Stay informed with the
Recent Articles
Best of Donald Catlin

# Lightning Craps

31 May 2014

Lightning Craps

One of my readers, Robby Bonter, recently sent me the rules for a new game called Lightning Craps. In Robby’s own words “Lightning Craps was introduced to some visitors of the Turning Stone Casino last August by a patron of the casino. I liked what he showed me so I wrote down the specifics and am happy to share what I know about this game with you.”

“The entire purpose here is to speed up the decision time flow of the game, eliminating the cumbersome extra rolling by shooters trying to hit their point vs. the 7. Any modifications you can add to the basic rules would be appreciated…”

Robby doesn’t say if the game was actually played at Turning Stone or if it was just discussed. It really doesn’t matter to me though because I found the game interesting enough to put in a bit of time looking it over. By the way, I don’t have any modifications.

Here are the rules:

• On the come-out roll the player (and pass line bettors) win on a roll of 7 or 11; the house (and don’t pass bettors) win on a roll of 2, 3 or 12.

• When a point number 4, 5, 6, 8, 9, or 10 is rolled the player then rolls until resolution is reached according to the following chart:

Point
4 Player wins 4, 5, 6 House wins 2, 3, 7, 8, 9 ,10 ,11, 12 Reroll --
5 Player wins 3, 4, 5, 6 House wins 7, 8, 9 ,10, 11, 12 Reoll 2
6 Player wins 2, 3, 4, 5, 6 House wins 7, 8, 9 ,10 Reroll 11, 12
8 Player wins 8, 9, 10, 11, 12 House wins 4, 5, 6, 7 Reroll 2, 3
9 Player wins 8, 9, 10, 11 House wins 2, 3, 4, 5, 6, 7 Reroll 12
10 Player wins 8, 9, 10 House wins 2, 3, 4, 5 , 6, 7 11, 12 Reroll --

Notice that the above chart produces exactly the same probabilities as those in the standard Craps game. For example if the point is 5 the there are 14 ways to win and 21 ways to lose hence the probabilities are 2/5 and 3/5 respectively. This means that the house edge in this game is 1.414% of the line bet just as it is in the usual Craps game. Moreover, if we refer to the sets of numbers in the Player Wins and House Wins column above for each point as the point set and miss-out set respectively then one can offer an odds bet that, for each point, the player will hit a number in the point set before a number in the miss-out set. As in regular Craps this is a fair bet.

There are more similarities. Because of the way the probabilities are set up the probability that a miss-out number occurs given that a pass line decision is reached is 196/495 just as in regular craps. So is Lightning Craps essentially the same as regular craps? No indeed! In regular craps the expected number of rolls for a Pass Line decision is approximately 3.376 (check the archives for my January 5, 2000 article How Long is a Craps Roll). We want to calculate this same statistic for Lightning Craps.

First off if "p" is the probability of “success” in a series of success/failure trials then the expected number of trails to reach the first success is 1/p. The proof of this is in my January 2000 article cited above. This result will be used below.

If either a Craps of a Natural is rolled on the come-out roll then the bet is decided so the expected number of rolls is 1. This happens with probability 12/36. If, for example, a point of 5 is established then a subsequent pass line decision is reached with probability 35/36. Thus in this case the expected number of rolls is 1 + 36/35 (the come-out roll plus the expected number of rolls to obtain anything but a 2). This number is weighted by 4/36, the probability of rolling the 5. All of this is summarized in the following table:

Event Probability Expected Rolls Product
Craps/Natural 12/36 1 12/36
Point 4 3/36 1 + 36/36 3/36+1155/13860
Point 5 4/36 1 + 36/35 4/36+1584/13860
Point 6 5/36 1 + 36/33 5/36+2100/13860
Point 8 5/36 1 + 36/33 5/36+2100/13860
Point 9 4/36 1 + 36/35 4/36 +1584/13860
Point 10 3/36 1 + 36/36 3/36+1155/13860
Total - 1+9678/13860

The figure 1 + 9678/13860 is approximately 1.6983 and represents the average number of rolls per pass line decision. In regular Craps the figure is 3.376. The ratio of these numbers is approximately 1.9879. Hence in Lightning Craps the player will play approximately twice as many line bets in a given time period as in regular Craps. So although the house edge per unit bet is the same as regular Craps the player will make twice as many bets and thus lose twice as much money on average.

One final thought. Using the miss-out sets in place of the 7 the average length of a player’s roll in Lightning Craps will be 1.6983 x 495/196 or approximately 4.3 rolls. My thanks to Robby for showing me this interesting game.

Don Catlin can be reached at 711cat@comcast.net
Recent Articles
Best of Donald Catlin
Donald Catlin

Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

#### Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers
Donald Catlin
Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

#### Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers