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Best of Alan Krigman

Gaming Guru

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The Experts Hedge on Wall Street, Why not at the Casino?

10 April 2001

Hedges in gambling are means of "protecting" one bet with another -- akin to taking out an insurance policy. The idea is widely employed by sophisticated investors in the stock and bond markets. It can be applied in the casino as well.

Casino gambling hedges are most common at craps. An example would be $2 "any craps" to cover $15 on the Pass Line during come-out rolls. The former would pay $14 on a two, three, or 12 -- just the bets the latter lose. The trouble is that craps bets used this way have high edges and therefore raise net house advantage.

Roulette players can also hedge. And, they can do it without increasing the house advantage. In fact, in double-zero games where even-money outside bets lose only half when the ball stops in 0 or 00, hedging with these wagers lowers the overall edge.

The practical effects of hedging go well beyond edge, however. To illustrate, consider a typical hedge at single-zero roulette:

a) $2 on each of five black numbers -- five ways to win $62, 32 ways to lose $10;

b) $1 on each of five black numbers, hedged with $5 on red -- five ways to win $26, 18 ways to push, 14 ways to lose $10;

In both cases, the house edge is 2.7 percent. Where the options differ, on a spin-by-spin basis, is in the chances and amounts.
But the bottom line at the end of a session is more important to the majority of solid citizens than the results of individual spins. It's here that the real trade-offs of hedging become significant in terms of personal gambling objectives.

Two somewhat contradictory factors can be considered. First is the likelihood that players betting fixed fractions of their bankrolls in each round will survive the normal downswings of a game for some specified number of spins. Second is the prospect that, the number of spins notwithstanding, bettors will hit some win peak before losing their stakes.

Suppose, as a representative situation, players bet five percent of their stakes per spin -- for instance a total of $10 starting with $200. Also assume they want to survive at least 100 rounds without being busted by a normal cold streak, and hope to realize a gain equal to half of their stakes -- $100 in this example.

A "risk of ruin" analysis reveals the following for a single-zero table:

a) Betting $2 on each of five numbers, players have 55 percent chance of lasting at least 100 spins and almost 64 percent probability of earning $100 before losing $200.

b) Betting $1 on each of five black numbers and hedging with $5 on red, chances rise above 88 percent of surviving 100 spins but drop to 52 percent chance of reaching the $100 goal.

The projections for a double-zero game with the "return half" feature are:

a) Betting $2 on each of five numbers, players have 51 percent chance of lasting at least 100 spins and nearly 61 percent probability of earning $100 before losing $200.

b) Betting $1 on each of five black numbers and hedging with $5 on red, chances rise above 83 percent of surviving 100 spins but fall to 48 percent chance of reaching the $100 target.

Specific values would differ but the trend would be the same for any of countless other similar hedges. Namely, this conservative approach to gambling improves chances for a long session on a given bankroll, but makes reaching any specified profit level less likely.

Should you hedge or go flat out? Shoot for the moon or opt for as much action as your money can buy? You'll have to decide on your own, in light of your reasons for gambling in the first place. I can only give you the pros and cons of the approaches. More or less what the poet, Sumner A Ingmark, had in mind when he wrote:
What's best for me ain't best for you,

So I can help you with a clue,
But ought not say what you must do.

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.