Flopping a Set - Part II

In this four-part series, I am discussing a tournament situation in which you flop a big hand. I explain what to do when you flop trips, having called a preflop raise from the big blind – taking into account lots of possible actions your opponent could make, based upon the hands that he most likely holds. I will try to analyze all possible plays, hoping to find the situation/play that offers the highest possible expectation. Please note that this series is not an easy read, by any means – but I hope and expect that you will find it worthwhile.



The situation is as follows: You are in level two of a no-limit hold'em tournament. The blinds are $50-$100. Players have stacks varying from $5,200 to $15,225. Seat Nos. 3, 4, and 5 fold (assuming seats No. 1 and 2 are the blinds). Seat No. 6, who has been playing very tight, has a $14,850 stack and raises to $300. Seats No. 7, 8, and 9 fold. The small blind, with a $9,975 stack, calls, and you are calling with 5-5 from the big blind. Your remaining stack is $12,500. The pot is $900 now. The flop is A-8-5 rainbow. The small blind checks. Now the question is: Check or bet?



WHEN OUR OPPONENT CHECKS

As we saw in Part I of this series, a check-raise on the flop would gain us $1,965, provided that (a) our opponent has a (big) ace, and (b) that he bets the flop. Now let's see what happens if our opponent checks the flop. According to our previous assumptions, he would do this in 25 percent of the situations in which he has an ace. In this situation, I would respond to his flop check by betting $600 on the turn – a bet he would call for sure with an ace. As sort of a safety play, I assume that he also just calls (instead of raises) this $600 turn bet even when he hits his five-outer on the turn, for two reasons: first, because the pot is not big yet, and second, because the remaining stacks are big.



My river bet would then be around $1,200. If our opponent happens to have made a full house that beats us, he will probably make it about $4,000 more on the river, and we would be calling this raise about 60 percent of the time, probably. (Note that, for instance, 8,8 or ace,8 on the turn and the river are situations in which we don't call.)



Up Against Top Pair – and No Bets on the Flop: What Now?

Now, let's see what happens when our opponent has top pair, decent kicker on the flop, and we both have checked the flop. Let's take a look at the various possibilities.



A: 2/45 of the time, he hits an ace on the turn, or 6/45, he hits the 8 or his kicker – and then calls our $600 bet. Now he hits the river, as well (seven out of 44 cards after hitting an ace on the flop, and four out of 44 after hitting the turn with an 8 or his kicker), and would be raising our $1,200 river bet to $5,200. We would be calling 60 percent of the time. So, 1.9% of the time (2/45 × 7/44 + 6/45 × 4/44), we lose 0.4 x $1,800 + 0.6 x $5,800 = $4,200.



Result/expectation: 0.019 x -$4,200 = -$79.80



B: 2/45 of the time, he hits an ace on the turn and misses (37/44) the river, or 6/45, he hits the 8 or his kicker on the turn and misses (40/44) the river. (2/45 × 37/44 + 6/45 × 40/44) x 100% = 15.9%. So, in 15.9 percent of all situations, he would call our $600 bet on the turn, but misses the river and then calls our $1,200 river bet. So, in 15.9 percent of the situations, we would win: $900 + $600 + $1,200 = $2,700.



Result/expectation: 0.159 x $2,700 = $429



C: 37/45 of the time, he misses the turn (does not hit an ace, jack, or 8), calls the $600 bet, and then hits an ace or his kicker on the river (5/44). Now, he calls our $1,200 river bet. So, in 37/45 × 5/44 × 100% = 9.3% of the situations, we would win: $900 + $600 + $1,200 = $2,700.



Result/expectation: 0.093 x $2,700 = $252



D: 37/45 of the time, he misses the turn, calls the $600 bet, and misses the river, as well (39/44). Let's assume that he will call a $1,200 river bet approximately half the time. So, in 37/45 × 39/44 × 100% = 72.9% of the situations, we would win: 0.5 x ($900 + $600) + 0.5 x ($900 + $600 + $1,200) = $2,100.



Result/expectation: 0.729 x $2,100 = $1,530



Conclusion

Adding this together, our result when up against an ace if he checks the flop would be: -$80 + $429 + $252 + $1,530 = $2,131. So, when we try a check-raise on the flop and are up against an ace, our result is: 0.75 x $1,965 + 0.25 x $2,131 = $2,007.



That is nice, but would it be possible to extract some more from our opponent with this big hand that we hold?



Now let's see what happens if we just call his flop bet. Is it possible for us to extract a little bit more from him?



After we call his $500 flop bet, the pot is $1,900 and the remaining stacks are at least $12,000. Now, after calling his bet, he will (again, as before) start thinking about our possible holdings – and again he will acknowledge the possibility that he is beat already. When we check the turn to him, he almost certainly will check it back.



Not to make things too complicated, let's assume that he checks it back on the turn even when he hits his five-outer. It wouldn't be such a bad safety/minimizing losses play, and it would also be a good way for him to induce a possible bluff.

On the river, we would be betting about $1,000, then.



If he has hit the turn and river, and has made a full house that has us beat, he will raise on the river for sure. To keep it simple, I will ignore the very small possibility that we make quads and he has a full house. Let's assume he will raise us $4,000 when he makes a better full house on the river, and that we would be calling 60 percent of the time. (Please note that, for instance, 8,8 or ace,8 as the turn and river cards are easy folds for us.) His chances of making a full house (or quads) on the river that beats us are: 2/45 × 7/44 + 3/45 × 4/44 + 3/45 × 4/44 = 1.9%



• 1.9 percent of the time, he will win, and 98.1 percent of the time, he will lose on the river. Let's assume that he would call 70 percent of our river bets. We would be betting around $1,000 on the river. 1.9 percent of the time, he raises $4,000 more, and we call 60 percent of the time. Result: 0.019 × 0.4 x -$1,500 + 0.019 × 0.6 x -$5,500 = -$74.10.



• 70 percent of the time, he calls our $1,000 bet and loses. Result: 0.7 x $2,400 = $1,680



• 28.1 percent of the time, he folds to our river bet. Result: 0.281 x $1,400 = $393.40



Comparing the plays

Up against an ace: Putting all of these figures together, calling the flop and checking the turn when up against an ace would lead to the following result/expectation: -$74.10 + $1,680 + $393.40 = $1,999.30



As you can see, it's a result that is a little bit worse than the check-raise would yield.



Up against two paints: Against two paints, both strategies would lead to the same result (+$1,400).



Up against a pocket pair: A check on the turn would be extra bad when our opponent has a pair bigger than 5-5, because then the river could hit him – and cost us a lot of money.



Conclusions

With the results that we have already, it is clear that this strategy of a check-call on the flop and a check on the turn is significantly worse than the check-raise strategy – taking into account the assumptions that we have made, of course.



This could lead us to the next conclusion: Check-calling on the flop and then checking the turn is no option.



A simple check-raise on the flop would lead to the following results:

• +$1,400 (against a pair)

• +$1,999 (against an ace)

• +$1,400 (against two paints)



So, the overall result for a check-raise on the flop is: 0.4 x $1,400 + 0.4 x $1,999 + 0.2 x $1,400 = $1,640



This is a four-part series on how to extract the maximum when you flop a set, written by 2005 European Poker Champion Rob Hollink. Rob can be found playing at www.robspokerroom.com under his own name. For more poker information, see www.robhollinkpoker.com.