Flopping A Set - Part IV

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?

The Fourth and Final Option

Let's see what happens in our fourth and final option: when we bet the flop. Keeping in mind his three possible holdings, the size of the first bet might be important. If he has two paints, he will fold against any bet we may make. With a pair, some players might call a small bet, but very few will call a pot-size bet. The hand I want him to have is an ace, because then I can win some money from him while he is almost drawing dead. Taking into account this scenario, I suggest that a pot-size bet of about $900 might be a good strategy.



Of course, an opponent with just paints will probably muck right away. So, the result against two paints is +$900. We assume that 25 percent of the pairs are paying this flop bet, but will fold to the next bet unless they hit trips on the turn. So, when they call the flop, 95.5 percent of the time they lose this $900, and 4.5 percent of the time they hit trips. When they hit trips, they win an additional $11,600 on the river (the entire remaining stack) 98 percent of the time, and 2 percent of the time they lose an additional $11,600 (when I make quads). To make it not more complicated than it is already, we assume that a pair of fours, is a hand that folds to a flop bet.



So, coming out betting against a pair gives us this result: 0.75 x $900 + 0.25(0.955 x $1,800 + 0.045 (0.98 x -$12,500 + 0.02 x $13,400)) = $970



Coming out betting appears to be an especially good strategy against an ace. For most players, it's almost impossible to lay down a decent ace at this stage, and against this action. We assume that 90 percent of the players would call the flop bet. And after a player calls this flop bet, we are going to bet a little bit softer, to keep him guessing.



Finding the Proper Play on the Turn and River



Continuing with our assumption that 90 percent of the players would call on the flop, on the turn the pot has become $2,700. A turn bet of $2,700 could be a bit too much and could lead to our opponent folding – which we don't want.



I suggest that a turn bet of $1,500 is nice. For me, this is kind of a borderline bet that will be called 50 percent of the time. If he calls, he is still guessing about our hand; he has no clue as to where he stands.



After this play on the turn, the pot at the river would be $5,700. I think a $2,500 river bet would also be called about 50 percent of the time in this situation. These assumptions lead to the following result:



Again, we assume that when he hits the ace or his kicker on the turn, we will have an all-in situation. Let's take the following percentages:



A – He folds on the flop: 10 percent

B – He folds on the turn: 40 percent

C – We go all in on the turn: 11 percent

D – He calls $1,500 on the turn, but folds to a river bet: 19 percent

E – He calls the $1,500 turn and $2,500 river bets: 20 percent



Before we calculate the total result, let's first look at situation C. We both put in $12,500, giving us a profit of $10,339 (see above). The total result when up against an ace, having bet the flop ourselves, is: 0.1 x $900 + 0.4 x $1,800 + 0.11 x $10,339 + 0.19 x $3,300 + 0.2 x $5,800 = $3,734.



As we said, his probable holdings were estimated at 40 percent for an ace, 40 percent for a pair, and 20 percent for two paints. The expected value when we come out betting is:



+$970 against a pair

+$3,734 against an ace

+$900 against two paints

So, the total result for betting out is: 0.4 x $970 + 0.4 x $3,734 + 0.2 x $900 = $2,062.



Combined Results/Expectations of All Possible Plays Against Our Opponent's Three Probable Types of Holdings


To give you a clear view of what I have said in this long mathematical story, I have put all of the results in this chart:

Strategy Paints Ace Pair Total Actual*

Check-raise on the flop $1,400 $1,999 $1,400 $1,640 $1,340

Check-call the flop and bet the turn $1,400 $3,034 $867 $1,861 $1,561

Bet the flop $900 $3,734 $970 $2,062 $1,762

* In Part I, I said that I would calculate everything with a "$900 preflop pot," to make it more clear, and that I would subtract the $300 we put in ourselves when all of the calculations were completed. So, our real gain in this hand is in the last column of the chart, under "Actual."



Analysis



I hope all of my assumptions were pretty much in line with reality. Having said that, it is entirely possible that many readers may have made other assumptions. I also know that I did not examine all strategies, like a minimum check-raise on the flop and maybe some other options.



I am not really surprised with the results. As I expected, betting out ourselves and giving up the $500 (the automatic flop bet of the unimproved two paints in case we would have checked to him) is largely compensated for by the result against an ace. Paying off a $200 raise brought a result/expected profit of $1,762, almost 9-to-1 on our investment; and comparing this with the chances of hitting a set, it is very good.



I can imagine that it might be interesting in another column to look at how big a raise we can afford to pay off in all of the different situations. But I also can imagine that you are a bit fed up with my mathematics and want to read an uncomplicated column next time.



The purpose of this column series was to give you a mathematical view of particular situations, because we are not always able to do these calculations at the table. I hope that you enjoyed this analysis – and that you can possibly benefit from it.



This concludes this 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, see http://www.robhollinkpoker.com/.