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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:
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