[fnord_too]

Mark,

Let's take a basic strategy of calling any river bet with Q high or better whether we stay pat or not. (I'm at work, so I want to keep this as simple as possible).

For simplicities sake, let's look at the worst case scenario where he is drawing to 2347. Thats 20ish bad cards he can catch if we stand. (2 each of 234, 3 each of 7Q, 4 each of AK) out of a stub of 40ish (rounding for simplicities sake). So basicly he is 50/50 to beat us. If he bets perfectly, this costs us 0.5BB.

If we both draw, there are 4 sixes which are losers, 4 aces and kings, 2 3's and 4's and 3 5's we will fold to a bet. So we are calling 55% of the time there is a bet. He will be ahead of us on the hands we will call with about 30% of the time, but the whole thing gets complicated since we will win a few free ones we would fold to a bet, we will fold incorrectly when he bluffs his bad hands but snap those bluffs off 55% of the time, depending on what he value bets/calls with on our value bets/bluffs this gets complicated. Also, I don't think we can have such tight calling standards since villain will be so easily correct to bluff with all his misses.

This seems to come down to, if we break, other than 6's which are an easy fold, how often we end up ahead of villain if we both draw, and if that number is greater than if we stand pat. We also have to consider the 10% of the time we hit our straight, which is just lost expectation. I guess one way to look at it is that we improve with 7,8,9,T,J or a little less than half the time, are the same with Q's, and get worst with 2,3,4,5,6,K,A or a little more than 1/2 the time. This looks really close depending on how villain will play the river in each case, but I don't think standing is right or wrong by a whole lot in the case of a one card draw. With 2347Q, the extra 4 outs seem to be significant.