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Best of Alan Krigman

Gaming Guru

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Hedges in Roulette Are Exceptions that Challenge the Rule.

14 December 2005

Hedging bets in the casino, as in the real world, generally comes at a price. This, because the insurance or protection is an expense that rarely yields a return, and/or has a high cost premium. In casino gambling, the premium is typically a greater house advantage on the total at risk with the hedge than on the same amount bet entirely on the primary proposition.

Roulette offers exceptions to the rule. A representative situation might be $10 split between $1 on each of five odd numbers -- hedged with $5 on "Even," as opposed to $2 on each of the same five spots. The edge on the $10 is equal either way at all single-zero tables, and on double-zero wheels where bets on Even lose completely when the ball lands in 0 or 00. The bosses' bite is smaller when bettors use this hedge in double-zero roulette where wagers on Even lose only half when 0 or 00 pops.

Edge, though, is only one factor with which gamblers should be concerned. During sessions of reasonable duration, normal bankroll swings swamp the gradual erosive effect of house advantage. And hedging tends to temper this volatility. Independently of edge, hedging bets accordingly lowers the chance of going belly-up but simultaneously cuts profit potential.

Intuitively, this works with the prototype hedge because an average of 18 out of 38 spins push and are irrelevant -- $5 won on Even offsets $5 lost on the numbers. Only 15 out of 38 lose $10, as opposed to 33 out of 38 with $2 on each of five spots. Conversely, the five out of 38 ways to win earn $26 and not $62.

 

The accompanying chart shows how virtual players fared with the two indicated strategies after 100 spins of the wheel, about two hours, in 100,000 simulated sessions of double-zero roulette.

Effect of Hedging by Betting $5 on Even and $1 on each of five
odd numbers, as opposed to $2 on each of the same numbers

Comparative result

Even loses halfon 0 or 00

Even loses all on 0 or 00
hedge wins, no-hedge wins
33.1%
30.5%
hedge loses, no-hedge loses
52.6%
53.7%
hedge wins, no-hedge loses
2.6%
1.5%
hedge loses, no-hedge wins
11.7%
14.3%
hedge beats no-hedge
54.6%
51.2%
no-hedge beats hedge
45.3%
48.6%
hedge equals no-hedge
0.1%
0.2%
average bankroll low-point, hedge
-$104
-$113
average bankroll high-point, hedge
+$65
+$61
average bankroll low-point, no-hedge
-$878
-$878
average bankroll high-point, no-hedge
+$1,113
+$1,113

Hedging and non-hedging won or lost concurrently in the majority of instances. Outcomes were therefore usually more matters of degree than kind. In sessions where one approach won and the other lost, solid citizens going for broke succeeded more often than those who hedged by 11.7 to 2.6 percent with half-back and 14.3 to 1.5 percent with lose-all. However, hedgers finished ahead of those who bet only on numbers more frequently than the converse. The moderated volatility is also evident; average peaks and valleys were far less extreme with than without hedging. In the half-back game, the range was +$1,113 to -$878 without hedging and +$65 to -$104 with. At none-back tables, the no-hedge range was the same and that for hedging was +$61 to -$113.

The data also illustrate the benefit is derived from using the hedge to reduce house advantage when the half-back rule applies. For example, hedge won and no-hedge lost in 2.6 percent of all half-back games, compared to 1.5 percent when 0 or 00 take the entire bet. Likewise, hedging beat non-hedging -- in the sense of winning more or losing less -- in 54.6 percent of all half-back games, while the figure was 51.2 percent otherwise. Further, the average session minimum was not quite as deep while the maximum was somewhat greater hedging under half-back conditions then when the Even wagers lost completely on 0 or 00.

A plethora of roulette hedges is possible. Dreaming them up and watching them in action add to the fun of the game. The specifics differ among hedges. But the overall implications remain that in this game, spreading money across propositions that tend to offset one another can improve chances of modest success while lessening the likelihood of a serious failure. It's as the immortal muse, Sumner A Ingmark, memorably muttered:

One school of thought alleges you're unwise betting hedges,
But sometimes moderation has quite a firm foundation.

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.