November 2009

A Look At The Edge In The Short Term by John Grochowski

It all sounds so cut and dried when we talk about the house edges on casino games. The house has a 5.26 percent edge on nearly all bets at double-zero roulette, or 4 percent on place bets on 5 or 9 in craps, or 1.24 percent on the player bet in baccarat. But as anyone who has ever played the games knows, the house edge isn’t short-term destiny. As thousands of players take their turns at the roulette tables and tens of thousands of spins go by, the house is going to get its $5.26 per $100 wagered. But there are going to be winners, losers and some who break even.

The late Peter Griffin, mathematician and author of The Theory of Blackjack, used to tell a story to illustrate how the house edge works. I heard him tell it at a seminar for Harrah’s management up- and-comers in the 1990s — a crowd of bright young managers in non- gaming portions of the organization, getting a crash course on casino operations. It was a long time ago, and I can’t quote Griffin word for word, but it goes something like this. Imagine 100 players on a bus trip to a casino. It’s getting to be time to leave for home, so they all gather their things and meet in the departure area. Once they get there, they find the bus isn’t there yet. Somebody gets the bright idea of making one last bet, but there isn’t really time to get everyone into the casino and back again, so they enlist the help of a casino manager. This is in an imaginary state with particularly  lax regulations, so a casino manager agrees to help them. Each person  gives him 10 $1 bills to wager on roulette, with its 5.26 percent  house edge.

By now, the bus has arrived, so the manager takes a short cut. He  climbs the stairs to a balcony overlooking the bus departure area,  and puts the thousand $1 bills in a box, taking the time to pocket  $52 or $53 — the house edge. Then he turns the box upside down over  the balcony, sending all those remaining dollar bills floating into  the crowd. The 100 customers start scrambling for the money. Some  leap about, trying to snag it out of the air. Some dive to the  ground, snatching up whatever has landed. Some wind up just being  shoved out of the way. In the end, there are a few big winners who  have doubled their money. One lady is excited, he has 50 bucks. Most  of the people have something less than their original $10. A few walk  away with nothing. What they really wanted was a good seat on the  bus, anyway.

In total, the players have $947, or maybe $948, of the original  $1,000. The house has $52, or maybe $53. The house has its cut, there  are winners, there are losers, but most of the people have had a good  time. But, added Griffin — and this I do remember word for word — ask  anyone on the bus how they did, and they’ll say, “Oh, I paid for  gas.” That’s basically how the house edge works. The losses of the  many fund the wins of the few. The more wagers that are made, the  more likely the house is to approach the profits the math says the  games should make. And in the short term, anything can happen.

What has to happen to make you a winner in the short term? Not very  much, even on games with fairly high house edges. Double-zero  roulette is one table game with a fairly high house edge, 5.26  percent on all bets but one, the five-number bet on 0, 00, 1, 2 and  3, which gives the house a 7.89 percent advantage. Let’s say you play  for a couple of hours, and the wheel spins 76 times, a little slow,  but within the realm of reason at a crowded table where the dealer is  waiting for everyone to get bets down. Pick a single number, any  single number; I like to use No. 29, a family birthday number. In  those 76 spins, the average that would come up on No. 29 is two. If I  bet $5 on each spin, risking $380, and 29 came up twice, the 35-1  payoffs on single-number bets would leave me with $360. My expected  loss is $20. But if 29 comes up three times instead of two, I add  another $180 to my pile, and I’m a $160 winner overall. Even a house  edge of 5.26 percent is that thin. One extra win per couple of hours  makes me a big winner.

What about even-money bets, like red/black? If I bet $5 on red for  each of those 76 spins, I still risk $380. On average, I’ll win 36  bets, and have $360 left, again losing $20. If I win 38 bets, I have  my full $380 back and break even. On even-money bets, two extra wins  per 76 spins lets you break even, while anything more gives you a  profit. That doesn’t sound that hard, does it? A little short-term  luck, well within normal probability, and we’re there. But over the  long haul, with hundreds of players and thousands of spins, the math  is going to hold up and grind out that 5.26 percent for the house.

What about a REALLY bad bet, such as the one-roll wager on 12 in  craps? In the 36 possible combinations of two six-sided dice, only  one totals 12, a pair of 6s. The odds against rolling a 12 are 35-1,  but the most common payoff at craps tables is only 30-1. That’s a  house edge of 13.89 percent. I get the shakes even typing house edges  that large. But what would it take for you to have a winning session  if you were doing nothing but betting that 12 roll after roll? I’m  not advocating you do that, of course. In fact, I advise strongly  against it. I don’t bet the 12. Ever.

Imaginary games are the best way to approach that bet. So let’s  imagine we hang out at the craps table long enough for 108 rolls of  the dice. Craps moves a lot faster than roulette, so that should only  take us a little over an hour. If I bet $5 on 12 on each of those 108  rolls — all while yearning for cheaper tables — I risk $540. On the  average, three of those rolls will be 12s, and I’ll get a 30-1 payoff  on each, meaning I get $150 in winnings and get to keep my $5 wager  on each win. That leaves me with a total of $465, so I’ve lost $75.  That comes to 13.89 percent of my original $540 investment, and that  13.89 percent is the house edge. What if four 12s show up in those  108 rolls, one more than average. You can add another $155 to my  bankroll, and now I have $620 for an overall $80 profit.

In the short term, that’s all it takes to be a winner, one more  winning bet than the mathematical expectation, even on one of the  worst bets around. Of course, there’s a downside. If there wasn’t,  everyone would be saying, “Hey, I’ll risk an average $75 loss for the  chance that one extra win will bring an $80 profit.” Problem is,  you’re risking a $540 loss, not $75, because long streaks with no 12s  do happen. Even if you’re not in a 12-free zone, it’s just as likely  that 12 will turn up one time less than average as one time more,  meaning I’ll lose $230 on my 12 spree just as often as I win $80.

Bets with lower house edges give you a better chance to win.  Baccarat, the best bets at craps, blackjack, all give you a better  chance at winning sessions than do roulette or betting 12 at craps.  But at any game, you win some, you lose some, and in the end, the  house takes its share from the box.