Theoretical Heads-Up Decision

jimdmcevoy · #1 11-09-2004, 05:50 PM

You are playing in a heads-up cash game, and you have say 300 BB, and your opponent has you covered. You limp with 6[img]/images/graemlins/diamond.gif[/img]5[img]/images/graemlins/diamond.gif[/img] in the small blind. Your opponent raises 4 BB. Everything is normal so far, except before you make your decision to fold/call/raise your opponent flips his hand face up, he's go the A[img]/images/graemlins/spade.gif[/img]A[img]/images/graemlins/club.gif[/img]

Now suppose that your opponent plays exactly the way you do (as in had you both switched seats at this point and you could erase from your memory that you had the 6[img]/images/graemlins/diamond.gif[/img]5[img]/images/graemlins/diamond.gif[/img] , the hand would play out the same), would you fold or call in this situation? Does everyone agree re-raising is suicide?

For those of you that would fold, would you call if you both had sufficiently deep stacks? For those of you that would call, certainly you would fold if you both only had 5 BB to start with, but what is your threshold amount of BB in each of your stacks where you change your decission?

I realise that the odds of this situation ever happenning are about 1 in a gadzillion, and therefore this had no direct practical value, so please don't flame me for it.

reubenf · #2 11-09-2004, 06:32 PM

Does he know that we play exactly the same way?

Either way, I think the answer is fold. If I can get him to fold often enough when he's ahead postflop, that means I'd also fold too often when I'm ahead in his situation. It seems I'd have to have a really odd game where I lose money with AA vs 65s against myself, even with the AA revealed.

But, I don't really know. Interesting question, and I'll think about it some more.

EDIT: Oh, and reraising is absoluteley suicide. It can't be correct, because if it was, then it would be correct for him to respond by going all-in, which contradicts that it's correct for you to reraise.

jimdmcevoy · #3 11-09-2004, 07:06 PM

Thanks for the reply, and yes I forgot to mention that he knows we play the same way.

mmcd · #4 11-09-2004, 07:50 PM

Either he can be bet out of the pot when he fails to flop a set OR he will pay you off will his whole stack when you outflop him (except on a monotone diamond flop).

jimdmcevoy · #5 11-09-2004, 07:58 PM

Suppose the flop comes rag rag rag (no help for either player) I'm not so sure he can be bet out of the pot if he doesn't flop a set, since he knows you might try to bet him out of the pot. Also, he know the exact percentage of the time you will bluff at it since you both know each others playing style (the same style).

edge · #6 11-09-2004, 08:10 PM

I don't quite understand what you're asking here, but if you're asking whether I would fold 65s to a 4 BB raise with 300 BB stacks if I knew my opponent had AA, I wouldn't even consider it. I might fold it out of position if I didn't know my opponents exact cards, but anytime you know your opponent's hole cards, you will win the maximum/lose the minimum.

I think I'm missing the point?

mmcd · #7 11-09-2004, 08:22 PM

Either he will fold on a T92 flop OR he will call on a J65 flop. Either he will fold on a 772 flop OR he will call on a 662 flop.

If he's the type who would tend towards folding, you can even check-call the flop and push the turn to extract even more value.

jimdmcevoy · #8 11-09-2004, 08:24 PM

You may be right, but the only thing I have to say is when you hit your hand (two pair or better with no A on board) you are only going to get paid off by your opponent if he thinks you are trying to steal the pot.

jimdmcevoy · #9 11-09-2004, 08:28 PM

Why couldn't he have the option of calling 30% of the time on a T92 flop?

My question put another way, if you were the one with the aces wouldn't you call a certain percentage of the time, not just 0% or 100% ?

mmcd · #10 11-09-2004, 08:34 PM

And when you don't hit your hand, you are only going to get called those times he thinks you are trying to steal the pot. If each player will bluff/call the correct percentage of the time according to game theory then it's ev neutral, but given the fact that you know his hand, and he knows you know his hand, it essentially becomes a psychological battle between the two players. If you gave me XX and my opponent AA and we played this situation out 1000 times in a row, I guarantee you I'd make very nice profit.