Why it’s essential to know the mathematics behind poker
Bill Chen is a PhD mathematician turned poker player. Realising that he could win more than the $1,000 a month he got for his post grad degree by playing poker, Chen used his number skills to devastating effect. Along with young gun Jeff Madsen and a resurgent Phil Hellmuth, Bill Chen was one of the big successes of last year’s WSOP. Winning two bracelets and making six cashes for over $830,000, Chen established himself as a solid player and recently played in the third series of High Stakes Poker.
Why is it so important to know the maths of poker?
In today’s poker world even the ‘feel’ players realise that it’s important to know some of the maths, because even if you’re a good intuitive player, you’re not going to know what hands to play pre-flop and how often you need to bluff. You need that knowledge, just to be aware of base strategy.
What’s the most important concept to get to grips with?
A lot of my book – The Mathematics of Poker – is aimed at achieving the highest expectation of a play, which is how much money, on average, you’re going to get from a given situation. If a play makes $10 90 percent of the time and loses $50 10 percent of the time then your expectation is $4: (10 x 0.9) – (50 x 0.1) = 4. It’s a fundamental concept, not just in poker but in all gambling.
You want to maximise that expectation in the majority of cases. The place where you don’t want to do this is with your entire bankroll. The reason for that is because of a more global strategy of managing your money.
That’s where the concept of marginal value comes in?
Yes. There are some cases where you don’t want to make the play with the highest expectation [because it will cost too much of your bankroll]. If you can win a million dollars the next million isn’t worth as much. It has marginal value so you would much rather take one million than a coinflip between winning two million and going broke. However, for the sake of simplicity, if you always chose the decision with the best expectation you should be profitable.
Is the maths-based approach a boring way to play?
Some people may think it’s very predictable, maybe a little tighter and passive than usual and that it stifles the imagination somehow. That’s what Daniel Negreanu has said before! I kind of disagree. People get the image it’s a fairly dry style of play because of Sklansky’s books.
However, most of the mathematical school of players that I know are hyper-aggressive and try to be un-exploitable by being unpredictable. I can tell you the range of hands that I’m playing – that 80 percent of the time I’ll have a certain hand and 20 percent of the time I’ll be bluffing, but that information isn’t going to help you make a tough decision [against me].
How do you randomise those times that you choose to bluff?
You could look at a clock and if it’s a certain time then you go ahead and bluff! If I’m thinking that I’ll bluff 20 percent of the time, I’ll look at my hand and if it’s within the worst 20 percent of hands that I could have in that situation then I’ll bluff [as it’s probably the only way to win the pot].
Where do people go wrong?
People have this concept that you have to be creative and randomise your play. The example I want to bring up is your starting hands. People say that if you only play Aces and Kings you’ll be too predictable. That’s definitely true, so occasionally you have to mix in some other hands, but you shouldn’t loosen up to playing something like 7-2 off-suit. Include hands like smaller pairs and suited connectors such as 7-5 and 7-6.
Add in the hands that have more potential than just rags. Also, if you’re going to bluff on the turn make sure it’s a semi-bluff so that you have some kind of draw.
Once you’ve got to grips with some key concepts like outs and pot odds what should you learn next?
It’s important to get your head around the betting-to-bluffing ratio. The percentage that you’re bluffing should be proportional to the amount you’re value betting. For example, if you’re playing pot-limit and you’re betting the pot you should be bluffing about half the time that you’re value betting.
If you value bet 10 percent of your hands then you should bluff five percent of your other hands. If you do that and your opponent has a medium strength hand, he won’t know whether he should call or not. If you bluff more than that he has an easy call. Bluff any less than that and he has an easy fold. The reason you’re bluffing is because you want to get called when you’ve actually got the hand. There are some bluffs that have positive value in a given situation, but the reason you’re making the bluff is so you get called with other hands.
So bluffing is more to do with an overall strategy than one specific hand?
Bluffing makes the range of hands you can win with larger. The idea is that you’re going to get into a situation where you get to the river a bunch of times, often without having the winning hand. So you need to balance when to value bet and when to bluff to help you make a profit.