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# Protecting Craps Bets: Expensive, But Sometimes You Get Lucky

13 October 1997

My boyhood buddy, Bromley, invited me to dinner a while back. Bromley always has something up his sleeve. Since the restaurant was what passes for gourmet in a casino (cloth napkins), I made two guesses. He had a comp and wanted me to know the bosses considered him a high-roller. He wanted to talk gambling.

Right on both.

Bromley plays craps. I've convinced him over the years to shave the house edge, so he starts with \$25 on the pass line and takes full odds. Then he makes \$25 come bets, also taking full odds.

Where he abandons my advice is in "protecting" all his line and come bets on their come-out rolls. He does this with \$3 on any craps. His reasoning? When two, three, or 12 show up, he'll lose \$25 on pass or come but recover \$21 on any craps. If any other number appears, he asserts that the \$3 is cheap enough insurance.

I've argued that \$3 any craps is hardly cheap. It pays 7-to-1 but chances against winning are 8-to-1. The casino has a whopping 11 percent edge and theoretically earns \$0.33 on the \$3 bet. Compare this to \$0.35 earned on a \$25 line or come bet with full odds.

At dinner, Bromley got quickly to the point. "You're right about not protecting flat bets coming-out with any craps," he stated. "I don't understand all those decimal points you throw around," he continued, "but I figure it this way. The \$21 is \$4 short of the quarter on the line, so I ain't getting such hot coverage."

I started to say full protection was irrelevant. But why stir the pot? It's no sin to do the right thing for the wrong reason. Then, before I could comment, Bromley told me his new system.

"Forget \$3 any craps. Instead, bet \$3 three-way craps," he said. He must have seen my jaw drop. "Aha! A bet you don't know. Maybe I can teach you something," he gloated. "With \$3 on three-way craps, \$1 goes on each of the two, three, and 12," he explained. "If two or 12 hit, I get \$28 - \$30 for what wins minus \$1 for the others. If three scores, I get \$13 - \$15 for the three minus \$2 for the two and 12. My \$25 pass or come is covered with \$3 to spare on the two and 12. I cut my loss to \$12 on the three."

"I know the three-way craps bet. It's worse than any craps," I blurted out. "True, you can get lucky on a roll or even a whole game. Then, making either bet could save your hide. But they're both losers over the long term - three-way craps the more so."

"Prove it, Mr Mystical Statistical," he challenged. "How sure are you they'll cost me money if I bet them all the time?"

"Bromley, that's a great way to put the question," I replied. "I can't tell you off the top of my head. And the math is too much to do on the tablecloth. So I'll dope it out later and call you."

Here's the data I gave Bromley to show that the more often solid citizens make these bets, the more apt they are to be behind on them. "After 100 \$3 bets," I told him, "players are 67 percent sure to be in the hole with any craps; it's 80 percent with three-way craps. After 1,000 \$3 bets, losing is 92 percent certain with any craps; it's over 99 percent with three-way craps.

A few weeks later, I saw Bromley at a craps table. Betting \$25 pass and come with \$3 three-way craps.

"How ya doing, Bromley?" I asked, disappointed but not surprised.

"Like you said," he answered. "A guy can get lucky with these insurance bets. They're saving my skin today. Those twos and 12s are hitting to beat the band. Thanks for the advice."

"You're welcome," I groaned gamely. It recalled the reality roused by Sumner A Ingmark, the statisticians' Stevenson:

Though you give counsel most astutely,
Your words are often spoken futilely.
They won't be fathomed absolutely.

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Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.