Flopping a Set - Part III

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 that our opponent could take, based upon the hands that he most likely holds. I am trying 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 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?

The four options

In the first two parts of this column, we calculated that the first option, check-raising on the flop, yielded a result/expectation of $1,640. We also found out that the second option, check-calling on the flop and then checking on the turn, had a result that was significantly worse than the check-raise option.

In the final two parts of this series, we are going to calculate the result of two more options. The first one is check-calling on the flop and then betting out on the turn. And finally, we are going to look at what happens when we come out betting the flop ourselves.

Results/expectations based on our opponent's possible holdings

In Part I we found out that when up against two paints, we always had a $1,400 result if we checked the flop. Checking the flop and betting the turn against a pair had a result of $937.

Now, we have to find out what this strategy brings when our opponent has an ace. When we check the flop to the ace, we had established/assumed that he is going to bet 75 percent of the time. After a check-call on the flop, we are going to bet the turn. Let's say that we are betting $1,200 on the turn into a $1,900 pot. If he calls this bet, we will make another bet on the river – say, for about $2,200. Furthermore, we assume that when our opponent hits his five-outer on the turn, this is going to lead to an all-in situation.

Based on these assumptions, there are four possibilities, in my opinion:

1. He folds on turn.

2. He calls the turn, but then folds to our river bet.

3. He calls both our turn and river bet.

4. He goes all in on the turn after hitting his five-outer, and we call.

What does this all mean? It means that, as before, we both are putting $12,500 into the pot after the flop, with us being a big favorite. As we calculated earlier in Part I, this gives us a 40 percent chance (ace on the turn) for a +$9,280 result and a 60 percent (kicker hit on the turn) chance for a +$11,045 result. On average, we win: 0.4 x $9,280 + 0.6 x $11,045 = $10,339.

Now, we will have to estimate the probabilities of 1, 2, 3, and 4 as described above. It is hard to estimate what the average tight player would do. We know that when he calls the flop, the chance that he hits the five-outer is five out of 45, which is 11 percent. So, the probability of 4 is 11 percent. I suggest that, all in all, we take the following probabilities:

1. 41%

2. 32%

3. 16%

4. 11%

This would result in a profit of:

0.41 x $1,400 + 0.32 x $2,600 + 0.16 x $4,800 + 0.11 x $10,339 = $3,311.

Now, let's see what happens if he checks the flop, as well. (This he will do in 25 percent of the situations with an ace in his hand, as we assumed above. This was the situation with the four different possibilities that we examined in Part II.)

Our result/expectation against an ace if he would check it back on the flop was $2,131. So, if we check-call the flop and then bet the turn ourselves – up against an ace – the result will be:

0.25 x $2,131 + 0.75 x $3,311 = $3,016.

Results/expectation for the check-call on the flop and then betting out on the turn

I guess that by now we have examined all of the possibilities for check-calling the flop and then betting the turn. Let's take a look at our expectation:

• Against an ace: $3,016

• Against a pair: $937

• Against two paints: $1,400

Taking into account our assumptions from before (a 40 percent chance that our opponent has an ace, a 40 percent chance that he has a pair, and a 20 percent chance left that he has two paints), things look like this:

The total result for a check-call on the flop and a bet on the turn is:

0.4 x $3,016 + 0.4 x $937 + 0.2 x $1,400 = $1,861

Results/expectation for the check-raise on the flop

A check-raise on the flop brought the following results:

• Against an ace: $1,999

• Against a pair: $1,400

• Against two paints: $1,400

Based on this, the expectation for a check-raise on the flop would be: 0.4 x $1,400 + 0.4 x $2,074 + 0.2 x $1,400 = $1,640

So, when we check the flop, the best strategy would be to call his flop bet and come out betting the turn ourselves.

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 http://www.robspokerroom.com/ under his own name. For more poker information, visit http://www.robhollinkpoker.com/.