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Is It Worth What It Costs to Hedge Your Bets?2 October 2000
Some casino table game players relish opportunities to hedge. That is, to make opposing secondary wagers which -- for a price -- eliminate or reduce risks associated with their primary bets.
Arguably, the most common casino hedge is money on Any Craps to protect the Pass Line during the come-out roll at a dice table. Any Craps pays 7-to-1 if the dice show a two, three, or 12; it loses otherwise. Pass loses on the same numbers, wins on a seven or 11, and moves to the second stage and awaits a decision on the point for anything else. Assume you "protect" $10 on the Pass Line with $2 Any Craps. The good news is that a two, three, or 12 coming‑out yields $4 profit rather than $10 loss. The bad news is that a seven or 11 coming-out yields $8 rather than $10 profit, and any other come-out result sacrifices $2 immediately so decisions on the point are ultimately debited by this amount.
Other craps hedges are legion. Some are baroque. For instance, solid citizens may make equal flat wagers on Pass and Don't Pass, then bet the Odds on one or the other side. The theory is to cut the chance of losing on the come-out to one in 36, then risk only the Odds -- where the house has no edge. Another example would be to bet $12 Don't Pass, then place points of six and eight for $12 and other numbers for $10. Now, six and eight break even or gain $2, five and nine always win $2, and four and 10 earn $2 or $6.
Typical roulette hedges offset small bets on multiple individual numbers with bigger bucks on an opposing outside proposition. An illustration might be $1 each on 15 high numbers and $20 on Low. In a single-zero game, this offers 18 ways to net $5 (on a low number), 15 ways to net $1 (on one of the selected high numbers), and four ways to lose $35 (on zero or an uncovered high number).
Blackjack buffs often hedge when they receive naturals and the
dealer gets ace-up. Taking insurance guarantees winning 1-to-1, rather than chancing a push against a 1.5-to-1 payoff.
Hedging may or may not pay in any given situation, but particular post-facto results aren't the criteria by which to judge their value. Instead, realize that in hedging, house edge depends on the sum of the bets while player fortunes hinge on the difference. This essentially raises edge for the action at hand.
I'll put some numbers onto the phenomenon for the roulette hedge mentioned earlier because it's easy to envision. Similar effects occur, to a greater or lesser degree, for other hedges.
Consider 37 statistically-correct spins of a single-zero roulette wheel, betting $35 in all, as indicated. The win will be $5 x 18 = $90 on Low plus $1 x 15 = $15 on the individual numbers, for a total of $105. The overall loss will be $35 x 4 = $140. The house nets $140 - $105 = $35 by virtue of the edge. That's an average commission of $35/37, nearly $0.95 per spin. Players effectively pay $0.95 for a 48.6 percent chance to win $5, a 40.6 percent chance to win $1, and a 10.8 percent chance to lose $35.
Contrast this with betting $35 on Low for the same 37 statistically-correct spins. The win would be $35 x 18 = $630, offset by a loss of $35 x 19 = $665, for a $35 net the casino derives from the edge. That's also an average of $35/37 or just under $0.95 per spin. But now, players have a 48.6 percent chance to win $35 and a 51.4 percent chance to lose $35. The casino's fee is a much smaller fraction of the action.
Hedging always exacts a hidden premium. In the extreme, it can literally be driven to a point of no return -- or worse. Say, equal bets on Pass and Don't Pass with no Odds. Maybe $35 on high and $1 each on all the low numbers. Nobody would be so stupid? Where along the spectrum from no hedge to no possible profit would you draw the line between ignorance and intelligence? As usual, it boils down to personal preference -- hopefully predicated on fact and not fancy. The bettors' bard, Sumner A Ingmark, may have given the best advice by urging:
Is only known through introspection.
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