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Probability and Gambling

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We hope you enjoyed our previous article about how the “idea of luck” is leveraged by the gambling industry to attract more players.

Today we want to cover something much more real and practical, which has a great significance in gambling: probability.

“Yes, probably!”  This is a familiar statement that is quite common in real life conversations. For example, if there is a probability that it will rain tomorrow, no one can be 100% certain whether it will actually happen or not.

So, what does probability stand for? In short, probability is a term used in mathematics to describe the likelihood of a certain event happening.

This judgment comes in handy when we are faced with situations that require to make decisions of uncertain outcomes. When we are dealing with mutually exclusive events, the sum of the probabilities for all possible outcomes is 100%.

Let’s say the probability of raining tomorrow is 20%, then the probability of a dry day will be 80% and the sum of both outcomes is 100%. Giving this knowledge, when going out tomorrow you will then decide whether to take an umbrella with you or not: if you decide to bring the umbrella, you know there will be a 80% chance that you will be carrying it for nothing; on the other hand, if you decide not to bring the umbrella, you know that there is a 20% chance you’ll be getting back home soaking wet.

The same formulas are used in gambling when operators decides the payouts for each possible betting outcome.

However, when gambling things work a bit differently, because there is another element to take into consideration: the HOUSE EDGE. The house hedge is the mathematical advantage that the casino has over you as you play over time. This advantage results in an assured percentage return for the operator (and for you an assured loss) of what you bet.

Basically, if you consider your bets, the sum of all possible outcomes is lower than the total amount you wagered.

This is brilliantly put into practice in the game of Roulette. Say you have $5 and you decide to bet $5 on black and $5 on red. The casino payout for these bets is double your wagered sum. But the probability of hitting either black or red is not 100% (50% + 50%), because there is also the possibility that the ball will stop on the 0 (in French Roulette) or even on the 00 (in American Roulette). That makes your overall chances of hitting either black or red at 97.3% (French Roulette) and at 94.7% (American Roulette).

Unfair? Yes. Well, this is essentially how gambling operators make money in the long-term. Consider it as a fee for their services.

How much the casinos keep as ‘House Edge’ varies from game to game; some have it higher, some lower. Licensed operators are obligated to provide such information, to have it available for their customers. However, sometimes it’s difficult to find it.

Here’s a brief guide of typical payouts (often referred to as RTP – return to players) for some of the most popular casino games:

  • Classical Blackjack: 99.4%
  • European Roulette: 97.3%
  • American Roulette: 94.7%
  • Slot Machines: anywhere from 91% to 99%
  • Craps: 98.6%
  • Baccarat: 97.3%

To calculate the house edge, you can simply do 100% – RTP. For example, in American Roulette, the house edge is 100 – 94.7 = 5.3%. Which means that for every $100 you wager, the casino (on average) keeps more than $5.

Poker and sports betting are also subject to house edge.

In poker tournaments, operators usually take a fixed fee every time you join a table: consider a Texas Hold’em game that has $10 game joining fee, if $9 go to the prize-pool and $1 goes to the casino, then the house edge is 10%.

In sports betting, like in casino games, operators simply apply a lower payout than the probability of a given outcome: consider a penalty shootout where either Team A or Team B will prevail, with pretty balanced probabilities (let’s say 50-50). If betting $10 on Team A would return $19, and betting $10 on Team B would return $18, then the bookmaker’s house edge is 7.5% (I will spare you the math).

What is important to specify at this point is that these RTPs are calculated based on the best strategy a player can use. If the gameplay is not perfect in every move, if the player doesn’t know the game, gambles while intoxicated, or bets based purely on instinct, the profits the casinos can make are much greater.

Also important to specify is that these probabilities and RTPs are calculated over the long run. Single bets are subject to greater volatility (or as some like to believe, luck). The more a player wagers, the more these predictions become accurate. The more a player gambles, the more they are guaranteed to lose against the casino.