The Puzzle of Poker Odds Explained mathematical

top feature image

The Puzzle of Poker Odds Explained mathematical

The Puzzle of Poker Odds Explained mathematical, Without any shadow of a doubt, the mathematical part of the game and knowing the poker hand odds in various situations is one of the key skills that a poker player needs to acquire. Poker odds are inbuilt into everything that you do around the poker table from the probabilities of being dealt certain types of hands to the likelihood that your opponent is betting with a made hand as opposed to a piece of garbage and is bluffing or semi-bluffing

The good news is that you can learn the basic poker odds that are pertinent to your game in a very small amount of time. Although it has to be said that in many cases it isn’t quite as straight forward as learning some numbers. Holdem odds for example can be affected by your outs being tarnished by not being able to make the best hand even if you make the hand that you are trying to make, let me explain.

You are involved in a pot with the As-7s on a board of 10d-9c-8h, in this situation then you theoretically have an eight out straight draw as the four remaining sixes and the four remaining jacks give you a straight. The problem with this hand is that you may not have the best hand even if you make it and if a jack arrives then anyone with a queen will make a higher straight and someone with another seven would be splitting the pot with you.

So calculating holdem odds can get very complex in situations where you are not even sure if you can make the best hand or not. Thankfully for novice players however there is a very well known and easy to learn formula for players trying to find out what their chances are of making a specific hand on the turn and river and this process makes calculating poker hand odds relatively easy.

The process that I am about to show you will provide you with a very close approximation for calculating poker hand odds that will get you to within a couple of percent either way which is easily close enough in the heat of battle. Firstly let us look at how to calculate the odds of you making a specific hand on the next card.

If your opponent bets and your hand is a straight draw then you have eight outs to make the best hand. This assumes that you improving to a straight will make you the best hand in the first place and that your opponent isn’t drawing to a higher straight. In this instance then you simply multiply your number of outs which in this case is eight by two and this gives you the percentage probability of making your hand on the next card.

So eight multiplied by two is sixteen so you have a sixteen percent probability of making the straight on the next card. This also means that 84% of the time that we will not complete our straight on the next card and 84 divided by 16 gives us our actual poker hand odds of 5.25-1.

Now I did say that this was a close approximation because these are not the actual true odds. It is actually a 17.2% chance of hitting your straight on the next card and not 16% and 17.2% when converted to odds is 4.8-1 and not 5.25-1. But you can see that when you are quickly trying to calculate the pot size and whether or not you are getting the proper odds to continue on with the hand then this is a good short cut that will get you pretty close.

So you will quickly begin to see that poker odds and the calculation of them does not require you to have advanced qualifications in mathematics. Your next question may be to ask how to look at this same problem if you are faced with an all-in situation on the flop and there are two cards to come and not one. This is also simple because the short cut process merely states that you multiply your outs by four and not two in order to get your percentage probability.
So in this instance your number of outs is still eight but eight multiplied by four gives us a 32% chance of completing our straight by the river when we have two cards to come. This means that we will not make the straight 68% of the time and 68 divided by 32 equals 2.12 so our poker odds are 2.12-1 of making the straight with two cards to come. This is very close to the actual odds of 2.2-1 so you can see the effectiveness of this method when calculating poker odds.

There is one slight difference that needs to be factored in when your number of outs get bigger. If for instance you have a fifteen out hand like a straight draw with a flush draw then you need to make one tiny adjustment. If your outs are more than eight then you need to deduct one percent for every out above eight.

For example with two cards to come then we simply multiply our outs by four as before and fifteen multiplied by four is sixty or in this case 60%. But we then deduct 1% for every out above eight which in this case is seven so we deduct 7% from that total which gives us 53%. This necessary process is important because our poker odds calculation would be more adrift the more outs we have so we need to do this to achieve the same level of relative accuracy.

When we now look at what the actual odds are of making a fifteen out hand with two cards to come then you will see what I mean. You have a 54.1% chance of making that hand which is some way out from our short cut method which arrived at 60%. But the adjustment now drags us back into line and we are little more than 1% away from what the actual true probability really is. So poker odds and the calculation of them and the respective percentages of making certain hands should no longer be the complex problem that you think it is.

This article was written by a professional online poker player, poker theorist and writer for eight years. Prior to that he was a blackjack player and has written three books on poker and casino games. He is a regular writer for Poker Strategy, if you found this useful then have a look at his other articles.

Leave a Reply

Your email address will not be published. Required fields are marked *