This post will analyze pre-flop bet sizing in a heads up situation.
I was 5-tabling a 50NL game, although we had unlimited buyins and the effective stack was around $300.
One of my friends Eric was raising PFR quite frequently to $2, and I would 3-bet to $5 to induce calls\folds.
After a few rounds of folds, he started 4-betting me with $15. Luckily, the 2nd time this happened, I had pocket aces. I re-raised to $40 and he folded.
However, on hind-sight I had a hunch that this was not the most +ev play I could have made and that I should have bet slightly less.
Let's consider the reasoning behind it.
The pot: The blinds are posted (75 cents) + $2(his bet) + $5(my raise) + $13(his re-raise) = $20.75
My bet of $40 induces a fold. Let's consider the profitability of different bet sizes.
Assuming he calls with AK, KK, QQ and folds with other possibilities AQ, KQ, AJ, JJ.
ev when he folds = $20.75
Equity against AK - 92%, Equity against KK and QQ - 82%
Total combinations of AK = 8
Total combinations of KK + QQ = 6 + 6 = 12 (We can group KK and QQ as they have similar equities)
Total combinations of AQ, KQ, AJ, JJ = 8 + 16 + 8 + 6 = 38
Total hands in his range= 58
If he calls our bet the pot will have have = 20.75 + 35 + 25 = $80.75
So our expected value against his range =
(8/58)* (.92*(80.75)) + (12/58)*(.82*(80.75)) + (38/58)*(20.75) = 10.24 + 13.7 + 13.59 = $37.53
Suppose, a re-raise of $30 would make him call with AK,KK,QQ, AQ, AJ and fold KQ and JJ.
Equity against AQ and AJ = approx 92.8%
Total combinations of AK, AQ, AJ = 24
Total combinations of KQ and JJ = 16 + 6 = 22
Ev =
24/58(.928 * 80.75) + (12/58)*(.82*(80.75)) + (22/58) * (20.75) = 31 + 13.7 + 7.87 = $52.57
My hunch was right, a smaller bet would have in fact brought me a much higher payout by the flop. (of 52.57 - 37.53) = $15.04 Of course this difference is likely to increase with implied odds.
I was 5-tabling a 50NL game, although we had unlimited buyins and the effective stack was around $300.
One of my friends Eric was raising PFR quite frequently to $2, and I would 3-bet to $5 to induce calls\folds.
After a few rounds of folds, he started 4-betting me with $15. Luckily, the 2nd time this happened, I had pocket aces. I re-raised to $40 and he folded.
However, on hind-sight I had a hunch that this was not the most +ev play I could have made and that I should have bet slightly less.
Let's consider the reasoning behind it.
The pot: The blinds are posted (75 cents) + $2(his bet) + $5(my raise) + $13(his re-raise) = $20.75
My bet of $40 induces a fold. Let's consider the profitability of different bet sizes.
Assuming he calls with AK, KK, QQ and folds with other possibilities AQ, KQ, AJ, JJ.
ev when he folds = $20.75
Equity against AK - 92%, Equity against KK and QQ - 82%
Total combinations of AK = 8
Total combinations of KK + QQ = 6 + 6 = 12 (We can group KK and QQ as they have similar equities)
Total combinations of AQ, KQ, AJ, JJ = 8 + 16 + 8 + 6 = 38
Total hands in his range= 58
If he calls our bet the pot will have have = 20.75 + 35 + 25 = $80.75
So our expected value against his range =
(8/58)* (.92*(80.75)) + (12/58)*(.82*(80.75)) + (38/58)*(20.75) = 10.24 + 13.7 + 13.59 = $37.53
Suppose, a re-raise of $30 would make him call with AK,KK,QQ, AQ, AJ and fold KQ and JJ.
Equity against AQ and AJ = approx 92.8%
Total combinations of AK, AQ, AJ = 24
Total combinations of KQ and JJ = 16 + 6 = 22
Ev =
24/58(.928 * 80.75) + (12/58)*(.82*(80.75)) + (22/58) * (20.75) = 31 + 13.7 + 7.87 = $52.57
My hunch was right, a smaller bet would have in fact brought me a much higher payout by the flop. (of 52.57 - 37.53) = $15.04 Of course this difference is likely to increase with implied odds.
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