Flopping a Set - Part I

In this four-part series, I am going to discuss a tournament situation in which you flop a big hand. I will explain what to do when you flop a set, having called a preflop raise from the big blind - taking into account lots of possible actions that your opponent could take, based upon the hands that he most likely holds. I will try to analyze all possible plays, hoping to find the situation/play that would offer 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 that seat Nos. 1 and 2 are the blinds). Seat No. 6, who has been playing very tight, has a $14,850 stack and raises to $300. Seat Nos. 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?

To not make this situation more complicated than it already is, we will assume that the small blind will simply give up to any bet. With that in mind, we are going to try to calculate the optimum strategy for us with our flopped set. In this particular situation, I have a very strong preference for coming out betting. To find out if my thoughts are right, I will try to make some calculations. In these calculations, I have to make a couple of assumptions, and I also have to make estimations of how probable certain decisions from my opponents are.

To make a good decision about checking or betting, it might be interesting to look at what hands the player in seat No. 6 could have raised with. Let's say the possibilities are a pocket pair, an ace with a good kicker, or two paints (probably suited). When we count pairs from 4-4 to A-A, and assume that an ace with good kicker also includes the 10 kicker, I think the percentages for our opponent's specific hands are more or less 40 percent for the pair, 40 percent for an ace, and 20 percent for two paints. We will need these percentages for our calculations. I guess you understand that I am not going to discuss the possibility that my opponent flopped a set, as well. In that situation, I will simply go broke, provided I don't hit my one-outer.

Up Against A Pocket Pair
The next thing to look at is what we expect our opponent to do if it is checked to him. Starting with a pair in his hand, I think that almost any player will like to find out where he's at when there is an ace on the flop. I guess that he will probably bet something like $500. If we check-raise him here, he will certainly lay down his hand. If we just call him, he will also give it up when we make a decent bet on the turn or river - unless he hits a set, as well. So, against a pair, the best thing to do would be to check-raise him. Your gain would be $500 + $900 (already in pot) = $1,400 without giving a free turn card. (I know that the actual result/net gain in this spot is $1,100 and not $1,400, because we already have contributed $300 in the $900 preflop pot. To keep it more clear for you, I will at all times use the "$900 preflop pot," and finally subtract from each result, $300.)

Let's see what happens when our opponent has a pair and we check-call the flop and bet the turn ourselves. If he misses his set on the turn, which will occur 95.5 percent of the time, we have the +$1,400 result from before. And if by chance he does hit his set higher than fives, he wins our remaining $12,000, unless we hit our 2 percent chance at a one-outer on the river. When he hits a set of fours on the turn, we will win his stack for 98 percent sure. When he makes a set on the turn, the chance that this set is lower than ours (4-4-4) is 1-in-8. The other sets are sixes, sevens, nines, tens, jacks, queens, or kings.

Putting all of this together, when we are up against a pocket pair, and just call on the flop and then bet the turn ourselves, our result/expectation would be: 0.955 x $1,400 + 0.045 x ((0.875(0.98 x -$12,500 + 0.02 x $13,400) + 0.125 (0.98 x $13,400 + 0.02 x -$12,500)) = $937. Note that the $13,400 is our remaining stack of $12,500 and the $900 that already was in the pot preflop. Conclusion: A check-raise on the flop and raising the pocket pair out of the pot gains us $1,400 - while giving him a free turn card gains us only $937. It's interesting to see the impact of such an "innocent" free card to a mere two-outer.

Up Against Two Paint Cards
What can we expect from an opponent with two paints in his hand? If the two paints have totally missed and we check to him, he will probably fire an "automatic" $500, trying to pick up the pot. When we check-raise him here, he will almost certainly fold.

Check-calling on the flop and then betting out on the turn against two paints won't be too risky (as very few, if any, turn cards could give him a winner), and he will almost certainly fold to any bet we may make. So, I am free to set our result against two paints at $500 + $900 = $1,400, no matter how we play it, check-raise or check-call followed by a turn bet.

Up Against A Big Ace
Now we are going to investigate what happens if we are up against an ace with a king, queen, jack, or 10 kicker. Let's assume the chance of him betting the flop when checked to is 75 percent and checking it back is 25 percent. If he makes a flop bet, there are two possibilities for us: just call, or check-raise right away. If we raise him here, he will probably start thinking what we could have to make this play. There's no flush draw out there. The only decent straight draw is the 7-6. Hmm … he probably doesn't like his hand that much anymore.

I guess the majority of tight players who bet this flop would lay down this hand when they are check-raised. Let's assume that if we make it $1,000 more by raising from $500 to $1,500, 70 percent of our opponents will fold and 30 percent will pay the $1,000 more. But they would not pay another $2,000 or $3,000 bet on the turn or river unless they hit their kicker or another ace. To make it not more complicated than it is already, let's assume that when our opponent hits his five-outer on the turn, it simply leads to an all-in situation in which both players put another $11,000 into the pot, totalling $12,500 each. So, when he hits one of the two remaining aces on the turn, he has seven outs on the river out of the 44 cards left in the deck. Our expected gain in that case would be 37/44 x $25,900 - $12,500 = +$9,280. And when he hits one of the three remaining kickers on the turn, he has four outs on the river. Our result in that case would be 40/44 x $25,900 - $12,500 = +$11,045. This will lead to the following expected gain for us if we check-raise on the flop: 0.7 x $1,400 + 0.3 x (40/45 x $2,400 + 2/45 x $9,280 + 3/45 x $11,045) = $1,965. (Of course, this also depends upon our image. The tighter image we have, the more likely it is that our check-raise will make our opponent fold.)

When Our Opponent Checks
So, a check-raise on the flop against an ace brings us $1,965, provided that our opponent 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 very big yet, and second, because the remaining stacks are big.

My river bet would then be around $1,200. My opponent's probable actions after my river bet will be discussed extensively in the second part of this series.

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.