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Best of Alan Krigman

Gaming Guru

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Can Bias in Roulette Wheels Give You an Edge?

9 February 1998

Roulette players love systems. Of all kinds. Systems based on combining numbers and groups. On raising bets after losses or wins. On the supposed ability of certain dexterous dealers to drop the ball into designated grooves. On the phases of the moon.

Systems based on patterns of past results are especially interesting. And adherents are steadfast, convinced beyond argument they're relying on math and science - the law of averages, the theory of probability - to guarantee success. Maybe not on every spin. Or during every session. But surely over the "long term."

The simplest such systems involve outcomes that haven't hit lately. Specific numbers, highs or lows, reds or blacks, odds or evens, one or two of the three columns, you name it. The law of averages supposedly says they're "due." This is lame logic, pseudo-statistics. Roulette is a game of independent trials. The wheel and ball have no memory. After six or 60 reds in a row, the chance of a red on the next spin is - as always - 18 out of 38 and 18 out of 37 in double- and single-zero games, respectively.

More esoteric systems involve detecting irregularities in the apparatus which make some results more likely than normal, then betting accordingly. If such bias existed, and were great enough, players could indeed gain an edge. Here's how this might work.

In an unbiased double-zero game, the probability of each number is 1/38 or 2.63 percent. Paying 35-to-1, the house has a 5.26 percent edge. Say the bottom of one slot was spongy or the frets around it were high, raising its probability of winning to 3 percent. Bets on this number would have an 8 percent edge.

What if a wheel were tilted in some way favoring half the grooves? Ordinarily, bets on each of 19 numbers have 50-50 chance of losing $19 or winning $17 - giving the house its usual 5.26 percent edge. Instead, assume the bias creates 53 percent chance the ball will land on a known half of the wheel. Now betting on each number in that half gives the player 0.42 percent edge.

Biased wheel systems hold in theory but fail in practice. Roulette wheel construction and maintenance make large biases unlikely, and problems such as broken bearings would be noticed immediately and result in a game being shut down. Small biases require numerous observations and complex calculations before solid citizens can be confident that the effect is not random; even then, they may shift the edge toward the player too little to be significant during a session of reasonable duration.

The example of the bias on a single number involved a 0.37 percent increase in probability. To be 95 percent confident in detecting this small an anomaly, data would have to be analyzed from roughly 71,000 spins. A 99 percent confidence level would require about 122,500 spins. Neither is even remotely feasible.

The second example involved a hefty 3 percent change in probability. To be 95 percent confident of detecting this large a bias, a player would have to analyze data from only 1,100 spins. To be 99 percent confident of the bias before going for broke on the favored half of the wheel, data would have to be analyzed from 1,850 spins. These many observations might be possible, for instance with a team of trained observers monitoring results and relaying the data to their computer experts for analysis. But this doesn't account for the time wasted checking unbiased wheels. Further, this much bias is unlikely to occur or persist - and still only gives players under half a percent advantage.

Next time you see a roulette table, look for the electronic display of the last few dozen hits. Most tables now have them. Think: are the casino bosses foolish enough to broadcast information that will help clever players get an edge in their games? Sumner A Ingmark, whose songs often have an unpredictable spin, said it this way:


Roulette contenders hardly nettle
Casinos when they test their mettle,
Foretelling where the ball will settle.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.