View Full Version : Drawing to a drawing hand. How to calculate the odds?

04-18-2005, 12:03 AM
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/images/graemlins/heart.gif, 2/images/graemlins/heart.gif.
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/images/graemlins/spade.gif, J/images/graemlins/club.gif, Q/images/graemlins/heart.gif (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/images/graemlins/heart.gif (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/images/graemlins/heart.gif (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.