Understanding Poker Odds and Probabilities

The Maths Behind the Cards

If youíre interested in learning how to play some of the card games from Betfair, youíll need to get your head around the different odds and probabilities involved. Card games are a little different from the other table games, because thereís more of a focus on player decisions, and knowing how to make the right call requires a decent understanding of probability and the odds involved. Thatís why we put together this handy visual guide to give you an introduction to the maths involved.

Step 1: Understanding Odds and Probabilities

The Maths Behind the Cards

First things first, if weíre talking about odds then we need to decide how weíre going to represent them. Itís common to show probability in a gambling context as odds, i.e. as 3:1, but this can be confusing for some people as there can be a tendency to mistake it for a fraction. If something is shown as 3:1 it means the probability of it happening is 25% not 33%. The fractional representation is done by adding the numbers together with the Ďwiní choice on top, so 3:1 becomes 1/4. Or 25%.

For ease of understanding, weíve elected to use percentages throughout this guide to make sure that itís easy to understand.

Step 2: Understanding Card Probabilities

The Maths Behind the Cards

As a deck of cards contains 52 individual cards, any calculation of probability is worked out by dividing the number of cards youíre curious about by 52 and multiplying the answer by 100.

For example, you divide 1 by 52 and multiply by 100 for a card of a set value and suit Ė which equals about 1.9%, i.e. thatís the probability of being dealt that exact card.

If youíre after a certain value (a 7 for instance) then there are 4 in the deck and 13 possible values, so itís 4/52 which can be reduced to 1/13, and this means that the probability is 7.7%.

For a card of a given suit, itís 13/52 or 1/4, so itís a 25% chance.

The important thing to remember is that, as cards are dealt, the odds will alter and, if you want to employ technique this in a game, youíll need to adjust accordingly which is easiest explained with a single deck game like poker.

Step 3: Understanding Poker Outs

Calculating Outs

A poker Ďoutí is the card you need in order to have the strongest possible hand from what you started with. So, if you hold two spades, and there are two more on the turn, then you only need one more to come out in order to have a flush.

Even if you already have a strong hand such as a pair of aces, a flush would beat it and your opponent might have three of a kind so, realistically, youíd want the flush.

You might assume that the odds of getting the card you need are 25%, but with 6 cards already out and 4 of them being spades, you need to factor that in. You know that 6 cards have been dealt, so there are 46 remaining and 4 of them are spades so there are 9 spades left in the pack.

9/46 gives you the percentage chance you have of receiving the card you need, which is around 19%.

When it comes to calculating this, you should only count the cards youíve seen so whatever the other players have isnít included in the calculation. This is because you canít know what they have and it doesnít help you to guess when trying to consider the out.

Step 4: Quick Calculations

Outs to Odds

The rule of four and two is something like mathematical shorthand for calculating the odds of an out. Itís only an approximation but it tends to come pretty close to what the actual figures are in most cases. Basically, when youíve only seen the flop, you multiply the out by 4 and if youíve just seen the turn you multiply by 2.

Looking at the results you get, you might be curious as to why our previous estimate of 19% has been replaced by 36% for the turn and 18% for the river. As you have two chances of the card you draw being the one you need, the probability is doubled for the first draw, but with just one card left to come out, it then reverts to 18% for the next.

Neither is EXACTLY right but itís close enough that you can make some choices based on it.

Step 5: Other Games

Other Card Games

Thatís great for poker, but what about other casino games? Well, the majority of games in the casino use multiple decks to make calculating odds even harder. Blackjack and baccarat are prime examples, for blackjack itís a case of the casino wanting to stop people from card counting, while baccarat is working to increase the randomness for a more luck-based experience. You can still use the rough calculation of X/52 to work out your odds but with multiple decks it could be a bit off.

Blackjack basic strategy, as you can see below, gives you the calculations for the best play you can make whilst working from those same figures. Itís still possible to apply the general rule of probabilities but youíll struggle to keep the outs clear as you go. If you want to use these techniques, online games that use random number generator software or single deck games such as poker are your best bet.

Blackjack Basic Strategy


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