Throwing it all in may improve odds
john grochowski firstname.lastname@example.org January 16, 2013 2:36PM
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Updated: February 19, 2013 1:25PM
When most players go to the casino, they have more than wins and losses in mind. Profit may be the reason for the games’ existence to blackjack card counters and poker pros, but for most players, entertainment lives in harmony with a shot to win.
If all you wanted was a chance to double your money and you were willing to risk losing your entire stake, your best chance is to bet it all at once. It’s not an approach I recommend, of course, but making multiple bets does increase your exposure to the house edge and makes it more certain the house will come up on top.
To quantify the effect, I like the approach taken by Ken Ross in his 2007 book “A Mathematician at the Ballpark.”
Ross used double-zero roulette as an example. If you’re wagering on even-money bets such as red/black or odd/even, you have 18 ways to win and 20 ways to lose. On red/black, you’d win on the 18 black numbers, lose on the 18 reds and also lose on 0 and 00. Your chances of winning are 18:20, which can be reduced to 9:10.
To express that as a percentage, divide the 9, representing your chances to win, by 19, your chances to win plus your chances to lose. That comes to 0.4737. Multiply by 100 to convert to percent, and you have a 47.37 percent chance of doubling your money with a single wager.
What if you divide your wager into two equal-sized bets, and keep re-wagering until you’ve doubled your money or lost it? Your chances are 9 squared:10 squared, or 81:100. That’s a step down from 9:10, a 44.75 percent chance of doubling your money.
What about wagering a 10th of your bankroll each time? Your chance becomes 910:1010 — 9 times itself 10 times compared to 10 times itself 10 times. And your chances drop to about 35 percent.
The smaller the share of your bankroll you wager, the smaller your chances of doubling up.
I still recommend that you stay within your bankroll, not bet too large a share of your gambling money at once, and give yourself a chance to enjoy your casino visit. After all, for most players, a day at the casino isn’t all about winning. It’s about entertainment, too, and most of us won’t find a one-play day all that entertaining.
John Grochowski is a local freelance writer. Look for him on Facebook (http://tinyurl.com/7lzdt44); Twitter (@GrochowskiJ).