[deadbart]

Well, I was the first person to correctly answer the last Fourth Street Decision problem, but you gave all the credit to pudley4. I've learned my lesson - I'm just going to estimate this one. [img]/forums/images/icons/wink.gif[/img]

The bettor can have 9 hands that don't have a diamond (AQ) and 15 that do. If he does have any diamonds, you just want to call, because it only costs you one bet and you get the same number of bets into the pot. The weighted average of diamonds left in the deck is (9*9+12*8+3*7)/24 = 8.25. 8.25/42 is pretty darn close to 20%, so the diamond will hit 20% of the time. So, raising will save you the pot 20% of the times that the bettor doesn't have a diamond, or 0.2*9/24 = 7.5% of the time. So you want to raise when 7.5% of the pot is greater than the amount it "costs" you to raise.

Raising costs you about 20% of a bet when the bettor holds a diamond and one comes to beat you on the river (12 of 14 hands) and around 76% of a bet when the bettor has a made flush (3 of 24 hands). In the hands where the bettor is drawing dead, raising costs you nothing. So raising costs you about (12*.2+3*.76)/24 = 0.195, or about 20% of a bet.

So you want to raise when 7.5% of the pot is greater than 19.5% of a bet. So if the pot is 2.6 big bets or bigger, you want to raise. I still claim this is an estimate, and again I probably messed it up somewhere.

David