Trip 8s vs Draws
Hero (CO): $1.91
So, this was a hand I lost a while ago on PokerStars. For a while after, I wondered whether I misplayed it. So let me do a simple analysis and see whether I can come up with a mathematical reasoning for what I should have played (if I did in fact misplay it).
Pre Flop: ($0.03) Hero is CO with 8 8
1 fold, Hero calls $0.02, 1 fold, SB raises to $0.10, 1 fold, Hero calls $0.08
First, calling pre-flop. I didn’t want to raise because I just wanted to see the flop. A mid-pair for me, is quite hard to play. If I miss the flop with one or two overcards, I’d be very tempted to defend my hand. I’d rather see the flop and then make a decision. It’d be hard for me to steal the blinds at these low levels, I think, because people tend to call raises with a very wide range of hands. So that’s why I made the initial call to $0.02
Not very mathematical so far, I know, but I’m coming to that. The small blind raises to $0.10, and this is where the first bit of math comes in. First I have to put my opponent on a hand. Given the low level (1c/2c blinds), I think he could easily be making this play with anything from a pair of 5s or higher, AT or higher, or KJ or higher. He could also be trying to steal the blinds with an even worse hand than this range.
Let’s recap what I’ve gone through so far. There’s 14c in the pot, I need 8c to call. I put him of a range of 55+, AT+, KJ+. So using these values, I’ve created a sheet of my expected value against each of these hands. And as you can see from the chart, my average expected value against this range is +2.62 cents. As such, the call is mathematically profitable (against this range).
Why didn’t I re-raise? For the same reason why I didn’t raise initially – I didn’t want to build the pot too much before I saw the flop.
Flop: ($0.22) T 6 8 (2 players)
SB bets $0.10, Hero raises to $0.20, SB calls $0.10
The SB’s bet could mean anything given the range of hands I put him on. He could have hit a pair, or he could just be placing a continuation bet. Either way, I think I’m ahead. I didn’t want to chase him out, but was that the right play?
Against any of the hands he could have, I’m more than a 70% favorite to win (unless he has TT, in which cas I’m dead behind). If I raised too much, it’d chase out the weaker hands. What hands would stay with a higher raise? I think a flush draw, a high ten, an overpair, maybe a straight draw. A min raise to $0.20 requires him to put $0.10 more to call the bet. That gives him the right odds to call if he’s on a flush draw, and makes it likely for him to call on two overs, and any pair – essentially any hand within that opening range. I have more than an 85% chance of winning at this moment against that range.
There might be an argument for betting more, but until I have some sort of model to predict if he would fold, I can’t make a quantitative analysis of that. What I will say is that my gut feel said that a flush draw wouldn’t fold to any reasonable bet, and I was far enough ahead that I shouldn’t worry about any sort of hand at this point. And if a flush did hit, I could limit my losses then.
Turn: ($0.62) 9 (2 players)
SB bets $0.06, Hero raises to $0.30, SB calls $0.24
I really did not like the turn card. It put a 4 card straight on the board, as well as two flush draws. At this point I started thinking maybe I should have chased out the gutshot flush draws (so I wouldn’t have had to deal with this). He bet 6c, which was a small bet to me.
At this point, I wanted to chase out the draws, because two flush draws was just a bit scary. Which is why I raised. But I think I was afraid he’d already hit his straight, and as such miscalculated the bet size.
After his bet, there is 68c in the pot. My raise to 30c makes it 98c, and 24c to my opponent to call. If he’s on a flush draw, he has 9 outs, and as such has an expected value of about ( 98 + 24 ) * 0.196 – 24 = -0.088c. Though this is below 0, it’s only very slightly so, and the implied odds after hitting his flush would probably put him on a positive expected value.
River: ($1.22) 7 (2 players)
SB checks, Hero checks
At this point there’s no point in betting anymore because the hand on the board beats my hand; my pocket 8s are irrelevant.
Final Pot: $1.22
Hero mucks 8 8
SB shows K J (a straight, Seven to Jack)
SB wins $1.17
When he showed this, I was really surprised. In retrospect, I think the play pre-flop and on the flop made sense given his hand. But I didn’t expect him to call the 24c raise with a KJ.
So was his call on the turn raise with a KJ correct? Let’s assume he put me on a ten, then he would believe he has 10 outs. 3 Ks, 3 Js, and the 4 7s to complete his straight (which would be a higher straight than the board). That means he has about a 21.7% chance of hitting one of his outs. He needs 24c to call. If he hits, he wins the $1.22 (including his 24c). This gives him an expected value of 0.217 * 122 – 24 = 2.47c > 0. So therefore he should indeed call. What if I had raised to 43c? His expected value would then be -4.88c, and the call would be incorrect. Again, this seems to suggest I should have raised a higher amount on the turn.
What I still don’t understand, though, is why he didn’t bet the river, but anyway, that helped me save money.
So what is my conclusion? I probably could and should have raised higher on the dangerous turn card.
What do you think? How would you have played this hand?