Monday, November 23, 2009

Beating the Odds in Vegas

I actually enjoy the occasional trip to Las Vegas, but I’m not the kind of gambler casinos want to see. It’s nearly impossible to beat the odds playing games against the house in a casino, but I do have one small idea for beating the house (sort of) at the dice game craps.

Before I go any further, I should mention that this idea hasn’t worked for anyone else who has played craps with me. It requires patience that the typical gambler doesn’t have. So, I don’t recommend trying this.

I start by finding a craps table that allows bets as small as $5. Some casinos don’t have any tables with bets this small. Then I only bet what is called the pass line. It is the most boring possible bet, but it has very close to fair odds. Out of 495 bets, the casino expects the player to win 244 times and lose 251 times, a net loss of 7 bets. Out of 495 bets, I expect to lose $35, which works out to just over 7 cents per bet.

It takes about 3.2 rolls of the dice, on average, to decide each bet. So, my loss per dice roll averages about 2.2 cents. In a very unscientific experiment, I timed the rolls at one table and found that each one took about 40 seconds. That’s 90 rolls per hour for an average loss of just under $2 per hour for me.

So far, all this sounds like losing money: where does the beating the house come in? They bring free drinks while you play. I wander over to a craps table and play for an hour before dinner and (statistically) lose $2, but have a couple of drinks while playing. The way I see it I come out ahead.

Of course, I could actually win or lose money each time I do this, but the long-term average will be losing roughly $2 per hour. And I enjoy the fun of being part of a group of excited people who tend to all win and lose together.

A few friends who have tried this with me couldn’t resist making bigger bets and making some of the other more exciting bets on the table that have worse odds. So, be warned: if you try this, it is likely to work out badly for you.


  1. Having ice water in your veins doesn't hurt. The ability to not "play a hunch" or "bet with your heart" is what Vegas hopes folks can't resist. One time I'll put it all on "00", I might win!

    Being boring seems to be the way to make money in this world, strange but funny and mostly true.

  2. Big Cajun Man: Your observation about how boring is the way to make money is interesting. Buying a few index ETFs and doing nothing for 20 years is pretty boring, but it would put an investor ahead of a strong majority of other investors.

  3. Yup, that's the boring way to play craps. Considering I play the game for the fun and excitement, it wouldn't work with me.

    It also looks less impressive if you use percentages.

    Let's take the hardest points to hit - 4 and 10. If you bet $5 on the pass line and nothing else, then for every 3 times a 4 is set, you'll have $10 and have wagered $15, for a $5 loss. That's a 33% loss.

    But if you put down just the odds bet behind it, you drop the house edge. If you put the standard 3x max odds bet on 4, you'd statistically have $55 and have wagered $60. STILL a $5 loss, but only 8.33%.

    5 & 9, and 6 & 8 are similar, with even smaller percentage losses when you put out the max odds. The absolute loss never changes from $5 though.

    That, of course, is statistically speaking. In reality, sometimes you win more than you lose, and sometimes you lose more than the math says. After all, we aren't there for an infinite period of time.

  4. Astin: You're right that when making the "odds" bets, you're dropping the house edge (as a percentage). However, the house edge expressed in dollars (or cents) remains the same. I actually like to play the "odds" bets, but I didn't mention it because these bets have fair odds and don't affect the amount I expect to lose per hour (but they do increase the standard deviation of my outcomes). These odds bets weren't what I was referring to as the exciting bets. The middle of a craps table has an array of other bets that all have worse odds than playing the pass line.

  5. Oh, I've had bets all over the table, but I was shocked that you'd play ONLY the pass-line bet and not the odds too. Knowing you play the odds makes it a more palatable game :).

    But if I want a game to get my profit in drinks, I find the $5 Pai Gow table.

  6. Astin: The cheapest Pai Gow table I've seen is $25. But, I haven't exactly been looking either.