Why High-Volatility Games Make Sense for some Low-Limit Bettors

Wins and losses in a casino are ultimately a matter of luck. But the chances associated with varying degrees of good or poor performance are a matter of mathematics. And knowing or having well-founded intuition about those chances, as well as how to manage them to suit your personal preferences, demonstrate the adage "luck favors the well prepared."

A simple relationship gives an upper bound on the chance of a bankroll reaching some peak before falling to a designated low point. It's the low divided by the high value. So, the chance of leaving with $500 before losing $200 is no better than 200/500 or 40 percent. This is a helpful rule of thumb if you set win goals and loss limits for your gambling. Or, if you say to yourself, "I started with x and now I have y. I had only x/y percent chance of getting this far before scraping the bottom of my fanny pack. Maybe I should stop rather than push my luck any further."

Many solid citizens, however, don't think in terms of loss limits and win goals or even sensible budgets and winnings that would merit them bragging rights on the street. Rather, lots of players set their sights on making their stakes last for as long as they envisioned before leaving home. Partly because nobody wants to go bust and be stuck in the casino feeling like a loser and having nothing to do but pretend to be enjoying the joint's other amenities. Also, due to the feeling that if they're in the game, there's always the hope of catching a streak and winning big.

The probability of surviving on a specified stake for a desired number of coups is a function of the edge held by the house and the average jump a bankroll takes up or down during a round. The jump depends on bet size and the characteristic volatility of the game. The critical factor is bet size times the "standard deviation" the latter being a measure of the volatility expressed in terms of equivalent number of units wagered.

To put an upper bound on chance of survival, assume a game with no edge. Say you either won even money or lost such that standard deviation would be equal to one bet, your bust-out bankroll is $200, and you want to stay in action for at least 500 coups. At $5 per round, your chance of survival is 93 percent. At $10 it's 63 percent. Were the standard deviation equal to two bets, because of steeper but less frequent payoffs, risking $5 per round would put your chance of survival at 63 percent while $10 wagers would cut it to 34 percent. At a standard deviation of four bets, $5 wagers would also put you at 34 percent.

Edge acts more strongly on the amount you bet than on the volatility. To see the effect, consider the above conditions with a house advantage of 1 percent. The chances that your money will be enough to weather normal downswings for the various cases are compared with those for zero edge in the following table.

Chances of staying in action for 500 coups,
starting with a $200 bankroll, for various values
of bet size, standard deviation (std) and edge

bet	std	bet x std	zero edge chance	1% edge chance
$5	1	5	93%	89%
$10	1	10	63%	55%
$5	2	10	63%	59%
$10	2	20	34%	31%
$5	4	20	34%	33%

You can draw two relevant conclusions from the data. First, if your main concern is getting lots of action for your money, make small bets in games with low volatility payoff multiples equal or close to 1-to-1; this strategy typically gives you a good shot at a modest payday but won't send you home in a limo. Second, the more you bet or the greater the volatility, presumably because you'll only be content with a hefty haul, the less the likelihood that any given stake will get you through the cold streaks; however, players hell bent on leather to hit the mother lode have better chances of outriding those inevitable downswings by wagering low in games with high volatility than conversely.

Good gamblers understand the trade-offs and make them wisely. As the beloved bard, Sumner A Ingmark, poignantly penned:

If wagering big makes you feel like a hero,
Just think how you'll feel if your bankroll hits zero.