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Are hedges in craps as bad as the experts say?

Every gambling know-it-all knows that hedges in craps are sucker bets. But, legions of craps buffs swear by them anyway.

Perhaps the most common example involves “protecting” something like $10 on the Pass line with $1 on Any Craps during come-out rolls…

Full article :

http://www.casino-folk.com/archives/2005/01/01/casino-hedges-in-craps/

A couple of interesting things about Krigman’s article struck me.
The first one is trivial; he equates 100 passline decisions to about an hour’s play. Since the average number of rolls to a decision on the pass line is 3.375, that’s assuming 337 rolls/hour, an astonishing rate. WinCraps defaults to an assumption of 120 rolls/hour, which is 35-36 decisions/hour.

The second is more interesting. He compares an $11 pass bet to a $10 pass bet with a $1 Any Craps hedge. This keeps the bet handles the same, and makes the increase in expected loss very small, since you

$1 @1.414% for $1 @11.11%. This, however, is not how most player hedge, taking $1 off the pass bet and putting it on the Any Craps. In my view, the comparison should be between betting $10 on the line and $10 plus $1 Any Craps. Who makes an $11 pass bet? It seems to me the question is: “Should I ADD a hedge to my regular line bet.” That is certainly the way the casinos recommend it when they conduct those little “Introductory Craps” sessions. When I took the “Fun Train” to Reno a couple of years ago, I saw a dealer do one of those sessions, and that’s what he recommended. Of course, when you do this, you not only make a bet with a higher HA than the line bets, but you also increase the bet handle. This is why many people and craps
authors recommend against hedging. However, if we look at it Krigman’s way, we get another picture.

Let’s talk about the doey-don’t. If we compare a $5 bet on either side

with a $5 doey-don’t, $5 pass and $5 DP, naturally we are doubling the expected loss. But if a $10 bettor instead bets $5 and $5, then takes or lays odds on the points, the expected loss remains the same. I did a comparison between a $10 pass with $20 odds and a $5 pass, $5 DP, taking $20 odds (obviously, you need a 5X table for this). I set it up for 60 bets. The expected losses were almost exactly the same, of course, but the Standard Deviations were $221 vs. $155, since the
doey-don’t damps out the variation on the flat part. This would give one a lower risk of ruin on the doey-don’t, which is really what a hedge is for, isn’t it? Basically, if you have a positive session, anything better than -$8, you are better off without the hedge; otherwise, you are better off with the hedge.

So, when you think about hedging, in addition to thinking about making the hedge bet IN ADDITION to the “main” bet, think about MOVING part of the “main” bet to the hedge. Of course, if you are making a minimum bet to begin with, you can’t do that. The more money you are willing to risk, the more flexibility you have. A $10 bettor can instead bet $5 and take $5 odds, which does reduce the expected loss. A $25 bettor can, if the casinos allow it, bet $5 and take 5X odds, reducing the expected loss by 80% while increasing the variance by less than 20%.
Cheers,
Alan Shank

By Alan Krigman. For At The Shore

Every gambling know-it-all knows that hedges in craps are sucker bets. But, legions of craps buffs swear by them anyway.

Perhaps the most common example involves “protecting” something like $10 on the Pass line with $1 on Any Craps during come-out rolls. The idea is that if the dice show a two, three, or 12 on these throws, the main bets lose but the hedges win $7 — reducing the hurt from $10 to $3. The $1 loss on Any Craps when anything else appears? Well, hey, it’s chump change.

Or, is it?

If the Any Craps hedge seems sublime, others can be ridiculous. One in this category is equal bets on Pass and Don’t Pass. Supposedly, these offset each other so players who take or lay Odds give the house no edge.

What about losses on Pass not matched by wins on Don’t Pass when 12s pop during the come-out? The rationale is that 12s are rare enough to be ignored. This, of course, ignores the subtle fact that the one out of 36 chance of a 12 is equivalent to the edge on the sum of the two bets.

On paper and over the “long run,” the premium the casino squeezes from the edge on the hedge is money out of the player’s fanny pack. Still, these wagers seem brilliant when they work. And, as a result, many solid citizens not only mock the math but pooh-pooh the pundits who propound it.

The truth can’t be discovered by asking around. This, because folks who like hedges tend to claim they’re successful, while those who don’t say they’re not. And monitoring thousands of sessions to get enough data for a proper analysis is infeasible.

Fortunately, gamblers and other folks who make life’s important decisions have computers at their behest. And computers can be programmed to simulate the real world such that lots of events can be executed and documented automatically in a brief time.

Accordingly, as yet another in a long string of services to humanity, I wrote a program simulating two individuals playing identical games — one betting $11 flat on the Pass line and the other dropping $10 on Pass and $1 on Any Craps. Totals of $11 were put at risk in both modes. Simulated sessions were of moderate duration, and only the indicated wagers were made. Other hedges, differing amounts, or bells and whistles such as taking Odds would alter the details somewhat but not the general conclusions leaping out of the results.

One set of sessions was simulated for 10,000 games of 100 decisions each, about an hour at the rail. Data were gathered for only the wagers indicated — no Odds, no auxiliary bets, no pressing or regressing. In a typical series, both the straight $11 Pass bettors and the $10 Pass plus $1 Any Craps players finished even or ahead in 3,957 sessions and lost in 4,993; the no-hedge approach won and the hedging strategy lost in 918 while the converse held in the remaining 132. Perhaps more tellingly, the no-hedge players did better than their hedging counterparts in 6,277 sessions, worse in 3,477, and the same in the other 246.

Another simulation run extended the sessions to 200 decisions, roughly two hours. Here, both approaches left bettors even or ahead 3,604 times and behind 5,354; no-hedging won and hedging lost in 944 series, and conversely in 98. The straight Pass bettor beat the hedge player 6,754 times, the reverse was true 3,071, and the bottom line was the same in the remaining 175.

Repeating these simulations yields figures that differ, but not by much. Overall, players appear twice as likely to win less or lose more by hedging. However, the hedge helped often enough to reinforce the notion that it’s good insurance for those who want to believe it is. Can a simulation be written that offers clues to predict conditions under which hedging will succeed? Only if a prophet happens to hold a day job as a programmer. So, until such an oracle steps forward, we’ll just have to muddle through with this maxim by the immortal Sumner A Ingmark:

Gamblers whose fanny packs grow fatter,

Learned just what does and doesn’t matter.

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(Alan Krigman is an MIT graduate and gaming aficionado. He believes that informed players can optimize their choices in the casino to improve their chances of achieving their personal goals as recreational gamblers. However, Mr Krigman and At The Shore caution that gambling is inherently risky and assume no responsibility for losses incurred by applying the information presented.)