How Come You Can Win when Edge Says You'll Go Bust?

27 September 2006

By Alan Krigman

Many casino games offer players options to increase payout with a smaller chance of winning or decrease return with a better shot at success, for the same total bet. One versus several blackjack hands, fewer as opposed to more craps outcomes, even lesser rather than greater numbers of "matrix" slot machine lines.

The most flexibility in balancing returns and odds is available at roulette. As an example, in a double-zero game, $20 split in half on two 12-number columns has a 63.2 percent chance to win $10; on a single spot, $20 has a 2.6 percent chance to grab $700.

The bosses don't, or shouldn't, care how solid citizens swap risks and rewards. Over an extended period, the gross wager and house advantage or edge on the action are the sole considerations governing how much gelt goes into a casino's coffers. This, because a joint's proceeds are predicated on performance over the long run, when the law of averages holds sway.

Not so for individuals. Nobody gambles convinced that betting $20 in each of 190 rounds, on a proposition with 5.26 percent house advantage, will leave them behind by 5.26 percent of $20 x 190 or close to $200. Sessions are almost always of statistically short duration. Then, volatility the inherent fluctuation of the game swamps the erosive effect of the edge. Players look for profits in normal bankroll upswings, presumably recognizing that the downswings may cost them their entire stakes. A cost that may greatly exceed what's projected by edge and gross wager.

Still, the trade-off between odds and payouts does affect results bettors can anticipate in typical sessions. But, how?

To explore the phenomenon, consider three ways to bet $20 per spin, with the same 5.26 percent edge, at double-zero roulette. They are a) high volatility: $4 on each of five spots for a 13.2 percent grab at $124; b) medium volatility: $2 on each of 10 spots for a 26.3 percent attempt at $52; c) low-volatility: $1 on each of 20 spots for a 52.6 percent go at $16. Make believe that the players start with $200 and continue for 190 spins (three to four hours' action) or until they run out of dough.

As noted, in 190 rounds of double-zero roulette at $20 each, edge says that players will lose $200. Were this the only factor, everyone who followed any of the prototype strategies would therefore bust out on the 190th coup. In fact, players may bite the dust earlier, survive but lose money, or finish flush.

A computer simulation of 100,000 players using each of these approaches suggests the probabilities of concluding 190 spins in one or another of these possible states. Values are presented in the accompanying table.

 

 

The figures demonstrate how volatility can overcome edge during sessions of reasonable duration. Under the conditions proposed, probabilities are 16 to 19 percent of earning a profit with the low- and moderate-volatility strategies offering slightly greater chance of doing so than the high-volatility approaches. For all three strategies, the likelihood is greatest of getting wiped out before completing 190 spins. However, the prospect of hitting the skids drops as volatility decreases.

Of course, the gambling gurus will tell you that $20 per round is too large a bet on a $200 casino bankroll. Far fewer players would go belly-up in 190 rounds with $500, although the tendency for volatility to worsen the threat would remain. The improved chance of survival would yield more probability of making money by outriding the downswings and catching some winners, but here higher-volatility strategies would help and not hurt. All of which emphasizes the value of sizing bets to bankroll and not pretending to be a big mahaf while gambling in short pants. It's as that pragmatic poet, Sumner A Ingmark, sagaciously scribbled:

Gamblers wise and gamblers wary,
Heed suggestions budgetary.