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How Betting Progressions Affect Likely Bankroll Swings12 January 2000
Misconceptions and misunderstandings mire casino gambling in mystery. But no puzzle perplexes more punters than the impact of betting progressions on player prosperity at table games.
Hosts of hopefuls have firm faith that somehow, somewhere, a magical method of manipulating money exists that will excise the house advantage. So they devise or buy secret schemes of raising, lowering, or combining bets. Schemes that almost work, usually work, or would have worked if the bosses didn't change dealers, or their spouses didn't come by and distract them by asking whether they had a comp yet for the all-you-can-eat buffet.
No system of changing and combining bets can overcome the statistical edge built into independent-trial casino games. Edge, however, isn't everything. In fact, during sessions of reasonable duration, it isn't even what dominates bettors' chances of success or failure. This role falls to the volatility -- the bankroll fluctuations resulting from individual wins and losses.
I'll illustrate by examining what an intrepid trio faces, averaging an initial $50 per round at blackjack but betting three different ways. Huey slides out a flat $50 each time on a single spot. Louie bets $25 on one spot a third of the time, but goes to $25 on each of two spots another third, and to $25 on each of three spots for the rest. Janet also starts with $25 but sticks to one spot -- pressing to $50 a third of the time and to $75 another third. Assume that the rules and the way these folks play give the house a 0.75 percent advantage.
After 500 rounds, the house's theoretical earnings based on edge are $187 per person. This is 500 rounds times the $50 average per round, times the 0.75 percent whammy.
Exactly where the players finish depends on the particular cards drawn. The luck factor. Nobody can predict this with certainty.
Confidence limits, however, can be assigned to the ranges in which these nominally equivalent $50 bettors are apt to find themselves at the end of the session. And the ranges differ owing to the varying volatility. Huey, betting $50 flat, is 50 percent sure of being from $1,040 in the hole to $665 in the clover. Louie, adding second and third $25 spots, has a 50-50 chance of finishing between a $931 tragedy and a $556 triumph. And Janet, pressing on a single spot, has an even shot at ending as low as $1,108 in the red or as high as $773 in the black. Compared to flat betting the same average, moving to more lower-level spots moderates bankroll swings while jumping from a smaller to a larger wager exaggerates potential routs as well as conquests.
Betting strategies also affect the chance a player will deplete a bankroll before completing a stated number of rounds. Pretend each apocryphal blackjack buff in the example has a $2,500 ceiling. Betting flat, Huey runs 37 percent risk of running out of ammo before concluding 500 rounds. With the tempered swings achieved by betting lesser amounts on more spots, Louie has only 31 percent risk of ruin. Conversely, Janet's aggressive strategy gives her a 41 percent prospect of going broke within 500 rounds.
An alternate criterion for selecting a betting system is the chance of reaching a desired profit level before exhausting a specified stake, regardless of session length. Make believe each player starts with $5,000 and stays until this stake is either doubled or gone. Huey's chance of success is 24 percent. Louie's is 18 percent. Janet's is 27 percent.
Same game. Same rules. Same decision strategy. Same average wager. Same theoretical contribution to the Casino Mortgage Fund. But different betting systems and consequent larger or smaller bankroll swings -- up as well as down. Which is best? As is often the case, it's a matter of personal preference. But the illustrations cited show you can't have it both ways. As the troubadour of the tables, Sumner A Ingmark, observed:
Beware of a system that promises all,
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