Jul
14

Texas Hold’em – Playing a Draw out of position

Preflop:
Sucker MC is SB with Jd , Qd.
2 folds, CO calls, Button calls, Sucker MC completes, BB raises, CO calls, Button calls, Sucker MC calls.

Flop:
(8 SB) 8d , 6d, 5s (4 players)
Sucker MC checks, BB bets, CO calls, Button folds, Sucker MC raises, BB calls, CO folds.

Turn:
(6.50 BB) 3d (2 players)
Sucker MC bets, BB calls.

River:
(8.50 BB) Kd (2 players)
Sucker MC bets, BB raises, Sucker MC calls

For simplicity’s sake, let’s say that:

1/3 of the time he has the A
1/3 of the time he has a worse diamond
1/3 of the time he does not have a diamond at all

I suspect this is fairly close to accurate.

If he has the nut diamond, the EV’s of various plays are as follows:

Bet-fold: -1.00 BB
Bet-call: -2.00 BB
Check-call: -1.00 BB

That one was easy.

If he has a worse diamond, he will always call if you bet and will raise perhaps 1/4 of the time (this percentage might be higher if you did not hold both the second *and* the third nut diamond). If you check it to him, he will bet for value 4/5 of the time.

Bet-fold: Costs you the pot (9.50 BB) the 1/4 of the time that he raises with a worse diamond. Otherwise you make 1.00 BB. EV = 1 x 3/4 + (-9.5) x 1/4 = -1.63 BB

Bet-call: You always make 1 BB plus an extra BB those times that he raises with a worse hand. EV = 1.25 BB.

Check-call. You only make a bet when he goes ahead and bets for value. EV = 0.80 BB.

If he has no diamond. This is the most complicated situation and depends a lot on the player in question. I am guessing that, if you bet, he will call 1/2 of the time (note that this percentage is higher than it might otherwise be since there is a good chance that the King has paired him), raise as a bluff 1/10 of the time, and fold the other 2/5 of the time. If you check it to him, he will bet 2/3 of the time, but may check behind if he has paired up.
Bet-fold: Costs you the pot (9.50 BB) the 1/10 of the time that he bluff-raises. You make 1 BB the 1/2 of times that he calls and nothing the 2/5 of times that he folds. EV = 1 x (1/2) + (-9.5) x (1/10) = -0.45 BB.
Bet-call: You always make 1 BB the 50% of the time that he calls. You will make 2 BB the 10% of the time that he raises with a worse hand. Otherwise, you will make nothing. EV = 1 x (1/2) + 2 x (1/10) = 0.70 BB.
Check-call: You will make 1 BB the 2/3 of the time that he bets with a worse hand and nothing otherwise. EV = 0.67 BB.
The average EV’s of the three plays are as follows:
Bet-fold: (-1.0, -1.63, -0.45) = -1.02 BB

Bet-call: (-2.0, 1.25, 0.7) = -0.02 BB

Check-call: (-1.0, 0.80, 0.67) = +0.16 BB
Check-call looks to be a little bit better than bet-call, but it is close enough that the answer could plausibly change depending on opponent characteristics. Bet-fold is patently terrible.

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