winner."

Sean_in_NJ · by **Sean_in_NJ** » Fri Jun 16, 2006 9:26 pm GMT

Jefecaminador wrote:"A strange game, there is no winner."

I hate it when people BUTCHER great quotes.

Jefecaminador · by **Jefecaminador** » Fri Jun 16, 2006 10:28 pm GMT

eh, it was a cover for me messing up my original post

xDiamond_CutteRx · by **xDiamond_CutteRx** » Sun Jun 18, 2006 8:44 pm GMT

Sean_in_NJ wrote:
Jefecaminador wrote:"A strange game, there is no winner."

I hate it when people BUTCHER great quotes.

A strange game. The only way to win is not to play.

I think the approximate answer is anything stronger than Q7, or possibly any two cards eight or higher, or suited cards slightly worse than Q7 with similar equity. But I'm on vacation now, so I'll give more thought to it when I come back.

Sean_in_NJ · by **Sean_in_NJ** » Sun Jun 18, 2006 9:10 pm GMT

xDiamond_CutteRx wrote:
Sean_in_NJ wrote:
Jefecaminador wrote:"A strange game, there is no winner."

I hate it when people BUTCHER great quotes.

A strange game. The only way to win is not to play.

OMFG!

A strange game. The only winning move is not to play.

For the love of god, people, STOP HELPING!

Jefecaminador · by **Jefecaminador** » Sun Jun 18, 2006 9:58 pm GMT

Well the only thing I know for sure is that the raising hand is lower than the calling hand, and that they're both less than Q7. Basically the raiser will win 1 BB if there is a fold and win 10 - equity% of 20BB if there is a call. So the equilibrium lies when 1* %of hands that will be folded - (10-equity%*20 vs random hand from set that will call) = 0

Jefecaminador · by **Jefecaminador** » Tue Jul 25, 2006 3:09 am GMT

So... whats the answer?

shorn7 · by **shorn7** » Tue Jul 25, 2006 9:41 am GMT

I say Q8 is the answer. It is slightly better than the computer generated "average" hand.

Jefecaminador · by **Jefecaminador** » Tue Jul 25, 2006 1:59 pm GMT

Well, my best guess would be the sklansky-chubucov # for 10$ which is 96s.

But since your opponent doesnt know what you have it should be slightly lower than this. So I'm gonna go with j3o.

Difficult HU Game thoery problem

Difficult HU Game thoery problem

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