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# Should you bet on the Field at craps?

27 August 2012

One-roll bets at craps are resolved whenever the dice are thrown. Because the game is fast-paced, wagers of this type may induce steep bankroll climbs and falls during runs of good and bad luck, respectively. Usually, however, wins and loses occur in roughly the theoretical proportions, and frequent decisions in a given time period means that the house advantage or edge takes its toll.

The Field is a bet of this type. Novices, especially, like it for several reasons. First, it’s easy to understand because the seven winning totals are clearly printed on the layout: 2, 3, 4, 9, 10, 11, and 12. Second, although most results pay 1-to-1, 2 and 12 have bonuses – usually 2-to-1 on each but sometimes 2-to-1 on one and 3-to-1 on the other. Third, it’s located on the layout for self-service, a plus for players daunted by dealers. Fourth, it gives the impression of being easy to win because seven totals lead to victory while only four – 5, 6, 7, and 8 – by elimination, to defeat.

Everyone knows that appearances can be deceiving – and nowhere more than in palaces of smoke and mirrors, aka casinos. Seven propitious and four adverse totals don’t favor players by 7-to-4. The dice can land 36, not 11, ways. As the nearby table shows, 16 combinations bring joy and 20 sorrow on the Field, so five losses are expected for every four wins. In consequence, with 2s and 12s paying 2-to-1, edge is (2/36)x2 + (14/36)x1 - (20/36)x1 = -5.56 percent – the minus sign indicating the house is in the catbird seat. When either 2 or 12 pays 3-to-1 and the other 2-to-1, edge drops to (1/36)x3 + (1/36)x2 + (14/36)x1 -(20/36) x 1 = -2.78 percent.

Numbers of winning and losing combinations of the dice for bets on the Field at craps

```                  win              lose
total      2 3 4 9 10 11 12     5 6 7 8
ways       1 2 3 4 3  2  1      4 5 6 5
total ways       16                20
```

Maybe you don’t think -5.56 and -2.78 percent edge are exorbitant. After all, it’s -6.67 percent Placing the four or 10 and -4.00 percent the five or nine. And experienced players often make these bets rather than drive edge below 1 percent on Pass, Don’t Pass, Come, and Don’t Come with Odds. The fly in the ointment is decision rate. On the average, in 36 throws, Field bets are resolved 36 times while wagers on 4 or 10 have nine, and those on 5 or 9 have 10 decisions. What happens when \$5 is risked on each of these propositions for 36 statistically-correct throws?

• 4s and 10s pay \$9, winning three for a \$9x3 = \$27 gain and losing six for a \$5x6 = \$30 setback – a net \$3 deficit (note that 6.67 percent of \$5x9 is \$3);
• 5s and 9s pay \$7, winning four for a \$7x4 = \$28 gain and losing six for a \$5x6 = \$30 setback – a net \$2 deficit (note that 4.00 percent of \$5x10 is \$2);
• the Field with 2-to-1 bonuses on both 2 and 12 pay \$5 on 14 outcomes and \$10 on two results for a \$5x14 + \$10x2 = \$90 gain, and lose \$5 on 20 throws for a \$5x\$20 = \$100 setback – a \$10 net loss (note that 5.56 percent of \$5x36 is \$10);
• the Field with bonuses of 3-to-1 on either 2 or 12 and 2-to-1 on the other pay \$5 on 14 outcomes, \$10 on one result, and \$15 on one resolution for a \$5x14 + \$15x1 + \$10x1 = \$95 gain and lose \$5 on 20 decisions for a \$5x20 = \$100 setback – a \$5 net loss (note that 2.78 percent of \$5x36 is \$5).

Of course, casino aficionados don’t plan to finish a series of rolls losing precisely the amount corresponding to the edge. That’s where volatility, a measure of actual bankroll swings per decision, enters the picture. Losses cost \$5 in all these cases. Wins yield \$5, \$7, \$9, \$10, or \$15 depending on the particulars. Over huge numbers of coups, edge proves to be a reliable indicator of where players will finish. After relatively short stretches, the cumulative effect of individual jumps up and down can push solid citizens well below the loss due to edge, or can put them in the profit column. Assuming bettors have the dough to ride through 36 throws without busting out, the nearby table shows the chance they’ll be even or ahead at the end of such a series.

Chance of being even or ahead after 36 throws, flat betting the indicated propositions

```Proposition                                          % ahead

Field (two and 12 each pay 2-to-1)                   37.9%
Field (two or 12 pay 2-to-1, the other pays 3-to-1)  44.2%
Place the nine                                       46.1%
Place the 10                                         43.4%
```

The Field with the 2-to-1 payouts on 2s and 12s is the worst of the lot. If the chances of being ahead don’t look much lower for the Field than they do for Place bets on the 4, 5, 9, or 10, remember that the most sophisticated craps buffs don’t wager on these either. They opt for Pass, Come, Don’t pass, or Don’t Come with as much in Odds as the bosses allow and they can afford. The celebrated songster, Sumner A Ingmark, may have said it best in his catchy couplet:

Casino bets that don’t seem scary,
Are often traps for the unwary.