Probabilities Lesson for the Nonmathematical Player

Understanding probabilities can seem like a complex idea, which I believe keeps lots of good poker players from truly incorporating them into their games. For example, some writers recommend assigning a probability percentage to whether your opponent is bluffing, or the likelihood that a player has a flush when four of a suit are on board.

When I first began really working hard at playing profitable poker, the idea of being able to assign percentages that could then translate to accurate decisions in situations such as the above was foreign to me and seemed nearly impossible. And that was in the quiet of a Las Vegas library, where I used to study the reference copy of Super/System, not in the heat of battle at a poker table, where I had all of about 20 seconds to determine my action. In other words, probabilities initially played virtually no part in my game.

As is common on the path to mastery, determination over time and persistence have a rather gentle way of opening one up to such a point that what was once a mystery now becomes understandable and usable. In this column, I will present a less technical and more intuitive approach to using probabilies.

Think About Everyday Situations

What is the chance that you will lose your keys within the next month? Or, what about misplacing your keys (as in, you are likely to find them within a half-hour of misplacing them)? For most of us, the chance of the latter is significantly higher. Roughly, I estimate the chance of losing my keys within the next month to be 3 percent, and of misplacing them, 15 percent; and those estimates would feel close enough.

I came up with these answers based primarily on past experience, with an awareness of what the future looks like for me. Since I have rarely lost my keys and usually leave them in the same spot at home, I see these figures as being low and not likely to vary much. But let's look at a new example, adding another person to the mix. What is the likelihood that someone to whom you are attracted will also find you attractive? Obviously, this is harder to figure, because it's no longer just about you, but about the other person, his/her past experiences, the situation, and factors we may never know about or understand. Still, I think most of us can get a sense for how the other person feels about us and if there is some attraction developing.

At the poker table, we often hope for certain outcomes, which affects us emotionally. Also, we have the ability to more objectively intuit a situation based on our observations. Assigning a probability figure that may then translate to the best decision in the hand is best achieved without emotional interference. Recognizing that being attached to a certain outcome (winning the pot or just wanting to beat a specific player) often gets in the way of using probabilities effectively is the first step toward greater mastery.

A Poker Example

Preflop action: You hold the Q Q on the button. A middle-position player raises. Everyone folds to you, and you three-bet. The small blind calls. The middle-position player just calls. Three players are in and the pot contains nine bets.

Your thoughts before the flop is dealt: The raiser is a good, tricky player who is capable of raising with marginal (but better than average) hands. He may have aces or kings, and be setting a trap. The small blind is likely incorrect in calling both raises, and probably holds a strong ace or medium pair.

Your probability thoughts: There is an 85 percent chance that my queens are the best hand right now. Note: This figure is based on feeling only, and was not calculated according to any mathematical process.

Flop: J 10 7

Action: It's checked to you, you bet, the small blind calls, and the middle-position player check-raises.

Your thoughts: The check-raiser is saying he has an overpair, has paired his jack, has made two pair (holding J-10), holds an ace-high diamond draw, has flopped a straight and flush draw (for example, K 9), or has flopped a set. The small blind's hand is still largely undefined.

Your probability thoughts: It feels like about 65 percent that my queens beat the check-raiser, and 95 percent that they beat the small blind. Again, these figures are deduced from the feel of the situation at the moment.

Action: You reraise, with the intention of shutting out the small blind, but he calls both bets cold. The check-raiser just calls. The pot contains 18 bets.

Turn: Q – a mixed blessing if you ever saw one!

Action: The small blind now fires and the middle-position player raises.

Your thoughts: Why do I bother playing this game?! At least one of them holds A-K, and since it's the stone-cold nuts, if it's the small blind, he will likely three-bet. The pot contains 24 bets. I have to call four bets to win at least 28, and very likely two more with the small blind's call. My pot odds are 7-to-1, with a draw to a full house or quads being about 4.6-to-1.

Action: You call, the small blind reraises, the middle-position player calls, and you call. The pot contains 36 bets.

Your probability thoughts: There's a 2 percent chance my queens are good, maybe less!

River: 6

Action: The small blind bets, and the other player calls.

Thoughts of a losing player: I have three queens; I have to call.

Thoughts of an aspiring player: The pot is too big to muck. I need to call two bets to win 42. That's 21-to-1. He might be bluffing.

Your thoughts: The only possible hand the small blind can hold to three-bet the turn is A-K. He can't have pocket queens, and is the type of player who wouldn't reraise with a set, fearing one of his opponents holds A-K.

Your probability thoughts: My queens are garbage. It's less than a 1 percent chance they're good.

Action: Muck. Then, step away from the table and get some fresh air before you steam off all of your chips.

Conclusions

Go through your regular day in the world and ask yourself, what are the chances … ? What are the chances the bus will come within the next 10 minutes? What are the chances my wife or husband will call me before noon? What are the chances that the clerk will give me back too much change? Everything has a probability, and these probabilities can be easily guesstimated. Realize that being able to assign a percentage for a particular likelihood at the poker table is not that difficult. Relax into it. Try it. Incorporate it as second nature. There's a 95 percent chance it will improve your bottom line, and maybe higher.