Analysis of a Tourney Hand

I got home from work at about 11:30 and decided to play in a few tournaments. I busted in all of them quite early. Here's how

Here is a hand from a 20/20 SNG on Stars. I haven't played one of these in a while because I usually like to play tourneys with bigger fields, but the fields in these are soft and there was nothing else going.

$20+$2 Hold'em No Limit - Level I (10/20)
9-max Seat #5 is the button
Seat 1: sixbulls180 (2780 in chips)
Seat 2: soju (1710 in chips)
Seat 4: BRA51 (1380 in chips)
Seat 5: Hero (1410 in chips)
Seat 6: novadova (1560 in chips)
Seat 7: 1021rounder (710 in chips)
Seat 8: money_hunte (1140 in chips)
Seat 9: xxjohnnykxx (2810 in chips)
novadova: posts small blind 10
1021rounder: posts big blind 20
*** HOLE CARDS ***
Dealt to Hero [Ah Kd]
money_hunte: folds
xxjohnnykxx: calls 20
sixbulls180: raises 20 to 40
soju: calls 40
BRA51: calls 40
Hero: raises 280 to 320
novadova: folds
1021rounder: folds
xxjohnnykxx: folds
sixbulls180: folds
soju: folds
BRA51: calls 280
*** FLOP *** [Th 8h Ks]
BRA51: checks
Hero: bets 500
BRA51: calls 500
*** TURN *** [Th 8h Ks] [Ad]
BRA51: checks
Hero: bets 590 and is all-in
BRA51: calls 560 and is all-in
*** RIVER *** [Th 8h Ks Ad] [2c]
*** SHOW DOWN ***
BRA51: shows [Qc Jc] (a straight, Ten to Ace)
Hero: shows [Ah Kd] (two pair, Aces and Kings)
BRA51 collected 2890 from pot
Hero said, "weeeeeeeeeeeeee"
*** SUMMARY ***
Total pot 2890 | Rake 0
Board [Th 8h Ks Ad 2c]
Seat 1: sixbulls180 folded before Flop
Seat 2: soju folded before Flop
Seat 4: BRA51 showed [Qc Jc] and won (2890) with a straight, Ten to Ace
Seat 5: Hero (button) showed [Ah Kd] and lost with two pair, Aces and Kings
Seat 6: novadova (small blind) folded before Flop
Seat 7: 1021rounder (big blind) folded before Flop
Seat 8: money_hunte folded before Flop (didn't bet)
Seat 9: xxjohnnykxx folded before Flop

This may not seem too bad, but let's just try to quantify how bad it is. Against my particular hand, he has 7 outs. 3 of those outs (Ac, Ad, As) give me a 4 card redraw and 1 of them (9h) gives me a 9 card redraw. Also, note that there are some cards that help the villian on the turn but that don't put him ahead in the hand. There are 6 of these (Jh, Js, Jd, Qh, Qs, Qd). For the sake of simplicity, let's assume that the Hero will always move in or call all in on the turn, regardless of the turn card.

Now let's look at the set of possible outcomes/actions for the villian to see which action is the best. I won't look at the play of check-raising all in on the flop, because we would have to take fold equity into account. Against this particular Hero (me) and most other decent players, their fold equity should be close to 0 anyway. This is the case because there are very few hands that I will re-raise preflop in this scenario and lay down on this flop, particularly with all those available draws out there.

1) Fold on the flop. EV=0

2) Call the flop. We'll need to evaluate certain scenarios to see what action we should take on the turn also.

**** NOTE **** Skip the rest of this paragraph unless you want to read a bunch of combinatorial reasoning and arithmetic.

2a) Nobody gets help on the turn. This occurs 24/45 times. Now, we'll be facing a bet of 560 into a pot of 1750 and we still have 7 outs.
2ai) We call the turn bet. We'll win 750+1060 with 7/44 rivers and lose 1060 on the other 37/44 rivers. Our expectation by calling the flop and turn when we get no help on the turn is then (1810)(7/44) - (1060)(37/44) = 288.0 - 891.4 = -603.4.
2aii) We fold on the turn. We'll never win the pot in this case, and we'll lose 500 each time.
2b) The Hero gets help on the turn in the form of a heart that isn't the 9h, Jh or Qh. This happens 7 times, and leaves the villian with only 6 outs.
2bi) We call the turn anyway. The EV of this is (1810)(6/44) - (1060)(38/44) = 246.8 - 915.5 = -668.7
2bii) We fold on the turn, losing only the 500 we put in on the flop.
2c) We hit a pair on the turn, which happens 6/45 times. In this case, we will have to hit exactly our straight or trips to win, since making 2 pair gives the Hero a straight (or flush in some cases). We then have 9 outs going to the river.
2ci) We call on the turn. Our EV is (1810)(9/44) - (1060)(35/44) = 370.2 - 843.2 = -473.0
2cii) We fold on the turn. We lose 500 each time this happens.
2d) We hit the 9h on the turn. We stand to win 750+1060 on the 35/44 river cards where another heart doesn't come, but lose 1060 on the 9/44 river hearts. The expectation in this case is for this play is (1810)(35/44) - (1060)(9/44) = 1439.8 - 216.8 = 1223.0
2e) We hit one of 3 A's on the turn, giving the hero 4 outs. 4/44 rivers lose us 1060, and 40/44 rivers win us 1810. The EV of this play is 1645.4 - 96.4 = 1549.0.
2f) We hit one of our 3 outs (9c, 9s, 9d) that does not give the hero any redraw. Obviously we're not folding, so we win 750+1060 = 1810 every time this happens.


