Using the Power of Mathematics to Understand Top Card Game Odds

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29 Nov 17
The odds of drawing a single card from a deck are only 1.9%

The odds of drawing a single card from a deck are only 1.9%

‘Probability’ is the chance that a certain outcome will happen. For example, if you flip a coin, there is a 50% chance it will land on heads and a 50% chance that it will land on tails. All card games involve a degree of probability. Using the power of mathematics, you can understand more about these games, how to play them, and which ones allow you to play odds that are more in your favour.

Luck or skill?

Games such as ‘War’ are pure chance. You and the other player are dealt half of the deck and take turns to expose cards. The highest value card wins. In this case, your chance of winning is the same as a coin flip. There is a 50% chance that you will be dealt a more favourable hand than your opponent and there’s nothing you can do to make these odds better for yourself.

Other games, such as poker and blackjack, have elements of skill or decision-making, which mean the odds can be directly influenced by your actions. Yet many card games have elements of strategy, which make them more challenging and enjoyable. It still helps to get the best hand on that day, but talented players can win more often than new players because they know the game and some of the maths behind it.

Enhance Your Odds in Blackjack

Casino games like blackjack rely on the house taking a small edge over players. The dealer wins a little more than the player because they are in position and can decide when to draw based on whether players have already gone bust.

But there’s a big difference in odds between good play and bad play. If your current hand adds up to 12, for example, you only have a 31% chance of going bust if you draw another card. If your hand adds up to 16, then you bust 62% of the time; anything above that and the odds goes up again. There’s a bit more to it than that, though, as you need to know the dealer’s hand to make the right call, but hitting the right cards will give you much better odds.

Why You Never Get That Ace

There are many card games that rely on drawing the right card. There may be elements of skill, such as what you do with the cards when you get them, but you still need to land the right hand in the first place. You might be playing ‘Chase the Ace’ or another power card game, and you never seem to get the special card that could win you the game.

The reason for this is that the odds of drawing a single card, say the ace of hearts, is only 1/52, which is a little over 1.9%. Even if you need an ace (or any King, or whatever you need to make your hand), your odds of drawing a specific card of any suit are only 4/52, which is around 7.69%. You don’t get that Ace often because simple maths says that you shouldn’t get it often.

When working out the odds of getting certain cards, make sure you account for the size of the deck. For example, the card game Taki, a more complex version of Uno, uses two identical sets of 56 cards for a total of 112 cards.

Solitaire appears in many different variations and UX designs. Source: Wikimedia

Solitaire appears in many different variations and UX designs. Source: Wikimedia

Stop Paying for Your Flush Draw

If the chances of drawing a single ace, or even an ace from the pack are so slim, then why do so many poker players pay so much to try to hit their draws? Probably because they don’t understand the maths. Say you are dealt 5-6 suited before the flop in Texas Hold ‘Em. At that point in the hand, you only have a 1.29% chance of hitting a straight and a 0.82% chance of hitting a flush. That means you make your hand a little over 2% of the time.

It gets a little more complicated when it comes to poker due to the influence you have on the hand. In the example above, you could also consider betting when you hit a 5 or a 6, or betting when you make four out of the five cards needed for a straight or a flush. The odds of making the flush may be low overall, but there could be other opportunities to play the hand in creative ways.

Why Solitaire Isn’t Always Beatable

With there being a slim chance of drawing any single card from a deck, games like solitaire become very difficult despite their relatively simple concept. It seems like you should just be able to find the right cards and add them to the right stacks, but the game is frustratingly difficult.

This is because it isn’t always technically beatable. Even if you knew where all the cards were located, you still wouldn’t always be able to win. Only between 82-91.5% of games dealt are beatable, and with incomplete information (i.e., not knowing where the cards are located), the actual chances are much slimmer. So, don’t stress too much when you can’t beat solitaire!