Casino War, Tossing Coins, & Expectation

If you're going to gamble at a casino, online or land-based, it's important to know how the casino makes its money from you. Casinos make money from the players because they don't pay out at the real odds for the game. Expectation is what you can expect to win or lose long term on a given bet if you make it over and over again.

If you flip a coin, you have a 50% chance of it landing on heads, and you have a 50% chance of it landing on tails. If you paid someone $1 every time you were wrong, and they paid you a dollar every time you were right, you'd be making an even money bet (also known as an even odds proposition). Your long term expectation would be 0. You would break even.

The way a casino would pay out in this situation would vary from the actual odds of the game so that they could make a profit. They might pay you 95 cents every time you were right, and you would pay them $1 every time you were wrong. This would create a positive expectation for the casino, and a negative expectation for you. Half the time you would lose $1, and the other half of the time you would win 95 cents. Instead of breaking even, you would lose 2.5 cents per bet over time. (Because half the time you would win.) If you stated this in percentage terms, the house would be said to have a 2.5% advantage in this game.

This might sound like an oversimplification, but it's really not at all. One of the newer casino games in Las Vegas is casino war, which is a gambling version of the card game War that you used to play as a kid. You and the dealer each get dealt a playing card. If your card's value is higher than the dealer's, you win, and vice-versa, just like when you were playing as a kid.

Here's where the casino changes the expectation in their favor though: If your card is the SAME as the dealer's card, you can either surrender (in which case you lose half your bet), or you can go to war, which means you have to make another bet the same size as your original bet. When you go to war, three cards are burned and you each get another card. If you win the "war", you ONLY get paid out on the original bet. If you lose, the house gets both bets.

So you're facing even odds unless you go to war. If you go to war, the house has an advantage, because if you win, you only get paid $1 for every $2 you've wagered. The casino could just as easily create a game called "casino coin toss war", with very similar rules, and it wouldn't be too different from the coin-tossing game I described earlier. The single difference would be that the casino would have an almost 3% edge over you.

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