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The maths behind the cards!

If you have a firm understanding of probabilities, itís likely you know that youíll have better odds in the casino if you play one of the card-based games. While you can have plenty of fun playing slots or roulette, the odds are much more in your favour when playing Betfair casino card games. But do you know how to work out the odds for yourself?

Weíve got this handy guide, courtesy of Betfair, that helps you to calculate your own probabilities and maximise your chances of winning.

Step 1: Odds and probability explained

Starting from the beginning, itís important that you understand how to calculate odds and probabilities and choose a method of expression thatís easiest for you. Itís a common mistake that odds can be mistaken as fractions, as explained above.

If you want to express odds as a fraction, the simplest method is to add the odds together and then place the number that represents the chance of the event occurring on the top. In our example above, you add 3 and 1 to get 4 which leads to a fraction of ľ.

To convert that into a percentage is the standard calculation, you multiple the result by 100. In our example again, we divide 4/100 and get 0.25. If we multiply by 100 we get 25%.

It may help you to make the calculation if you remember that casinos will tend to express odds in a similar method to a pay-out: 3:1 sees you win 3 in addition to your pay-out so if you bet 1 and win, your total at the end is 4. Any translation of odds into a different form needs to factor this in.

Step 2: Odds with cards

As there are 52 cards in a deck, any assessment of probabilities will need to work as a fraction of 52. As weíve illustrated here, the probability of getting a certain card is about 1.9% as you need a result that is 1/52. Likewise, the odds of getting of getting a card of a given suit is around 25% with 1 in 4 of the cards in the deck being of the suit you need.

The important thing to remember is that, as cards are dealt, the odds will alter and you need to subtract any known cards that have been played from your mental record. This is easiest explained with poker as we shall do below.

Step 3: How to calculate Ďoutsí

In simple terms, an Ďoutí is a card that will produce the strongest possible hand including the two you start with. For instance, if you hold two same-suited cards and there are two on the turn then you only need one more in order to have a flush. You may already have a pair but a flush is a far stronger hand and more likely to beat the opposition, meaning you need another card of the same suit.

You might assume the odds are 25% but, with 6 cards already out, you need to subtract the total out of the cards you know have been dealt. You know 6 cards have been dealt and 4 of them are the suit you need for a flush, so there are 9 left.

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

When calculating this, you only count the cards youíve seen, so the other playersí hands arenít taken into consideration (because you donít know what they have).

Step 4: Quick calculations

The rule of four and two is a helpful way of helping you quickly calculate your odds. Itís only approximate, but it can help you work them out in a hectic environment. If youíve only seen the flop, you multiply by 4 and if you see the turn you multiply by 2.

You might be wondering why the odds say itís 36% likely when we estimated 19% in the previous section. As you have two chances of the card being the one you need, the probability is doubled. This is why the next probability drops it to 18%.

While neither is the precise probability, itís close enough that it can be used at the poker table.

Step 5: Other games

The odds calculations for other casino games are a little harder as they rarely use a single deck. If youíre playing blackjack or baccarat, the dealer will be using several decks at once. The essentials of the poker odds is the same, you calculate within 52 Ė but with so many decks being used, working out true odds is something youíre unlikely to be successful at. If youíre playing casino games on mobile then youíll likely only have one deck to deal, powered by a Random Number Generator, and itíll be a bit easier to work out the odds if you want to make an informed choice.

But what do you think? Do you feel ready? Why not have a go and see if your mental maths is up to the task!

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