With its array of one-roll bets and wagers that take multiple rolls to decide, craps gives us an opportunity to look at the house edge in a couple of different ways. We can look at the edge per decision. That’s the common way of doing it, the way that tells us the house has a 1.41% edge on the pass line, 1.52% on place bets on 6 and 8 and a whopping 16.67% on any 7.
The other way of looking at it is the house edge per roll. For the one-roll bets, the edge per roll and per decision are the same -- 2.78% on the field if either the 2 or 12 pays 3-1 and other pays 2-1; 5.56% on the field if both 2 and 12 pay 2-1; 11.1% on 3, 11, or any craps; 16.67% on any 7, to give a partial list.
But for multi-roll bets, it’s different. Per roll, the house edge on the pass line is 0.42% and on place bets on 6 and 8 it’s 0.46%, to choose a couple of low-edge options.
Which is the appropriate way of looking at the edge? For the pass line and its cousins -- don’t pass, come and don’t come -- per decision is the way to go. You don’t have the option of taking those bets down, so it’s the per-decision number that tells us what we need to know about average loss per wager.
Same deal when you’re trying to compare individual wagers. Per $100 bet, are you getting a better deal on the pass line, place 6, or any 7? The house edge per decision tells us your average loss will be $1.41 of that $100 on pass, $1.52 on 6 and $16.67 on any 7.
But sometimes in a comparison of multiple-bet combinations, the edge per roll can be a useful tool. The house edge on the Iron Cross, a combination of the field bet plus place bets on 5, 6 and 8 so that 7 is the only number not covered, is sometimes listed at 1.136%, assuming the 12, or less commonly, the 2, pays 3-1. In another combination suggested by a reader, with $6 place bets on 6 and 8 and a $3 bet on any 7, the house edge can be expressed as 3.7% per roll.
That gives information that might be useful to someone who plans to make the combination bet, wait for one roll, then take the wins or losses and run. Perhaps the Iron Cross bettor is on his way to dinner -- alternate names for the combination include the dinner bet and Darby’s field -- and is just trying to squeeze enough out to upgrade from the buffet to the coffee shop. Nothing says he has to keep the place bets on the table if the shooter rolls a field winner.
So that player wants to know the one-roll edge. And the edge per roll tells us the Iron Cross is a stronger combination than my reader’s place/any 7 combo.
But the utility of the one-roll evaluation is pretty much limited to comparing combinations. It’s not particularly useful in comparing combinations to a single bet, and can be misleading. That 1.136% house edge on the Iron Cross doesn’t mean it’s a superior bet to a couple of its components, the place bets on 6 and 8. I’ve heard from readers who wondered just that, whether the combination somehow had the right synergy to drop the edge below the 1.52% on the best component bets.
What’s happening there is an apples and oranges comparison. Since the Iron Cross is evaluated with a house edge per roll, then the appropriate comparison is the 0.46% edge per roll on 6 and 8. As with any combination, the overall edge is a weighted average of the components.
If instead of rating the combination on a per-roll basis you assume that each wager will be left in action until it either wins or loses, you get a different picture. Assume that after the field is decided on one roll, the place bets are left on the table until decision time rather than being picked up, and you need a house edge figure that reflects decisions on all the components. On the Iron Cross, that’s 2.4% -- higher than the lowest components (1.52% on 6 and 8) but lower than the highest (4% on 5).
Casino math tells us that’s the way it has to be. No combination can have a lower house edge than it’s lowest-edge component, nor higher than its highest-edge component.
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