Ease your bankroll swing

August 28, 2001 2:16 AM


Sophisticated gamblers anticipate the kinds of bankroll swings they may encounter during normal action. This knowledge of volatility helps avoid errors such as starting with too small a stake and consequently busting out prematurely, setting win goals too high and accordingly being unhappy with earnings that are actually quite good for the conditions in question, and getting manic or depressed over peaks and valleys and therefore acting impulsively rather than rationally. It also keeps solid citizens from jumping tables or machines in panic after a few bad rounds.

Volatility differs among games. And, within games, when there are choices, it varies according to propositions covered, numbers of bets in action, and amounts at risk ”” the latter particularly when players increase or decrease wagers as the action proceeds.

“Normal action,” in the context of upswings and downswings, is also highly subjective. Business as usual for Ethel may be bizarre for Fred. For this reason, and since games of chance are statistical as opposed to deterministic, bankroll swings are best expressed using confidence levels. Examples might be “95 percent confidence you’ll be within $200 up or down in an hour,” or “85 percent confidence you won’t fall below $100 during 20 rounds.”

To get an appreciation for the fluctuations you’re apt to find, picture a fundamental form of gambling. Flipping coins for money. Heads you win one unit ”” $1, $5, $100, or whatever you bet ”” tails you lose the same amount. Your fortune rises or falls by that unit on every decision. But, for what size swings should you be prepared if you play 100 rounds? Surely, not 100 units.

The accompanying table gives limiting swings at a conservative 97.5 percent confidence level. You’ll likely be below these limits 97.5 percent of the time during and at the end of sessions of the durations shown. That is, after 400 flips, you won’t go over 40 units ahead (behind) or have peaked more than 80 units up (down) in more than 100 minus 97.5 or 2.5 percent of all games.

Size of upswings and downswings which will be exceeded in fewer than 2.5% of all ”˜flip the coin’ games, equal bets on every round.




of flips  

during session  

at end of session
















If you’d accept as “normal,” a looser 85 instead of 97.5 percent confidence level, halve the values in the chart. So, within 25 tries, there’s just 100 minus 85 or 15 percent chance of soaring (or plummeting) more than 20/2 or 10 units; similarly, you shouldn’t complete over 15 percent of all 25-flip session above 10/2 or 5 units to the good (or bad).

Varying your wagers raises volatility relative to the average at risk. Say you parlay your bet after each winning flip, a 1-2-4-8 progression, returning to one unit after a loss. Your average bet doubles to 2 units, but volatility rises by a factor of 2.74. A swing up or down of 80 x 2.74 or 219 units within 400 flips would be normal at the 97.5 percent confidence level, compared with 80 x 2 or 160 units betting $2 ”” the average wager ”” flat.

Swings based on flipping coins must be tweaked for application to real games. House advantage raises the amplitude of losses and tempers that of wins. Longshots, small bets with big payoffs for low-probability results, raise the volatility; this implies that you’re apt to go deeper into the hole waiting for a goose over the top. At video poker, for instance, this effect multiplies the figures in the table by 4.5. Betting five coins in a $1 game means one unit is $5. So a peak up or down of 4.5 x $5 x 120 or $2,700 within 900 rounds wouldn’t overshoot the normal range for a 97.5 percent confidence ­­level. Half as much, $1,350, would cap the swings during the course of 85 percent of all games.

Volatility may be good or bad. Upswings are what make winners. Downswings, more than edge, send most losers to the lockers. The poet, Sumner A Ingmark, described this duality in his ditty:

With an upward fluctuation,
Winners get a paid vacation;
When the bankroll
swings are tumbling,
Losers leave casinos