QUESTION: How close to a 50-50 bet is blackjack? By that I don’t mean a zero house edge, I mean how close do players come to winning 50 percent of the hands. How does that compare to other casino games?
ANSWER: Disregarding pushes, basic strategy players at blackjack win about 48 percent of hands. If there were no makeup rules, that would give the house a 4 percent edge. You get some of that back from the house paying 3-2 on blackjacks, and some more from being able to double down or split pairs. In a six-deck game, you can narrow the house edge to half a percent or so depending on other rules, including whether the dealer hits soft 17.
There are a number of bets in which you win a greater percentage of decisions. You win a just under 49.3 percent of the time on pass and come in craps, just under 49.4 percent of decisions on the banker bet in baccarat and you win just over 50.6 percent of decisions banker --- that’s why baccarat players have to pay the house a commission on winning banker bets.
In games where winning hands can pay several times your bet size, the wins come less frequently. You win just over 44.9 percent of decisions on the ante-play portion of Three Card Poker, and only 25.6 percent of hands in the Pair Plus portion. In double-zero roulette, you’ll win a little under 47.4 percent of bets if you make wagers with even-money payoffs such as red or black, but win only 2.63 percent of the time if you bet single numbers.
The frequency of wins is just one factor that goes into the house edge. Payoffs matter. Blackjack basic strategy players win less often than baccarat players, but the baccarat house edges of 1.24 percent on player and 1.06 percent on banker are higher than that half a percent edge against blackjack basic strategy players. Single-number bettors win far less often than red/black bettors in roulette, but the house edge is 5.26 percent either way.
QUESTION: Can I take you away from casino games for a minute to talk about the Russian asteroid? It’s a question of probability that seems like the kind of thing you do with the games.
It was said that the meteor that hit in Russia (in the Chelyabinsk region) on Feb. 15, 2013 was the largest to strike the Earth since one in 1908 that also hit Russia (in the Tunguska area of Siberia). What are the chances that the two largest meteors in a time period like that would hit the same country?
ANSWER: To answer that, I’m going to have to assume that where meteors strike is random, as if the meteor is a ball and the Earth is a giant roulette wheel. A meteor that hits the Earth --- becoming a meteorite --- has equal chances of striking any spot on the globe, just as the ball has equal chances of landing on any given number.
I’m also going to have to answer in two different ways. Russia has 3.347 percent of the Earth’s surface area, so the chance of any one meteor landing in Russia is 3.347 percent. If before any meteors land we ask, “What are the chances of the two largest meteors of the next 100 years both landing in Russia?” we need to multiply 0.0347 times 0.0347. That’s 0.0012, and if we multiply by 100 to convert to percent, we get a one-tenth of 1 percent chance that the two largest meteors of a 105-year period would both land in Russia.
If we wait until after we know about the first huge meteor, then ask for the chances that the next largest meteor of the next 105 years also would land in Russia, the answer is simple. It’s the same 3.347 percent chance that any given meteor that hits the Earth has of landing in Russia.
It’s the same kind of calculation we’d make in roulette. On a double-zero wheel, there’s 2.63 percent chance of the next number being 17. The chances of the next two numbers both being 17 involve squaring 0.0263, then multiplying by 100 to convert to percent. That leaves about a 0.7 percent chance of the next two numbers both being 17. However, if we already know that the first number is 17, then the chance of the next number matching it is 2.63 percent.
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