Leftovers from last week

Dear Mark,

I enjoy reading your column in the Reno Gazette Journal each week. I am a craps dealer, but possibly a confused craps dealer. I always thought that the casino advantage was higher on the 6 and 8 hard ways than the 4 and 10 hard ways since there are more ways to roll easy sixes and eights. Your June 29th column lists the 4 and 10 casino advantage 11.1% and the 6 and 8 at 9.09%. Have you made an error or have I been under the wrong impression for 16 years? Please explain. Peter P.

I do thank you for those kind words, Peter P, and now to work.

The actual odds, Peter, pitted against the player's payout, determines what the casino's advantage is on a hard way bet, and NOT how many more ways you can roll an easy 6 or 8 versus 4 and 10. Let's examine this further, Peter, using the hard 10 and 8 as examples.

When betting a hard 10, there are eight ways to lose: six ways to throw a seven (4-3, 3-4, 5-2, 2-5, 6-1, 1-6) and two ways to throw a 10 the easy way (6-4, 4-6). This would mean that the correct payoff for a hard way 10 should be eight to one. Yet you, Peter, the 16-year Green Felt Jungle veteran, will pay the winning patron just seven to one, effectively giving the casino an 11.1% advantage on this wager.

As for a hard 8, there are 10 ways to lose: again, six ways to throw a 7, and four ways for an 8 the easy way (5-3, 3-5, 6-2, 2-6). Because there are 10 ways to lose, the correct payoff should be 10 to one on a hard 8, but your payoff to the player is only 9-to-1, which gives the house a 9.09% edge on this bet.

Yep, Peter, there is only one way to win a hard way bet, and oodles of ways of losing. So, with payouts not to the player's advantage, I'm hoping readers retain what they've just read and save their hard-earned money for more advantageous bets on the layout.

Dear Mark,

Last week you mentioned different proposition bets on a craps table but didn't mention a "hop" bet. I've heard it yelled out on a craps table before but I'm not quite clear how to play it, or even where it is located on the table.

Also, what are your thoughts about the "due factor" as it relates to craps? By reading last week's column I took away the fact that you are no fan of any proposition bets, but what are your thoughts that if the 11 hasn't appeared in let's say an hour, wouldn't a little side action on it (the 11) be justified? Neal C.

A hop bet, Neal, is a wager on any combination of the dice on the next roll. For example, "hard" 6 on the hop pays 30-1 (the actual odds, Neal, are 35-1) if matching threes appear on the dice on the next roll only. You may also bet "easy" combinations, such as a 4-2 or 5-1, which pays off at 15-to-1, with actual odds of 17-to-1.

The reason you can't ferret out a hop bet on most craps tables is that hop wagers do not have a designated space on the layout; instead, they are usually placed in front of the boxman, often with a "hop" marker placed on top of your chips.

As to the second part of your question, past die rolls do not influence the probabilities of future die rolls. The famous and costly Gambler's Fallacy, Neil, is the belief that a craps player should bet on 11 if an 11 has not appeared in the last umpteen rolls. In actuality, each roll of the dice is an independent event, with the probability of rolling an 11 not changing from one in 18, even if the 11 hasn't appeared in the last 24 hours. But . . . show me one gambler who really believes that, and I'll show eighteen who don't. That's called the Casino Owners' Magic Carpet.

Gambling wisdom of the Week: "If you've lost every penny you brought to gamble with, that might be a good time to leave." -- Frank Scoblete, Casino Gambling