Shaving the House Edge Lowers Your Need for Luck

20 February 1995

By Alan Krigman

asinos have a mathematical edge or advantage in every game you play against them. To overcome this edge and gain a profit, you have to be lucky to win more or larger bets than predicted purely by principles of probability. The essence of smart play is to reduce the amount of luck you need.

Maybe you're blessed by a bonanza right off the bat. Then, good gambling guidelines go by the boards.

Take the slots. Cutting through a casino on the way to showroom, you drop $3 into a Megabucks slot and win $2 or $3 million on one pull. You're not gonna care about the likelihood of winning, the casino "hold" percentage, or the bankroll suggested for this machine.

Ditto for the tables. Getting off the deluxe motor coach with $100 and a coupon for the buffet, you buy one black chip and bet the whole thing on Tie at mini-baccarat "to get it over with" before bolting toward nosher's nirvana. Player and banker Tie. You parlay and win again, then quit with $8000 profit. No solid citizen'll rush over, yelling "That was dumb. Tie's a sucker bet and $100 longshots oughtta have back-up bankrolls in the thousands."

Less spectacular runs of luck a blackjack dealer who busts hand after hand or a craps shooter who holds the dice for forty minutes also come along. When they do, you can forget all the rules except the one about quitting when you're ahead.

Ordinarily, you won't be this fortunate. So it helps to know how to make the most of probability law and rely the least on luck.

"Taking odds" in craps offers a good way to picture the links among probability, edge, and luck. "Odds" are secondary wagers, augmenting bets on the "pass line." Both win when a shooter repeats a point before throwing a seven. The primary bets pay even money and give the house an edge equivalent to about 1.4 cents on the dollar. The odds pay in exact proportion to the chances of winning and give the house no edge.

Say you make enough $10 line bets to experience 3960 decisions. If the distribution of outcomes is statistically correct, you'll lose $560 because of the house edge. When you take odds, the theoretical dollar loss per bet stays fixed. As odds rise, however, the amount becomes a diminishing fraction of the total bet, so edge drops on the combination.

Shaving the edge by taking odds reduces the luck you need by trimming the deviation above the mathematically-correct distribution necessary to break even. With no odds, you must win about 1.4 percent more than the statistically expected number of line bets to see daylight. Taking single odds ($10 odds, $10 line), 0.8 percent over the expected win rate zeroes out. At double odds ($20 odds, $10 line), the necessary deviation drops to 0.55 percent. Triple odds ($30 odds, $10 line) lowers it to around 0.4 percent. And five-times odds ($50 odds, $10 line) only requires an upshift around 0.3 percent from expected results to overcome the edge. It's no coincidence that these break-even deviations equal the house advantage on the combined bets.

The accompanying table gives another view on how shaving the house edge trims reliance on luck. It shows how profit grows with positive deviation from the statistically-expected distribution of results as well as with odds.

Taking odds to lessen the house advantage has a downside, of course. You're betting more, so the same negative deviation some bad luck deepens your loss.

The further you have to foray from the laws of probability to make a profit, the more you lean on luck. Conversely, strategies putting you deeper into the dough with smaller deviations from statistically-expected results demand less luck. As Sumner A Ingmark, madrigal master of the machines once mused:

With adroitness alone you may not succeed,
But the more skilled you are, the less luck you'll need.

           Dependence on luck, expressed as percent departure from          expected results, to make a profit on craps line bets                   taking different amounts of odds       deviation from				loss(-) or win(+) for $10 bet statistically-expected				in 3960 craps decisions ($)      distribution       (percent)			no odds	$10 odds $20 odds $30 odds $50 odds  	0.0			-560	-560	 -560	  -560	   -560 	0.5			-362	-205	 -48	  +108	   +422 	1.0			-164	+150	 +463	  +777	   +1404 	1.5			+34	+504	 +975	  +1445	   +2386 	2.0			+232	+859	 +1486	  +2114	   +3368 	2.5			+430	+1214	 +1998	  +2782	   +4350