Chris Ferguson (Game theory problem)

[gomer]

I'd love to see the original problem. I don't think you got it entirely right in the particulars, or maybe the original was flawed - here is my take on it, though.

In order for the call by the BB to be correct, he will have to win the pot 30% of the time (assuming, as we'll see later, that he breaks even on any subsequent action). If he wins 30% of the time, his result for this call is 0.3 x $7 - 0.7 x $3 -- i.e., he will break even.

I'll assume this is HU so the BB acts first, for simplicity. Then after the flop comes, the BB can either bet 50k or concede the pot (Again, i'm ignoring the millions of other things that could happen). As explained in TOP, the BB should bluff with such frequency that the SB is indifferent between calling and folding. In this case, we can ignore the pot relative to the $50,000 bet, so the BB sbould be 'bluffing' half the time that he bets. If he bluffs less, the SB will always fold, and if he bets more often, the SB will always call. (There is obviously another complication here, to wit, suck-outs - i'm trying to simplify this to the point where it makes sense [img]/images/graemlins/smile.gif[/img]).

So now we know that:
1) the BB needs to take 30% of these pots, and
2) the BB should bet twice as often as he is ahead

and i think this is where the 15% comes in...if the BB is ahead on 15% of flops, he can bet 30% of the flops, and break even on the whole deal.

So the question is, does the SB flop a hand that beats AA >15% of the time? If so, he can call (in theory) and make money.

Strictly speaking, i think the SB may need to do better than 15%. Something like 5-8% of the time, AA will flop the best possible hand, and the SB can't bluff at those pots.