Gambling Probability - Let's Invent a Slot Game

Let’s say you’re betting on George Washington, but now the wager is $4, and we’re flipping dollar bills on a video screen, two bills simultaneously. You get $15 every time that GeorgeBasil Nestor is the author of the new Playboy Complete Guide to Casino Gambling. This wonderful book teaches players how to avoid sucker bets and win more when playing gambling games.  He is also the author of The Smarter Bet Guide series for video poker, slots, craps, and many other books about gambling.  Basil's website is www.smarterbet.com  appears on both bills. Yay! How often does that happen? About one in four flips.

Does that sound like a good bet?

Fifteen dollars is enticing, especially if George hits a streak, but the other bettor (the casino) has a 6.25 percent edge in this contest. Number-wonks like me figure it this way:

Wow! Compare this to the original contest. I increased the payout from $0.99 to $15, and I still managed to balloon the house edge from 0.5% to 6.25%.

But what if you win once when playing Daffy Dollars, lose once, and then win once more? It’s hardly a streak, but that particular combination would put you ahead by $27. Should the casino be worried? Nope. You or someone else will continue playing the game. Hot and cold streaks will come and go, but the casino will get about a 6.25 percent return on all the action (money wagered) as the number of trials stretches into the thousands and then millions.

Measuring the House Edge

The following table, “Good and Bad Casino Bets,” gives examples of the house edge on various popular contests.

Notice that most games are negative expectation for players. It’s possible to shift some contests from negative to positive by using an optimal strategy (essentially, using game theory), but doing that requires a bit of effort and patience.

Keep in mind that the typical advantage remains around one percent or less when it’s pushed to the player’s side. The house gets more when they have the edge, but most games still earn 10 percent or less. There is no money spigot in a casino. In fact, an often-used phrase from late-night television absolutely applies here; casinos earn money with volume, volume, volume! That’s also how optimal-strategy players do it.

But why would a casino offer games that don’t give the house a huge advantage. Why would they play any contests with an edge that could be shifted against them? The answer is somewhat complex and involves public relations and marketing considerations, but it boils down to this; most players don’t use optimal strategy. They either don’t know that a strategy exists, or they think it’s too much trouble to learn. Some people want to be “spontaneous.” They prefer to choose whatever game strikes their fancy. Others rely on hunches and superstitions. Whatever the reasons, the result is that typical players win less and lose more on average than optimal-strategy players. Casinos get the PR boost of offering “certified games that pay back 100%” or “the best blackjack in town.” But the games still earn money.

Incredible but true.

The table below shows the average expected loss of a regular player compared to that of an average optimal-strategy player.

Of course, anything can happen. The regular player might smack a big jackpot or catch a winning streak, but consider how much less luck is required for the optimal-strategy player to turn a profit. And it’s easy to see which player will last longer if the tables and machines turn cold. Bad luck, good luck, or no luck, the optimal-strategy player will always lose less or win more in the long run.