The Maths Behind the Playing Cards!

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Jeffrey | Poker Strategy

When you’re trying to decide which Betfair casino table game you’re going to play many people will naturally gravitate towards the card games. Whether you know it or not, card games tend to have much better odds than other table games and allow for more player involvement in decision making.

If you’re not well versed in statistics, working out the maths might seem like a challenging proposition – that’s why we’ve put together this handy guide to help you make the smartest play you can.

Step 1: Understanding odds and probabilities

Before we begin to talk about the odds, it’s important that we make sure you know how to express odds in a way that makes sense. It’s a common mistake, when people see odds written as 3:1 to believe that this means they have a 33% of winning but in truth, they should expect to win only 25% of the time. Odds expressed as 3:1 mean that you’ll lose 3 times for every 1 win, the total number of events is every number in the odds added up (so in this example that gives us 4) and the single victory is then 1 in 4 or 25%.

If you want to express odds as a percentage, you can do so by working the odds into a fraction, i.e. dividing the top number by the bottom number and multiplying by 100. In the example, you see
¼ = 0.25 = 25%.

We’re going to be working with percentages as an easily understood way of expressing probability, but feel free to express the maths in whichever way is easiest for you.

Step 2: Understanding card probabilities

As there are 52 cards in a deck, any calculation will be working from that basis as the starting point. As we’ve illustrated here, the probability of getting a certain card is about 1.9% as the fraction odds of getting exactly what you need are 1/52. This holds true for a specific number too, there are 4 in the deck and 13 numbers so it’s 4/52 or 1/13 which is 7.7%. And for getting a card of a given suit, the odds are 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 from your calculation any known cards that have been played. This is easiest explained by using poker as the demonstrator.

Step 3: Understanding poker outs

In poker, an out is the card you’re looking for in order to complete a hand. For instance, if you hold two spades 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 since a flush is significantly better, you’d hope for that, so what you really want is another spade to be drawn.

You might assume the odds are still 25% like they were at the start but with 6 cards already out, you need to subtract the number of cards dealt (6) from the total at the beginning (52). You know 6 cards total have been dealt, and 4 of them are the suit you need, so there are 9 left.

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

Incidentally, you don’t count the other players’ cards because you can’t know what they have and it’ll just throw off your figures to make a guess.

Step 4: Quick calculations

The rule of four and two is a helpful way to approximate odds whilst at the table. You won’t get the exact probability but you get a close guess in most cases and can really help in poker. How it works is: if you’ve only seen the flop, you multiply the out by 4 and if you’ve just seen the turn you multiply by 2.

You might be wondering why the odds say it’s 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 for the first draw but with just one card left to come out, it’s dropped back to 18% for the next.

While neither is the precise probability, it’s close enough to give you a chance.

Step 5: Other games

As good as this is for explaining poker odds, what about the odds for other card based casino games? Well, these games have been designed with the intention of not being easy to predict. Blackjack previously used a single deck but, in order to prevent card counting, most casinos now use multiple decks. The core calculation of X/52 is still valid but it could well get thrown off by an unlucky shuffle that happened before you sat down, and baccarat always uses multiple decks. Luckily, the odds for blackjack have been largely condensed into basic strategy as seen below so optimal play is still within your reach!

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