Maximize EV? Help me do this calculation ...

Proofrock · #1 10-07-2005, 07:42 PM

OR explain to me why such a calculation is foolishness.

Assumptions:
(1) You are sitting in a 100BB max buy-in No-limit game.
(2) You have accumulated an 800BB stack, as have the other nine players at the table.

What is the minimum edge you need to get all-in preflop (e.g., donkey goes all-in with KQs in front of you -- what is the minimum hand you would call with?

Before I get berated for asking a stupid question ("you can profitably take any edge ... stop being risk-averse"), here is the motivation for the question: your goal is to maximize EV over your poker-playing lifetime. I.e., you want to maximize

sum(EV(hand_j), {j,1,N}),

where N is the total number of hands you play in your lifetime.

EV for preflop all-ins (assume negligible blinds) = (stack size)*(prob. win - prob. lose). If you lose, you can only rebuy to 100BB, and all future EV decisions will have a smaller magnitude than they would with a larger stack (until you rebuild). If you win, the effective stack size remains 800BB until somebody else doubles up, and you are free to take any small edge and it will clearly be maximizing EV (since the magnitude of future decisions is not affected by a loss).

Feel free to introduce any other parameters you think are important, and help sketch out how I would make the calculation, or if you see a flaw in the setup of the problem, let me know what you see.

Thanks.

-cj

Proofrock · #2 10-08-2005, 07:41 PM

bump. If the lack of response is because this is a dumb question, then either weigh in to tell me why or just let it fade away. I won't bump again.

-cj

eastbay · #3 10-09-2005, 02:15 AM

The problem is that as stated, we have no idea what opportunities we should be playing for in the future.

If we're the worst player at the table by far with a big negative edge, we might do best to take a small -EV proposition, because it's the best we'll get (assuming we can't just walk away).

On the other hand, if it's a bunch of goofballs who think it's fun to open-push 32o, and only 32o, we'll pass on quite big edges because we know we're going to be able to make a killing everytime we can catch someone doing that.

So, you're missing really the only information that matters here, as far as I can tell.

eastbay

Proofrock · #4 10-09-2005, 04:48 PM

Okay, assume other players will push any pocket pair 22+, AK-AJ,KQs. And for simplicity, assume that you're in the BB and there is only 1 push in front of you.

-cj

eastbay · #5 10-09-2005, 08:26 PM

It's still extremely underspecified for any kind of actual calculation. How long does it take to rebuild?

I'm not actually going to do this, btw, I'm just pointing out the barriers to doing it.

eastbay

Proofrock · #6 10-10-2005, 12:52 AM

[ QUOTE ]
It's still extremely underspecified for any kind of actual calculation. How long does it take to rebuild?

[/ QUOTE ]

well that's actually the primary question, as far as I see it.

-cj

#7 10-10-2005, 01:31 AM

dude, you're taking statistics waaaay too seriously.

#8 10-10-2005, 07:29 AM

Well, the first assumption should probably be that everyone at the table is an equal player. Therefore, the game as a whole would be 0 EV. This wont change at any point, regardless of how many chips you (or anyone else) at the table has. Unless, that is, you think there is a real difference in your EV when chip stacks are different.

So the real question then is not what your EV is on an all-in, but what the difference in your EV is at having an average chip stack, and in having a chip stack 800 BB below average. In this case, it is a matter of analyzing yourself and your opponents. If you know that you gain EV with a small or large stack, you would call more often. If you lose EV with a small stack, you would call less often.

Essentially, the important elements are unknowns in the original question. The solution involves your projected EV at all different stages of the game. This would be a more important question that that of your EV on this particular hand.

TaintedRogue · #9 10-10-2005, 01:43 PM

[ QUOTE ]
OR explain to me why such a calculation is foolishness.

Assumptions:
(1) You are sitting in a 100BB max buy-in No-limit game.
(2) You have accumulated an 800BB stack, as have the other nine players at the table.

[/ QUOTE ]

Attempting to calculate the above is foolish, as the only way you are going to find yourself in this in this situation, is for several people to come into the game, lose their $$ and go, and the lastly, 1 person buy in and the chips be redistributed amongst you all.

Even if that were probable, I would have been gone long before the last guy who bought in for 100BB got to 800BB, unless he were me, or he did it quickly.

You see, the probability of me being ready for dinner, would have occurred prior to there being 6300BB in winnings distributed amongst the 9 winning players.

Proofrock · #10 10-10-2005, 02:18 PM

[ QUOTE ]
Even if that were probable, I would have been gone long before the last guy who bought in for 100BB got to 800BB, unless he were me, or he did it quickly.

[/ QUOTE ]

So then what about this situation: You and one other player have 800BB (or 600BB if that value is more believable) at a 100BB max buy-in game. This player goes all-in in the SB, you're in the BB. What is the minimum edge you need to call?

Other stacks are all between 100BB and 200BB if this matters.

-cj