The trick to inventing a casino game is to come up with something that looks like a fair bet but isn’t. If you’re too obvious about putting the odds in favor of the casino, no one will want to play.
Let’s use a bet on a coin toss as an example.
Suppose you run a casino, and you offer to pay 25 cents to anyone who correctly guesses the correct result on a coin toss. Here’s how you get your edge—you make the player put up 50 cents in order to win that quarter.
The casino has an obvious large edge in that situation, even if you don’t know how to do the math. But we do know how to do the math, so let’s look at it:
You have a 50% chance of winning 25 cents.
You also have a 50% chance of losing 50 cents.
50% of 25 cents = 12.5 cents
50% of -50 cents = -25 cents
Your expected value is -12.5 cents. Your expected loss on every bet is 12.5 cents. Since you’re betting 50 cents on every bet, the house has an edge of 25%.
But let’s see if we can make the game a little more interesting.
Let’s say you have to bet a dollar, minimum.
This time, you toss a coin and so does the casino. If one of you gets heads and the other one gets tails, the party with heads is the winner. The party with tails is the loser.
And let’s say this game offers an even money payout.
Looks like a break even game, doesn’t it?
It is, but what do we do in the event of a tie?
What if you both get heads?
What if you both get tails?
If you want to give the casino an edge, you just add a rule that if you both get heads, the game is a push. Your bet is returned, but you don’t win anything.
But if you both get tails, the casino still wins.
Let’s look at the probabilities involved:
You have the following potential outcomes, all of which are equally likely:
- You both get heads.
- You both get tails.
- You get heads, and the house gets tails.
- The house gets heads, and you get tails.
So you have a 25% chance of a push, which has a net effect of 0. (You don’t win anything, but you don’t lose anything, either.)
You have a 25% chance of winning a dollar, which is an expected value of 25 cents.
You have a 25% chance of losing a dollar, which is an expected value of -25 cents.
And you have a 25% chance of losing a dollar, which is an expected value of -25 cents.
The house still has a 25% edge, but it isn’t nearly as obvious now, is it?
The house could make the game even more fair by returning half your bet in the case of both of you getting tails. That would reduce the house edge to 12.5%, which is better but not great.
Another option would be to take any tie result and have 2 options:
- You could put up another dollar in order to get another coin toss.
- You could just surrender your bet.
The catch is if you put up the other dollar and win, you only get $1 in winnings. But if the casino wins, you lose both dollars.
And in fact, this is almost exactly how casino war works.
That’s just a simplified version of how to create a new casino game. You could have multiple bets, multiple payouts, and multiple probabilities for each outcome. You just have to look at the expected value of all of them to determine how much of an edge the house.
Then you have to test the game in front of a live gambling audience to see how they respond. If the gamblers don’t like the game and refuse to play, you don’t have a potential casino game at all.
The house wins nothing if no one likes the game.