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The Importance of Probability in Table Games

20240710_122004

One of the most famous probability puzzles involved a goat and you won’t believe the outrage it caused

All table games have an element of luck and chance involved, but table games are particularly interesting when it comes to probability. After all, most table games require a bit of skill on your part too – whether it’s chess you want to play or blackjack, a bit of the task usually revolves around calculating probabilities. We’re going to take a look at a game-show that illustrates our misconceptions around probability particularly well, as well as one table game in particular that requires a keen understanding of this mathematical concept.

Let’s Make a Deal

It makes sense to start off with what’s actually a very simple problem, but one that many people couldn’t grasp. It most famously appeared on the Let’s Make a Deal game show, which was hosted by Monty Hall in the 1960s. In the game, contestants were asked to choose one door. Behind two doors were goats and behind the other was a car. The contestant would pick a door (no.1) and Monty Hall would open another door (no.3); he’d say there’s a goat behind it. Then he would ask the contestant if they’d like to switch which door they’d picked. The question was, would it be advantageous for that contestant to switch doors?

Many people believe that the chances of the car being behind the contestant’s door are the same as they always were, but actually, they aren’t. In this instance, it would always be beneficial (in terms of probability) to switch to the other door. This is because, when the contestant picked that door, they knew that two doors had goats and one had a car, giving them a ⅓ chance of picking the door with the car. Now, the contestant knows that door no.3 has a goat behind it. This means that switching to the other door has a ⅔ probability of winning the car, as opposed to the initial ⅓ chance.

After this solution was published by a renowned mathematician called Savant in a national newspaper, there was a uproar! People with PHDs (10,000 of them) wrote into the newspaper explaining Savant was wrong, but the maths is sound. This is a particularly useful puzzle because it shows just how difficult it can be to accept sound math in the face of our own thoughts.

 

Roulette

The Importance of Probability in Table Games
This American roulette wheel has a higher house edge than its European counterpart

Now that you understand probability and how tricky it can be, it’s time for a refreshingly easy look at the probability in a popular table game: roulette. The way that you calculate probability depends on the type of roulette that you’re playing – and there are lots to choose from at wildz.com there are options like Lightning Roulette, Immersive Roulette and plenty more, but we’re going to focus on the difference between American and European roulette.

Let’s imagine that you’re going to place a bet on the ball landing on the number 7. On a European roulette wheel there are 37 slots including a single zero slot. On an American roulette wheel there are 38 slots including a single zero, and a double zero slot. As it stands, your chances of scoring that 7 on the European wheel are 1/37 and on the American wheel, 1/38, so slightly smaller.

However, you now need to consider what those zero slots are for. If the ball lands on the zero then no bets pay out, so, in American roulette, there’s more chance of this happening. This means that whatever your bet, there’s now a 2/38 chance that the ball lands in a non-paying slot, rather than a 1/37 chance with European roulette. This gives the American roulette wheel a greater house edge than the European one, regardless of the type of bet you place.

 

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