Big wheel, stay clear

25 December 2014

By John Grochowski

In my Q&A column a few weeks ago, I answered a reader’s question on the Big Six wheel, and explained that the high house edge doesn’t make it a candidate for repeated play.

That brought this inquiry from another reader, who didn’t quite understand the answer. “The Big wheel – how can you lose?” she wrote. “The payoffs are for 1-1 to 45-1. If the worst bet pays even money; maybe it’s one for one, and 24 bets break even. All others win money. Could you explain it better? I don't get it.”

She didn’t understand that every possible space on the wheel is a winner if you bet on it, and the house still makes money. It’s the same situation as roulette, where every number is a potential winner, or craps, where every possible combination of two dice can win if you bet on the right number or combination.

Let’s take the Big Six wheel, were there usually are 54 spaces. Typically, 24 spaces are filled by $1 bills, 15 with $2, seven with $5, four with $10, two with $20, one with an eagle or other special symbol, and the other with a casino logo or another symbol. The currency spaces are paid in proportion to their values — $1 spaces pay 1-1, $2 spaces pay 2-1, and so on. The eagle space pays 40-1 on most wheels, but often 45-1 in Atlantic City, and the casino logo space also pays 40-1, or 45-1 in A.C.

Now let’s say we have a giant table surrounding the wheel, seating 54 players, or that there are 54 remote electronic betting terminals linked to the wheel. Each player bets $1 per spin, and to demonstrate how the house get its edge, we’ll say bets are made in proportion to the spaces on the wheel, so that 24 players bet on $1, 15 bet on $2 and so on.

On any given spin, $54 is wagered. If the wheel stops on the $1 space, the 24 players who bet on it get their $1 bet back and get $1 each in winnings, so that altogether they collect $48. The other $6 goes to the house.

If the wheel stops on the $2 space, the 15 winners each collect $3 – their $1 bet plus $2 in winnings. That’s a total of $45, and the house keeps $9. If it stops on $5, the seven winners get a total of $42, and the house keeps $12. On $10, the four winners get $44, the house keeps $8. On $20, the two winners get $42, with $12 to the house. On either the eagle or the casino logo, the single winner gets either $41 or $46, depending on whether it pays 40-1 or 45-1, and the casino keeps either $13 or $8.

No matter which number wins, the house makes a profit. At a real table with fewer players, not every number is going to draw wagers at once, and there can be short streaks where players make profits. But the house can be comfortable knowing it has a large edge on every possible wager, and will make money with repeated play.

Let’s try single-number bets on a double-zero roulette wheel as another example. There are 38 numbers, 1 through 36 plus 0 and 00. Let’s say we have 38 players each betting $1 on a different number so all 38 numbers are covered. On each spin, they risk a total of $38. No matter which number the ball lands on, the winner collects a 35-1 payoff, or a total of $36. The house keeps the other $2. That’s the house edge, and the house has that edge even though every possible wager is a potential winner.

The key is that the house pays less than true odds to winners. It pays 1-1 on winning $1 bets on Big Six, but the true odds against winning the bet are 30-24, which reduces to 5-4, or 1.25-1. It pays 20-1 on winning bets on the $20 space, but the true odds are 52-2, or 26-1. It pays 35-1 on winning single number bets at roulette, but the true odds are 37-1.

By paying less that true odds, the house ensures that it will make money as long as the outcomes remain in proportion to the odds of the game. If a roulette wheel was badly out of balance so that a number came up more often than once per 36 spins, it would open the potential for a sharp bettor to beat the game. Likewise, if a Big Six wheel was out of balance, or had an obstruction that caused the wheel to stop on $1 spaces more than half the time, a bettor who noticed the imbalance could make hay.

But those are rare circumstances. As a matter of course, the casino doesn’t care which numbers you bet on, because it knows it will be the long-term winner on every one.

Look for John Grochowski at www.casinoanswerman.com, on Facebook (http://tinyurl.com/7lzdt44) and Twitter (@GrochowskiJ).