Maths rules

There are 18 players left in a tournament and the big-stack has just raised your big blind for what seems to be the 100th time. The blinds are at 1,000/2,000 with a 200 ante and you have 20,000 left after posting your blind. You look down and see pocket Queens.

Finally! Here’s where you’re going to show the bully he can’t raise your blinds ever y time. You move all-in. He calls you with K?-10?. King-Ten offsuit? For 20k in chips? What the hell is this guy thinking? You rub your hands together expecting to double up and win a big pot. But it’s not to be. A King hits the flop and you are out of the tournament because of some loose donkey. But was he really that loose?

Too many players misunderstand the maths when it comes to late-tournament situations. In the above example, there was already 32,800 in the pot and he had to call 14,000. 32,800/14,000 = 2.34. He was getting 2.34/1 on his money. The call won’t cripple him but it will add to his already healthy stack. To top it off, there are only a few hands that you could hold that he would be bigger then a 2.34/1 dog to.

Aces, Kings – even dominating hands like a bigger King, a pair of Queens, Jacks or tens are right in that 2/1 to 2.5/1 range. In other words, given the price he is being given by your range of hands his call is correct.

That’s the easy scenario though. What about situations where you are faced with a tough decision but you aren’t the big stack. Say your opponent has moved all-in and you are getting 2.5/1 on your money but the call is for half your stack? In most tournaments (outside of deep-stack events) the structures make the play at the end very fast. When this is the case you will often be compelled to make a mathematically correct call even though your stack size dictates that you should probably fold.

Knowing when you should call or fold in these situations can best be explained using a real example. This particular hand took place online in one of the daily guaranteed tournaments. Everyone was already in the money and there would not be a significant prize jump until the final table.

NON-HERO CALLS

Our hero in this hand is dealt J?-10? in late position and raises to 4,000 total with the blinds at 800/1,600. He has 27k in chips to start the hand. The big blind moves all-in for 13k total. There are several things to consider here. What is the range of hands that the big blind could be pushing with?

It’s probably wider than usual because the hero’s raise was made from a steal position. Despite this, the hero knows he is probably going to be a 3/2 or 2/1 dog to almost any hand the big blind has except for a smaller pair (possible) or two small cards making a re-steal (not out of the question).

The hero has to call 9k to win about 20k, or 2.2/1 on his money. If he folds, he will have 23k. This is close to the danger zone at 14 times the big blind. If he calls and loses, he will have 13k or 8 times the big blind. If he wins, he will have 41k or 26 times the big blind.

Here is where understanding the maths becomes important. If you look at the hand from an ‘end of tournament’ perspective, you know that there is little difference between having 14 or 8 times the big blind. Both stacks are for the most part relegated to one- move poker, although the 14-times stack might be able to do one first-to-act raise and fold to a re-raise.

With the rapid increase in blinds in these types of tournaments, this difference is nominal. However, with 26 times the big blind you can play some poker. You can raise without worrying that you have to commit your entire stack. You can re-raise someone without having to move all-in pre-flop. You can call down the short-stacks when they move all-in.

In short, you’ve put yourself in a better position to win the tournament, and this is why it is often correct to overvalue the maths. Sure it sucks to have to make this kind of call and lose a big chunk of your stack more often than not, but it’s winning tournament poker.

ANALYSE THIS

Another thing to consider is that if you are going to fold hands like J-10 and Q-10 to re-raises when you are getting 2/1 or better on your money and the action is closed (meaning your opponent is all-in) then you should probably not be raising in the first place. In tournament poker, you just can’t do this. You might make the money this time, but over the long run you’ll end up blinding off and lose money.

The reality is you can’t just sit back and wait for big pairs and big Aces. You must find players whose blinds you can attack. You must find situations where you can steal.

Before you go all crazy and start raising every time you possibly can, you need to make sure you do a quick analysis of three things:

1. If you fold, what is your stack size in relation to the blinds?

3. If you call and win, what is your stack size in relation to the blinds?

When you do this analysis, you are making a comparison between the three categories. The first thing you need to do is look at the difference between 1 and 2. If it is large, then folding marginal hands is correct. If it is minimal (as was the case above), then you need to look at 3 in order to determine whether or not you should make the call with a marginal hand.

If the difference between 1, 2 and 3 is significant (as was the case above) then calling will often be correct with almost any hand if you are getting 2/1 or better on your money. The larger the difference, the more likely you should be to call. The better the price you are receiving (for example 3/1 or 4/1 on your money) the more likely you should be to call.

If the difference between 1, 2 and 3 is small, there is no real benefit to calling with a marginal hand regardless of the price. Although I don’t think you should ever fold when you are getting close to 4/1 on your money.

SUMMARY

Too many tournament players think only about the here and now. They don’t think about the long term. When it comes to making money (and lots of it) in tournament poker it’s all about winning. Winning is more important than survival. And here is where the importance of maths comes out the strongest.

What if you are getting 2.25/1 (which is what it was in the first example) against a hand that you are a 3/2 dog to? Now you have to call 20,000 to win 45,000. Three times you will lose 20,000 for a total loss of 60,000, and two times you will win 45,000 for a total win of 90,000. Your profit for the five hands equals 30,000 or 6,000 per hand, which is a 30% return on your 20k chip investment.

If someone told you that you could make 30% on your money over the course of a year, you’d do it, right? When it comes to these mathematically-based decisions this is the thought process you should follow.