Blackjack Probability: What do you Need to Know to Have an Edge?

Blackjack Probability: What do you Need to Know to Have an Edge?

May 24, 2021

When a person walks out of a casino the question that inevitably arises in their mind is Why did I lose? Most people that play casino games are losing players. That is because most casino games by nature have a negative expectation for the player. This means that for every wagered that is made on the game; machine or table game, gives back some amount less than the wagered amount over time.

If 1 million players wager 1 dollar and, one player wins 500K than the casino makes a profit of 500K and an average loss of 50 cents per wager is perceived. In slot machines the advertised pay back is often in the neighborhood of 97-99%. This is over the entire life of the machine where a machine may collect 100s of millions of dollars in action over its lifetime. Table games are slightly different because some include a skill component and the % advantage the casino has varies from player to player. But the same general principle applies. 

This article is an in depth analysis of the mathematics of casino gaming. The information presented here is valid for live blackjack play as well as online play. However; the Blackjack software programs that online casinos use include all of the cards in every new round of play. The analysis will apply to the game of Blackjack. Blackjack is a game of dynamic probabilities and shifting percentages. But even though the percents are constantly changing, the cumulative percentage of the overall advantage remains constant.

This is achieved by taking the sum of the advantages over all possibilities. For example, if one hand total has an advantage of positive 5% and another hand has a advantage of -6%, than the total advantage for the two hands is 1%. When the reader understands this game it will be easy to translate the concepts to any other casino game with a static advantage over the player.

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