Calculating odds not always simple
john grochowski firstname.lastname@example.org May 16, 2012 4:42PM
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Updated: June 29, 2012 8:33AM
There’s a coincidence of arithmetic about double-zero roulette that once led a reader to a minor confusion about the house edge.
If you’re making the wagers with even-money payoffs, including red/black, odd/even and first 18/last 18, the house wins 52.63 percent of the time. If you bet on red, you have 18 winning numbers, but there are 20 losers — the 18 black numbers plus 0 and 00.
The house edge on those bets is 5.26 percent, and the reader wondered if 10 times the house edge was the magic formula. Does a 5.26 percent house edge mean the house wins 52.6 percent of all spins? Can you apply that to any game with even-money payoffs?
It doesn’t work that way. After all, in craps the pass-line wager has a 1.41 percent house edge, and the bet on player in baccarat has a 1.36 percent house edge if ties are disregarded. Both pay even money to winners, but multiplying the house edge by 10 will leave you far short of the percentage of house wins.
In both cases, the house wins more than 50 percent of the time, coming at 50.705 percent on the pass line and 50.682 percent on player.
What you really want to know is the difference between frequency of house wins and bettor wins. On the pass line in craps, that house win rate of 50.705 percent means players win 49.295 percent of the time. Do the subtraction, and you get a difference of 1.41 percent. That’s the house edge.
That works for any one-part bet with an even-money payoff. You can go about it the opposite way, too, if you know the house edge and want to know how often you can expect to win. If you know the pass line’s house edge is 1.41 percent, you can divide that in two to get 0.705. Add that to 50 percent, and you know the house wins 50.705 percent of the time.
This only works for wagers with even-money payoffs. You can’t apply it to blackjack, where two-card 21s pay 3-2 or, on tables with high house edges, 6-5. It doesn’t work on bets that pay at higher odds such as place bets at craps or single numbers at roulette. There, the calculations become more complex.
But within the limits of even-money payoffs, calculating the average percentage of wins is as easy as dividing the house edge in half, and adding to 50 percent.
John Grochowski is a local free-lance writer. Look for him on Facebook (http://tinyurl.com/7lzdt44); Twitter (@GrochowskiJ) and at casinoanswerman.com.