Revenge of the Nerds

Pot odds are the mathematics of poker and while a lot of players have a good instinct for the probability of a particular situation there are great opportunities at the table to make better plays when you know the real numbers. Most top poker players are also incredible mathematicians and revalue their hands after every card. We have three questions; How do you calculate it? How do you use it? When doesn’t it apply?

How do you calculate the odds?

First you need to know how many “outs” you have, this is the number of cards to give you a winning hand. A good example is an open ended straight, you go into the hand with 7,9 and the flop comes 6, 8, A. You have 8 outs, 4-5s, and 4-10s there are 47 cards left and you have 2 draws make your hand. 8/47, this is about 1/6 (I round off) per draw so basically you have about 1/3 after the flop to make your hand, if you miss on the turn it will be 1/6 for the river. It’s very important to recalculate on the turn, for example what if the turn is a 9? I would add the 2-9s left and the 3-7s, as they will give you 3 of a kind or 2 pair. That makes 13 outs of the 46 cards left, now your odds are almost 30% to win on the last card. What if your cards were suited and you have a flush draw now you 6 outs for the straight ( the suited ones are now on the flush possibility) , 5 for 2 pair and 3 of kind, and 9 for the flush. This gives you a total of 20 outs out of 47 cards on the river this is over 40%.

How do you use these numbers?

As in most things in life it’s all about risk versus reward. As businessmen, investors and gamblers the world over will tell you if the payout of the reward is greater than the risk you should proceed. Very simply if you have a 1/3 risk to win and the payoff is greater than 1/3 it works. A risk of 1 in 3 versus a payoff of 4 to 1 would mean if you bet $1.00 - 3 times you would win $4.00 once.  This is a 33% return on your investment. At the poker table the payoff is based on what is in the pot versus the bet required to call.

We will go back to our previous example. The straight draw after the flop has given us a 1/3 chance to make our hand on the turn or the river, we are at 1/3. Dean raised the 4000 preflop and 3 players called, the pot is now 16,000. Now Mr. Bigstack raises 4000 again; the pot is now 20,000 versus a calling bet of 4000 – we are getting 5 to 1 on our money versus a 1 in 3 bet it’s an easy call. What if he raised the pot, 16,000? Now we have to call 16,000 to a pot of 32,000. We get 2 to 1 on our money for a 1/3 risk. This would be a smart bet by Dean and we must fold. That’s how pot odds work both defensively and offensively, Deans bet of 16,000 is based on making sure that he gets a return on his money if we call. On average he will win out; For us it’s 1 in 3 we win a payout of 2 to 1. If this played out 6 times we would bet 6 x 16,000 = 96,000 to win twice for a total of 64,000. Dean would come out ahead 32,000 for his 4 wins on average and we would come out less that amount.

Using this you can force someone on a flush draw ( aprox. 1 in 5 – 9 cards of the 47 ) to fold by betting so that the pot odds don’t pay more than 4 to 1. If they do call they have put you in a situation to win even more money. If the bettor has bet a small amount and it gives you a pay off of 5+ to 1 then you can confidently call knowing you are in the right place.

It isn’t all that easy, if it was computers would play poker. There is also “Implied Odds” that is based on money that isn’t in the pot but you are confident you can get. In the above example if you did hit your straight on the river can you get another bet out of Dean? If you are confident he will bet another 4000 you can include that into your calculations when the numbers are quite close.

When doesn’t pot odds work? 

Short stacked players quite often don’t have the luxury of folding. Forcing them to fold rarely works, they can easily end up in a situation where they have to run a bad risk / reward scenario. After 9:00 if you can’t buy in you have to think in terms of risking your stack. While a particular play will win out over time you don’t have the luxury of averaging out to win in the long run. Pot Odds are just a tool to use, there are lots of variables that can interfere with these calculations. You need to have a good read on your opponent’s hand. If you think they are on a open ended straight draw but actually they are sitting on 3 of a kind your calculations are meaningless.

Just something to ponder, pot odds can go much deeper and can really enhance your game. After awhile it becomes second nature to count your outs and roughly estimate your odds before betting. Measure twice, cut once, is it any wonder our carpenter Kevin is one of the best at using this tool at our table? 

 

See you tonight,