There's a formula for computing a player's average winnings (or losses) over repeated play. It's called expected value. As the expected value of a bet rises, the price of the bet falls.
At the roulette wheel, player's expected value of a $1 bet is 94.7 cents. That's $1 minus the 5.3 percent advantage to the house.
In the 1650's, the French con man Antoine Gomband--known as the Chevalier de Mere--offered even money odds that, in four rolls, a die would turn up at least one 6. The Chevalier reasoned--wrongly--that since the chances of a die turning up a 6 are 1 in 6, the chances of it turning up in four tries would be 4 in 6...or 2 in 3. Still, he made money with the game.
When interest in the game died down, the Chevalier modified it. He figured--again wrongly--that since the odds of throwing two 6's at the same time on two dice are 1 in 36, in 24 rolls the odds would be 24 in 36...or, again, 2 in 3.
He started losing money on the new game, so he contacted an acquaintance--the mathematician and philosopher Blaise Pascal--for help.
Pascal told the Chevalier that his first game offered him an advantage--what contemporary risk experts would call the house's edge--of 4 percent.
His second game offered his players an edge of 2 percent or an expected value of 1.02 francs per franc wagered. Put another way, players would win 51 times out of a hundred. Over time, the Chevalier was bound to lose money.
In modern times, this is known as "the gambler's ruin"--the fact that in a game with a negative expected value, a player will eventually lose his or her money over time.
In calculating an expected value, the ratio to remember is the number of favorable outcomes to the number of possible outcomes.
The payoff on a bet on red or black in roulette is 1 to 1. If your bet $1 on red and win, the casino will give you back your $1 and another $1 of its own. The payoff on betting a single number in roulette is 35 to 1. If you bet $1 on number 23 and it wins, the casino will give you back your $1 and $35 of its own.
If your bet $1 on red repeatedly, you'll win an average of 18 out of 38 bets. Since there are 18 red sections on a 38 section roulette wheel, the law of large numbers are that red will come up 18 times and not come up 20 times out of every 38 spins.
That will leave you with a net $2 loss. This means an average loss of $2 per 38 plays or 5.3 percent.
If you bet $1 on number 23 repeatedly, you'll win an average 1 out of 38 bets and you'll win $35 when you do. This leaves you with the same $2 net loss. And the casino keeps the same 5.3 percent edge.
In fact, all bets in roulette give a 5.3 percent edge to the house.