[elindauer]

Hi McNasty,

I wrote up an analysis of this hand for some other folks recently, thought I'd share it with you:

Villain raises the CO. Folded to Hero in big blind who holds Qh6h. Hero?

To answer this question, let's go to pokerstove. I'll assume villain is using Stox' opening standards from the CO (22+,A5o+,A2s+,K9o+,K5s+,QTo+,Q9s+,J8s+,T8s+,97s+, 87s,76s).

We plug this into pokerstove against our hand and find our equity in the pot: we have 38% equity in the pot, and we're getting 3.5:1 immediately. Seems like a call is in order.

In the hand, hero did call (no surprise... wouldn't be much of a post would it?).

On to the flop: Th 7d 5d

Now we can use the range calculator to see how this flop hits the villain's range:
villain flop results.

Here we can see that villain finds this board to be mediocre. He's almost never flopped 2-pair or better (only 3% of the time). On the other hand, he has never totally missed. That said, he's looking at 2 overcard or 1 overcard draws almost half the time on this board (46%).

So, we can conclude that we are unlikely to make villain fold this flop, and should probably play our hand fairly straight-forwardly. What does that mean? Well, we ask pokerstove for our equity vs his range by plugging in the board, and find that we are nearly 3:1 underdogs vs his range. Getting 5.5:1 when he (almost inevitably) bets, we should check and call. So far so good.

Turn: [Th 7d 5d] Kh

Let's go back to the range calculator and see how this effects his range. So far we haven't narrowed his range at all, since he would likely have bet any preflop raising hand on the flop. So this turn range analysis is likely to be very accurate as to where villain stands.

We can quickly see that villain likes this card. His probability of having 2-pair-or-better has gone up from 3% to 8.5%. He holds 1 pair another 55% of the time, and has some kind of good draw another 22% of the time. In fact, he can only fold this turn card with 15% of his hands, which are A9, A8, A6, A4s, A3s and A2s. With only 3 big bets in the pot, we should not bluff at this turn card. We should check.

After we check, hero bets. We're certainly calling... should we raise? We've seen that semi-bluff raising can sometimes be right. In this case, we can do the math very well. Let's assume he bets his whole range, and folds those terrible 15% of hands:

8.5% of the time we get 3-bet by 2-pair or better and lose 2 * .6 big bets = 1.2 big bets
15% of the time he folds, we gain 80% of the pot ~= 4 big bets
76.5% of the time he calls, and we lose 60% of 1 big bet = .6 big bets

So the EV of a raise is: -.085*1.2 + .15*4 - .765*.6 ~= .005 big bets.

So it's REALLY close. If we feel our opponent is a bit tight and passive, we raise. If he's just a touch loose and aggressive vs our assumptions (for example, maybe he doesn't bet the turn with weak hands), we just call. If we think the check-raise sets up profitable river bluffing situations, we raise. Probably the best play is to just call against a very tough player (game theory analysis would be very useful here).

Having done this analysis, it's no surprise that hero was unsure about his turn play. It's pretty close.


So, check-call the turn. Now to the river: [Th 7d 5d Kh] Qd

Let's start with a range analysis. villain's river range.

Yikes! We see that this was another very good card for the villain. He has made 2-pair-or-better more than 1 time in 4 (27%). He has 1 pair over 50% of the time, and of those, a quick glance reveals of his 1-pair hands, we can beat a lot of them, but still have to worry about quite a few combinations. He has rarely missed this board completely, so we shouldn't be bluffing here (more on that in a game theory analysis to come).

We know that villain will have a hard time raising a weak hand, and bluff-raising should be very rare on this board, particularly given that he can't hold many missed hands to begin with. Bet / fold looks reasonable.

So we know that villain will rarely be bluffing if we check. He's much more likely to call a bet with a hand we can beat than to bet it himself. Check-call looks clearly worse than bet / fold. (note that this is another example of betting mediocre made hands OOP on the river)

If we check and he bets, we'll be getting 6:1 to call. Given the range analysis, we can't call. Check-fold looks reasonable (edit: surprise! I'd have certainly called here. Looks like I just found a leak).

So, check-fold or bet / fold? In a vaccuum it looks like these are the only choices. Seems like we may be opening ourselves up to being exploited here, but we can discuss that in a game theory talk in a bit. For now... how do we choose between these?

That's a really tough decision based on player information. How often will he check behind a better hand? How often will he bluff if checked to? etc. Without diving into even more math, I'd say it looks pretty close. The numbers are all there though if anyone wants to look into it.


So, to sum up, hero's play this hand looks solid. The turn decision to just call is close, and you could raise if you felt your opponent was tight. The river decision to bet / fold looks fine, though check / fold could be slightly better.


good luck.
Eric