I'll guess that the best plays are (in descending order) 1) folding, 2) calling the flop and re-evaluating the turn, 3) calling the flop and folding the turn and 4) calling both the flop and turn.


Now, Here's how each play rates as far as EV goes.

1) Folding on the flop: EV = 0

2) Calling the flop and re-evaluating the turn (and making the best play there): EV = (25/45)(-500) + (7/45)(-500) + (6/45)(-473.0) + (1/45)(1223.0) + (3/45)(1549.0) + (3/45)(1810) = (-12500 - 3500 - 2838 + 1223 + 4647 + 5430)/45 = -7538/45 = -167.5

3) Calling on both the flop and turn: EV = (25/45)(-603.4) + (7/45)(-668.7) + (6/45)(-473.0) + (1/45)(1223.0) + (3/45)(1549.0) + (3/45)(1810) = (-15085 - 4680.9 - 2838 + 1223 + 4647 + 5430)/45 = -11303.9/45 = -251.2

4) Calling on the flop and folding the turn (unless we hit the str8): (25/45)(-500) + (7/45)(-500) + (6/45)(-500) + (1/45)(1223.0) + (3/45)(1549) + (3/45)(1810) = (-12500 - 3500 - 3000 + 1223 + 4647 + 5430) = -7700/45 = -171.1

So it looks like calling the flop and folding the turn is better than calling the flop AND turn automatically. But of course, folding is king here. Calling on the flop appears to lose us about 1/6th of our remaining stack on average.

This, of course, is why you shouldn't call preflop re-raises for 1/5 of your stack with QJs -- because you need a miracle flop to be able to continue the hand profitably. Flopping a decent draw still loses you money when you're up against a big hand! Of course, all the logic in the world isn't going to stop that A from hitting the turn to knock me out of the tournament.


And here's another hand that goes along with this same concept, except that this one is much, much worse.

NL Texas Hold'em Level:3 Blinds(50/100)
Table #24 (Real Money)
Seat 3 is the button
Total number of players : 10
Seat 1: HAPPY_JOKER ( $12186 )
Seat 2: Hero ( $6150 )
Seat 3: CPANTHERS ( $6525 )
Seat 4: ttuluna ( $2045 )
Seat 5: Minotaur888 ( $3880 )
Seat 8: mattkkkk ( $2713 )
Seat 7: tronter ( $2576 )
Seat 10: Jose33 ( $2620 )
Seat 9: tenbears222 ( $2770 )
Seat 6: Eidur888 ( $2389 )
Trny:22444021 Level:3
Blinds(50/100)
** Dealing down cards **
Dealt to Hero [ Kh Kc ]
Eidur888 raises [425].
tronter folds.
mattkkkk folds.
tenbears222 folds.
Jose33 folds.
HAPPY_JOKER folds.
Hero raises [1375].
CPANTHERS folds.
ttuluna folds.
Minotaur888 folds.
Eidur888 calls [950].
** Dealing Flop ** [ 7c, Jd, 9c ]
Eidur888 is all-In [1014]
Hero calls [1014].
** Dealing Turn ** [ 3h ]
** Dealing River ** [ 8c ]
Eidur888 shows [ Td, Qd ] a straight, eight to queen.
Hero shows [ Kh, Kc ] a pair of kings.
Eidur888 wins 4928 chips from the main pot with a straight, eight to queen.

This fellow decides to commit just shy of 60% of his stack preflop with QTs against a guy who re-raised his UTG raise. I don't even know where to begin on this one. This guy later got into a re-raised pot with 96s and got all-in against AA on an A9x flop and lost.


I also played some $3/$6 and won a little bit, but nothing interesting there. I think I'm going to begin drinking now. Enjoy the weekend!