Drawing to a drawing hand. How to calculate the odds?

[RandomUser]

The following is a tournament hand that I played very poorly, but it brought up a discussion on how to calculate odds when you need to catch a turn card to complete a draw for the river (runner-runner) and specifically about calling the flop.

This is late in the first hour of a $30 buy-in Limit hold'em tourney. Villain is a straightforward player who hasn't gotten out of line. The table has been fairly passive with <50% of hands being raised preflop which allowed me to limp in with marginal hands.

Party Poker Limit Hold'em Tourney, Big Blind t50 (9 handed) converter

saw flop|saw showdown

CO (t735)
Button (t915)
SB (t1395)
BB (t1680)
UTG (t110)
Hero (t2070)
MP1 (t488)
MP2 (t1600)
MP3 (t1137)

Preflop: Hero is UTG+1 with K[img]/images/graemlins/heart.gif[/img], 2[img]/images/graemlins/heart.gif[/img].
1 fold, Hero calls, MP1 calls, 4 folds, SB raises, 1 fold, Hero calls, MP1 calls.

Weak call, but I had an above average stack and was calling with Ax and Kx suited hands.

Flop: (7 SB, t350) 3[img]/images/graemlins/spade.gif[/img], J[img]/images/graemlins/club.gif[/img], Q[img]/images/graemlins/heart.gif[/img] (3 players)
SB bets, Hero calls, MP1 calls.

Not a great flop, but I have backdoor straight and flush draws. I need to catch a T or a heart on the turn so I am drawing to 13 outs to improve (that was my logic at least). I'm getting 8:1 to call and odds are improving are 2.6:1.

In retrospect, I should have realized that my T outs were probably not clean since villain could easily have AK and be making a continuation bet.

Turn: (5 BB, t500) A[img]/images/graemlins/heart.gif[/img] (3 players)
SB bets, Hero calls, MP1 calls.

This is perhaps the best of all possible cards to catch. It gives me the nut straight and nut flush draw. No difficulties calling here.

I was worried that MP1 might have KT to limit my straight outs, but if so he probably would have raised the flop.

River: (8 BB, t800) 4[img]/images/graemlins/heart.gif[/img] (3 players)
SB bets, Hero raises, MP1 folds, SB calls.

Runner-runner comes through.

Final Pot: 12 BB (t1200)


If you do the math based on the entire hand, this is what you get.

On the flop, I'm drawing to a heart or a ten. That gives me 13 outs giving me 2.61:1 odds with pot odds of 8:1.

72.4% of the time I'm done with the hand on a turn blank.

Net loss 50.

27.6% of the time I get my T or heart and continue.

19.8%(27.6%*71.7%) of the time I miss on the river and fold.

Net loss 150.

7.8%(27.6%*28.3%) of the time I hit on the river and raise.

Net gain 750

(-36.2) + (-29.7) + 58.6 = -7.4

Overall, this is a small -EV play, but I felt that I was basing my call on the pot odds for the turn only, and not the overall hand and talked myself into calling a single card so I could evaluate again on the turn.

For the entire hand, I'm a 11.8:1 underdog and getting 8:1 odds on the flop(9:1 if person call behind me). Should that figure have been the deciding factor which tells me to fold?

At the time of the hand, I felt that I had the odds to call a single bet on the flop since the pot had been raised preflop. If there had been no preflop raise I would have folded.

It was only afterwards that I discovered that the pot odds were minorly -EV.

Comments welcome, as are those that wish to laugh at my fishiness.