Different Bets May Not Offer Comparable Value

That incident came to mind when an acquaintance told me she'd played Sic-Bo and couldn't believe her bad luck. I said her loss didn't surprise me because Sic-Bo is strictly for bozos.

"It can't be all bad," she responded. "Surely, you can find a few good things to say about it."

"Give me some time," I answered. "I may be able to think of one." Unlike Eisenhower, I did. "Sic-Bo can serve a wonderful role as a horrible example for everything else," I later told her. "I'll use it in my next column to dispel the common belief that one bet is as good as another."

In Sic-Bo (Chinese for "big-small"), the dealer shakes a cage holding three dice. Players bet how the dice will land by placing chips on corresponding areas of the table. Betting options abound from sums of the spots to specific instances or combinations of numbers on one, two, or three dice. For instance, one person might bet on totals of four, five, 14, and 15. Another might go for doubles such as one-one or three-three on any two dice. Someone else might prefer any triples like two-two-two. Payoffs correspond loosely to the chance of the indicated results occurring, from even-money (1-to-1) to a substantial 180-to-1.

Sic-Bo vividly demonstrates how different bets may not offer comparable "value." Look at the accompanying table. The first two columns duplicate what's on part of the Sic-Bo layout: "payouts" for three-dice totals of four through 17. The other columns indicate gross outgo, gross income, and final net loss for statistically-correct distributions of $1 bets on each of these totals after 216 games.

The least unfavorable of the tabulated bets are on seven and 14, with expected net losses of $21 in 216 $1 tries. That's like paying the house almost a dime commission every time you bet $1. The most unfavorable bets are on nine and 12, with expected net losses of $41 in 216 $1 games. That's a commission just under nineteen cents on every $1 bet. For reference, the commission on a craps line bet with odds is below a penny per dollar.

Another sign of the relative value of bets is whether payouts are big enough to make up for high casino commissions. Use the table to explore this point, by finding how many wins you'd need to recover the loss expected after 216 $1 games with the statistically-correct distribution of results. Say you've been betting $1 on the nine and are $41 behind. A win pays $6, so you'd need seven extra hits to get $42 and be $1 ahead. But, odds against scoring just once are 7.64-to-1; the chance of seven winners close enough together to climb out of the hole is minuscule. If you'd been on four, you'd be $33 behind and would only need one extra hit to surge $27 ahead. Odds against four on any try are 71-to-1 adverse, but nowhere as bad as a run of seven nines.

This doesn't mean there's no money to be made at Sic-Bo. A solid citizen on a beeline to the all-you-can eat buffet might drop $10 on five-five-five at just the moment this 215-to-1 shot happens to hit, and wind up with a comp for the gourmet restaurant and $1800 to spend on tips. Sumner A Ingmark, odester to the oddsmakers, probably put it best:

Longshot players take solace:
When your chances are smallest,
Winning chips are stacked tallest.

 				status after 216 tries   				with the          				statistically-correct    				distribution of results   					 3-DICE	        payout on	gross	gross	net POINT TOTAL	$1 bet	        outgo	income	loss  four, 17	$60		$213	$180	$33 five, 16	30		210	180	30 six, 15	17	        	206	170	36 seven, 14	12		201	180	21 eight, 13	8		195	168	27 nine, 12	6		191	150	41 10, 11		6		189	162	27