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Why High-Volatility Games Make Sense for some Low-Limit Bettors17 May 2006
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."
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.
Chances of staying in action for 500 coups,
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,
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