Poker: not a game for the mathematically challenged!

Know your poker math?Justin Bonomo professional poker player

In my opinion the most under utilized form of learning in poker is simple algebra. I’m not talking about anything complicated like Bill Chen’s calculus in his “The Mathematics of Poker” book, but simple eighth grade algebra that you can use in all kinds of poker situations.

Here’s a quick example:
You have a draw. Your opponent bets on the flop, and you think calling is a bad option because you don’t think this particular opponent will pay you off if the draw hits, but he will put you all-in if it doesn’t. Your options are to raise all-in or to fold. There is $150 in the pot, and your opponent bets $100. If you were to move all-in, it would be an additional $200 for your opponent to call. You estimate that you would win approximately a third of the time when you are called.

Q. How often does your opponent need to fold for raising all-in to be better than folding?

Let’s split it up into two situations: x% of the time your opponent will fold, and you will win $250; y% of the time your opponent will call. Of that y%, 2/3 of the time, you will lose your entire stack of $300. The other 1/3 of the time, you will win $450 (your opponent’s stack + the pot).

Your raise equity is x(250) – 2/3(y)(300) + 1/3(y)(450) if you move all-in. That is the same as 250x – 200y + 150y = 250x – 50y. Since x and y add up to 100% of the time. (x = when he folds, y = when he calls), we can say that x+y = 1. That is the same as x=1-y.

So we now substitute for x: 250x-50y = 250(1-y)-50y = 250-250y-50y = 250-300y.

Re= 250-300y. Let’s set Re to 0 to find out when a raise is break even: 0=250-300y. 300y=250; y=250/300=5/6; x=1/6.

That means that if our opponent folds just 1/6th of the time, we have a break even play. Any more than that and we will show a profit. Let’s check our work to make sure it’s right.

So if 1/6 of the time we win 250 and 10/18 of the time [5/6 x 1/3] we lose 300; 5/18 [1/6 x 1/3] we win 450. Let’s see if that adds up to 0.

(1/6)(250) + (10/18)(-300) + (5/18)(450) = 41.667 – 166.667 + 125 = 0. That math is correct.

To some people, that answer may seem extreme. There is enough money in the pot that, with just a 33% chance of winning, our opponent has to fold only 1/6 for an all-in semi bluff to be the correct play.

Generally this math is too complicated to do at the table, but I like to do a simple calculation like this every now and then when I am curious about a situation. The math may seem hard if you haven’t done it in a while, but it’s straight out of your eighth or ninth grad algebra text book.

I figure that if a 14 year old is responsible for knowing this math, a successful professional poker player should be responsible for the same math if he wants to be able to claim that he knows the fundamentals.

Players from around the world including the United States of America can play at these top rating online poker rooms

Justin was the unfortunate pro who got caught with multiple entries and publicly outed for cheating in major online poker tournaments, but he also can claim fame as the youngest player (at that time) to have ever made a televised final table at 19 years, 5 months, and 20 days at the French Open in Deavuille, France, where he finished 4th.

TOP POKER ROOMS FOR USA RESIDENTS – Safe, reputable poker rooms that welcome Amercian players

No Comments so far
Leave a comment



Leave a comment
Line and paragraph breaks automatic, e-mail address never displayed, HTML allowed: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

(required)

(required)