'Dumbo Craps': The Newest, Hottest Game in Town

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Date

15 Jan 2008, 5:09 PM

By

Les Golden

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You can win at blackjack because the odds change as the cards are removed from the deck. This only happens in blackjack, baccarat, and poker, and that’s why only these games allow the skilled player to win in the long run. In all other games, because the odds never change and the house sets the rules to ensure a certain level of winnings, you can never win in the long run.

Here’s a simple game to illustrate this. This gets pretty hairy, but it shows exactly how the casinos operate. At least that’s what my inside pal Vito “Peach Fuzz” Angelini tells me.

I call my game “Dumbo Craps,” which for those of you with unclean minds is a compound noun, not a complete sentence. You throw a pair of dice and bet $1 that they’ll turn up a certain number.

Here’s how the casinos would figure the payout. First, you can get a total of 2 in only one way, from 1-1, cat’s eyes. You can get a total of 3 in two ways, either 1-2 or 2-1. You can get a total of 4 in three ways, either 1-3, 3-1, or 2-2, and so on.

These results are summarized in the Odds/Payout table. In the row entitled “Number of Ways to Roll” you see you can get a total of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, in 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1 ways, respectively. The most likely outcome is 7 and the least likely outcomes are 2 and 12.

Adding those figures together gives you 36. So, we have 36 possible ways the two dice can fall in Dumbo Craps, which is a pun only if your mind is in the gutter.

The Odds/Payout Table for the Game of Dumbo Craps

In an alternate way of looking at this, in the long run the fraction of times the dice comes up a 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12 are given by 1/36, 2/36, 3/36, 4/36, 5/36, 6/36, 5/36, 4/36, 3/36, 2/36, 1/36. Guys like Vito, the casino owner, know these odds and adjust their payouts.

This is how they would do it in Dumbo Craps. In the long run, in 36 attempts you get 2 only once. So if a player bets $1 on number 2, he would expect in an even payout game to win $36 if the dice came up cat’s eyes. “Tight Odz Resorts and Casino” would pay out $34.20. They base their game on a 5% take of the action. “Loose Odz Casino and Spa” would pay out $35.28, based on a 2% take from the action. They are still winning in the long run, but they can advertise “loosest Dumbo Craps.”

Similarly, in the long run, in 36 attempts you get a total of 6 in 6 ways out of the total 36 possible outcomes. So if a player bets $1 and wins, he would expect in an even game to get paid $6. At Tight Odz, they’d pay him $5.70; at Loose Odz they’d pay him $5.88. The other payouts for these two houses are given in the table.

Tight Odz Resorts and Casino would expect to have a profit of 11 x $0.05 = $0.55. You can calculate this by adding the expected house profits for each possible roll, 1/36 x $1.80 + 2/36 x $0.90 + 3/36 x $0.60 + etc. You’ll find that each of the 11 expected profits gives you $0.05 profit. Similarly, after 36 rolls of $1 bets Loose Odz Casino and Spa would expect to have a profit of 11 x $0.02 = $0.22.

If you’re the owner, in business lingo, those are your gaming revenues. Then you see how much you have to bribe the mayor and city councilmen to keep the inspectors away and how tough it will be to screw the labor unions to keep your costs down, and you become a quintillionaire. It’s that easy!

So far so good. That’s how these two casinos would set the payouts to ensure winning in the long run.

Now it gets a little more hairy. Let’s use the same kind of reasoning to see how a casino operator might change the rules of the game to ensure an income while being able to advertise “very loose Dumbo Craps” at their new house, “MaxLoose Casino and Convention Center.”

Easy. Make one face of one die, say the 4, red. The rule change is that if you get a red 4 in any combination, you automatically lose. Let’s go back to which combinations exist for each total. We see that to get a total of 5, 6, 7, 8, 9, and 10, we now only have 3, 4, 5, 4, 3, and 2 winning ways, respectively.

I’ve removed all the winning combinations that had the second die roll a 4. The number of ways to win with totals of 5, 6, 7, 8, 9, and 10 was reduced by 1 as you can see in the table.

The Odds/Payout Table for the Game of Dumbo Craps with ‘Red-4’ Rule Change

Because the player has fewer ways of winning, the casino owners can increase their payout. The payout increases, and they can advertise “the loosest Dumbo Craps.” Here I put the skim at only 1%. In the row labeled “Fair Even Payout New Rules” I give the payouts that should be paid based on the new rules. In fact, the payouts are based on the previous rules, without the red 4 rule change. As you can see from the row labeled “House Profit,” the house expects to make a killing when the total dice roll is 5, 6, 7, 8, 9, and 10, even advertising just a 1% skim, the loosest game in town.

Their expected profit will be 1/36 x $0.36 + 2/36 x $0.18 + 3/36 x $0.12 + 4/36 x $3.09 + 5/36 x $1.87 + 6/36 x $1.24 + 5/36 x $1.87 + 4/36 x $3.09 + 3/36 x $6.12 + 2/36 x $0.18 + 1/36 x $0.36 = $1.97. This is three and one-half times more than generated by the game with 5% skim without the red-4 rule change!

It’s even more insidious because the high payout rolls, getting 2, 3, 11, and 12, aren’t affected. The house makes its killings on the relatively low payout rolls of 5, 6, 7, 8, and 9. The naïve player won’t see much of a difference.

Now, this is a column on blackjack, remember? I’ve been discussing a game in which the odds never change. Set the rules, and the house can be sure in the long run that it will win a certain amount of cash. That’s the situation in craps, roulette, Keno, and in Dumbo Craps. It’s also the situation in any state-run numbers racket, sorry, lottery.

It is not the situation in poker, baccarat, and blackjack. In blackjack the house sets the rules. The odds, however, change as the deck is played. Knowing how they change and using that to their advantage is how card counters make their living.

In blackjack in the long run you can win. How much you win depends on how skillful of a card counter you are. In craps, roulette, and Keno, in the long run, you can never win. How much you lose depends on how the house sets the rules, just like in Dumbo Craps.

Okay, I know this may be confusing. Math often is.

I suggest those of you visiting the US come and visit me and I’ll show you how this all works in practice. I’ll even cook a nice dinner for you in my house and introduce you to Vito’s sister, Angelina. Then we can settle down to a nice friendly game of Dumbo Craps. If it’s all the same to you, I’ll be the house and use the die with the 4 painted red.

Les Golden supports environmental and animal welfare issues and realizes that, although math can be confusing, it’s not as confusing as why people are incarcerating elephants, camels, tigers, lions, rhinoceros, and other large mammals in zoos, slaughtering helpless Arctic pup seals with clubs, shooting imported African wildlife in enclosures for sport, reducing whale populations worldwide by 90%, and annihilating shark populations for their fins.

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