[BigAlChicago]

I like betting this flop, too. If we raise preflop and whiff -- say the same flop but we raised preflop with AJo -- aren't we c-betting to try and take it down right on the flop? If we are betting there, shouldn't we be betting when we hit?

As to the math, I will try to do an oversimplified calculation. Let's assume as the baseline that you will take down 4.5 BB's every time you bet that flop.

If you slowplay, you will take it down with just your turn bet X% of the time, winning the same 4.5 BBs. 1-X% of the time, someone will hit something that they will want to draw to so that they will pay 1 (or 2 BBs if you get in a raise, as here). More often than not, it will be to the backdoor flush than the runner runner overcards. To oversimplify things, I will again assume that if someone hits his draw, it will cost you 2 BBs (that is, 1 bet on the turn and a crying call on the river), but when villain misses, he will not pay you off on the river. Assume villain hits his draw Z% of the time.

Thus, slowplaying comes down to this:

+4.5 BB X%
+5.5 BB (1-X%)*(1-Z%)
-2.0 BB (1-X%)*Z%

For sake of looking at numbers, I assumed that 50% of the time your turn bet just takes down the pot. The other 50% of the time represents an opponent hitting a draw. If villain is roughly 20% to make his draw on the river (i.e., a flush draw) when he picks up the draw on the turn, then you will win 5.5 BB 40% of the time you slowplay and lose 2 BB 10% of the time. The overall expectation for this play is +4.25 BB (50% of 4.5 plus 40% of 5.5 minus 10% of 2.) If these assumptions are accurate, then slowplaying cost you .25 BB.

Of course, this oversimplifies the math. There will be times when the flush hits, but you make your boat. There will be other times when someone makes a pair, but calls you down to the river putting you on AK. Also, my assumptions of getting called versus taking the pot down on the river might be all wrong.

Based on this analysis (winning 1 BB when called and you win and losing 2 BB's when your opponent hits a draw on the river), if your opponent is drawing to six outs or less, then you will make money in this scenario.

Of course, what this calculation does not take into account is the number of times someone will bet into you and call your raise. In that case, if you assume you will win 2 more BB, instead of just 1 more BB, when you win, then this will be a money making proposition. (Of course, this assumes you fold to the river bet when you get beat on the river!) Based on the previous number, you would win an additional .4 BB. That makes this play worth 4.65 BBs compared to taking down the 4.5 BB pot with a flop bet.

Someone, please critique this analysis from a mathematical standpoint.