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Best of Donald Catlin

Gaming Guru

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$3 Craps versus $5 Craps

6 August 2010

Back in mid March I received the following email from Michael M., one of my readers from Laughlin, Nevada:

Hi Don,

I am an employee in a Laughlin casino. I have both dealt and supervised the craps table over the past 20 years and I am trying to convince my current director the advantages of a $3.00 minimum vs. $5.00 minimum. With the difficult economy times are tough here and a $3.00 minimum attracts more players. I also believe that it is a better game for the house. Since the player that bets only $3.00 place bets does not receive the full expected payoff, i.e., $3.00 on 6 and 8 pay only $3.00 instead of $3.50, bets on 5 and 9 pay just $4.00 instead of $4.20, and bets on 4 and 10 pay $5.00 instead of $5.40. All other bets remain the same. I have done some calculations based on your article on how to determine house advantage and by using the number of 1980 rolls of the dice, I deduct that the $3.00 bets would translate to an expected win of $44.00 increase per player for the house over the $5.00 minimum game, after those 1980 rolls. Can you confirm my findings?

Thank you,
Michael M.

Michael and I sent emails back and forth until late May trying to clarify the issues and the analysis and then my emails stopped. Here is why, Michael.

I had a trip to Las Vegas planned for my wife and me for late May and early June. We did indeed go and returned on June 5th. The following week, before I had a chance to write to you, my computer died. And I mean dead! I bought a whole new system (which I am now using to write this) and wanted to recycle the old system. Upon carrying my old monitor to the recycle service, I wrenched my back (it turned out to be a compression fracture) and, to make a long and painful story short, ended up in the hospital for a week stay. Today, July 3rd, is the first day I can sit and type. Bummer!

Before my Vegas trip I had settled your question, at least in my own mind, and had written software to carry out my analysis. My feeling is as follows. One does not need a house edge calculation to address your issue; I'm not even sure how one would interpret a house edge in this case. What you want to know is this. If two players play craps, one betting $5 and the other betting $3 on the line, taking odds, and placing the non point numbers, and each has the same number of comeouts (meaning comeouts after a point is made or a miss out occurs) who stands to lose more?

My program simulates the above situation. The program keeps a bet on every non-point number until the line bet is resolved, there are no place bets working on the comeout, and there are 100,000,000 comeouts for each player. Naturally the program's parameters have to be adjusted for each player. For example, if the $5 bettor's point is 6, then the amount he stands to lose on a miss out is 36 units; 38 units if the point is 5. For the $3 bettor the amount in this situation would be 23 units and 22 units, respectfully.

I ran the program twice, once for the $5 bettor and once for the $3 bettor. The results were as follows. In one hundred million comeouts the $5 player lost $110,676,176 and the $3 player lost $138,413,683; a 25% increase in loss for the $3 player. Not that it matters, since this is simply a yes/no experiment, but I ran several pairs of trials and each produced a 25% figure correct to two places. So Michael, assuming that players will bet as you describe, it appears your feeling about this was right. See you all next month.

Don Catlin can be reached at 711cat@comcast.net

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