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The More You Try Winning, The More You Risk Losing

26 March 1996

Everybody wants to bag a bundle in the casino. Nobody wants to go broke trying. The trouble is, the forces behind these objectives are at cross-purposes to each other.

Conventional wisdom says that too high an upside goal is risky because of the house advantage on the action. The argument goes something like "keep playing and the edge will eventually wipe out your whole bankroll." There's truth in this banality, especially on bets where odds and payoffs combine to give the casino an edge equivalent to a commission of 10 or 20 percent.

Yet, even fighting the high house advantage of some wagers, solid citizens can emerge triumphant. Also, explanations based entirely on edge don't account for wins and losses experienced when the casino has only a minor built-in advantage. For instance, the edge is just 2.7 percent on any bets at single-zero roulette, 1.5 percent placing the six or eight at craps, and about 0.5 percent following strict basic strategy at blackjack. In 100 rounds at these games, expectation due to edge alone would be losses of 2.7, 1.5, and 0.5 bet units, respectively. Players are typically ahead, or much further behind, after such action.

Another factor is at work in addition to edge. Volatility. The normal bankroll swings players should anticipate in various games due to the frequencies and payoffs of winning bets. On propositions that win often but yield even-money or other small payoffs, volatility is low. On longshots having scant probability of winning but substantial returns, volatility is high.

Volatility can be expressed numerically by the "fluctuation" -- statisticians would call it "standard deviation" -- given as a multiple of bet units. Think of fluctuation as characterizing the size jumps your bankroll is apt to take, averaged over several rounds of play. In a game with a fluctuation less than about 1.5, bankrolls tend to shift gradually up and down. As fluctuation gets larger, winning and losing swings get more pronounced.

Volatility is the root of the gambler's dilemma. Large fluctuation is needed both to overcome house advantage and produce profits many times greater than the amount of a single bet. But high values of fluctuation are also what lead heavy losers to wonder what hit them.

I'll illustrate the effect of volatility using results predicted by laws of probability from two video poker machines. Payment schedules are shown in the first of the accompanying tables. Both machines feature 97.2 percent payback -- giving the house only 2.8 percent edge. They differ significantly in volatility, however. Machine A dispenses two coins for two pairs, a high payout for a relatively frequent occurrence, but rewards longshots modestly; fluctuation is 4.4 bet units. Machine B pays one coin for two pairs, but renders more substantial sums for tougher hands with higher poker values; fluctuation is 12.8 bet units.

The second table shows how many players out of a thousand can expect to exceed specified wins or losses after 100, 500, or 1000 rounds. You can see from this table that players are much likelier to hit it big, or to deplete their bankrolls, on Machine B -- the more volatile of the two.

Is low or high volatility better? It depends on your motivations along with your financial and psychological ability to outride normal downswings. Low volatility moderates the potential of wins as well as losses. High volatility offers bigger rewards but threatens greater penalties. Smart players decide which they prefer, then find a game to match their requirements.

Remember, though, that for comparable values of house edge, increasing the chance of an upswing that'll break the bank also raises the likelihood of a downswing that'll break you first. As Sumner A Ingmark, who always inspires choirs of high flyers, warily warned wagerers:

With lofty goals, predestination
Delivers seeds of devastation

Payment schedules for low- and high-volatility
jacks-or-better video poker machines
with the same payback percentages

Machine AMachine B
Royal flush8002500
Straight flush50100
Four of a kind2550
Full house89
Three of a kind33
Two pairs21
High pair11
payback (%)97.297.2
edge (%)2.82.8
fluctuation (bet units)4.412.8

Players per thousand expected to have losses or wins exceeding
the indicated number of bet units ( -- means less than one player per thousand)

Machine AMachine B
100 rounds500 rounds1000 rounds100 rounds500 rounds1000 rounds
loss exceeding:
win exceeding:
Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.