Allocating Money on Don't Pass: Flat Bets or Odds?

Normally, Charlie finds a table with a $5 minimum, bets a nickel on don't pass, lays single odds, then waits for a seven. Trouble comes when the casinos get crowded and $5 tables are scarce. "If they jump from $5 to $10," he asked me, "should I stay, betting a dime on the back line and no odds? Or should I take a hike?"

I answered that the casino had a greater edge on $10 flat than on $5 with single odds. "It's 1.4 as opposed to 0.84 percent."

Charlie allowed as how he'd seen those numbers but never had a clear picture what they meant. "Think of 1 percent as paying the casino a penny in commission for every dollar bet," I explained.

That was no help. Charlie noted that since the choices actually entail different amounts of money, percentages alone don't offer a good comparison. "Betting flat involves $10 all the way through," he stated, "so 1.4 percent means the casino gets $0.14. The other way, the bet is $5 during the come-out roll, then $11 on points of six and eight, $14 on fives and nines, and $15 on fours and 10s - so what do you multiply by the 0.84 percent?"

"You have to work back from all the probabilities," I replied. "But the answer turns out to be fairly simple. To figure the 'juice,' ignore the odds and take 1.4 percent of the flat part of the bet. The casino earns $0.07 when you drop $5 on the don't pass line, no matter what odds you lay."

Charlie was still not satisfied. "The casino doesn't actually collect seven or 14 cents when I make the bet. What I really want to know," he continued, "is how going from one to the other changes my chances of winning and losing."

"That's the nub of it," I responded. "It's surprising more people don't evaluate alternatives this way. And it's not too tough to answer, although it takes more math than I can toss off the top of my head."

I called Charlie a few days later. "Say you're talking 10,000 decisions in a year - a lot of action, one don't pass bet at a time. With $5 and single odds, you'd have 22 percent chance to be ahead at the end of the period; $10 flat cuts this to 8 percent."

"What about my chances of making a day's pay or losing my hundred during a session?" Charlie asked.

"I knew that'd be your next question," I said. "I made a little table comparing the cases and sent it to you by e-mail." Here's what he found when he went on-line:

The figures show the degree to which $5 with single odds outperforms $10 flat. For instance, after 100 decisions, a player has a 33 percent chance of losing over $50 with the former versus 36 percent with the latter. Likewise, chances of being $50 ahead are 29 percent and 26 percent, respectively.

What should Charlie do? Quit when the limit goes up, and maybe not find another $5 game all day? Or switch to $10 flat despite less favorable conditions so he can be in on the action? Charlie has to decide that for himself. I can only tell him his chances - and maybe quote to him the candid commentary of Sumner A Ingmark, the crapshooters' Coleridge:

For some gamblers, wagering's romance is,
Less in winning, than in taking chances.