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Best of Donald Catlin

Gaming Guru

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Free Buy Bet

3 September 2010

As you may have noted in my last article, I finally got back to Michael in Laughlin who inquired about introducing a $3 line bet at Craps. Here is his reply:

Hi Don,

I was glad to hear from you. I hope all is O.K. I truly enjoyed our communications on this subject and it appears that my director at work has embraced the idea, and is currently offering a $3.00 game on a more consistent basis. I'm not sure that is the proper solution but it is a move in the right direction. I believe the information in regards to the difference between the $3.00 and $5.00 bet is better used to properly market the type of player that actually provides the increased revenue. Obviously if the player only bets a $3.00 pass line bet, the expected house revenue drops. Using the information and creatively making changes to minimum bets, i.e. $3.00 minimum pass line bets only if making place bets, and $5.00 minimum without place bets, the house could maximize their profit potential.

Anyhow, thank you for all the time you put into this subject. The results you attained helped me to verify my findings.

Hope you are feeling better soon. I do, however, have one more question. We have offered a "free buy bet" on the numbers 4 and 10, meaning the 5% vigorish is not paid until the bet wins. How does this impact the revenue?

Thank you,
Michael

Well, Michael, it is good to hear from you. I will address your "free buy bet" in this article. The bet is not "free" at all but it is, as we will see, considerably better than the usual buy bet. By the way, the usual name for this wager is the Fig Vig; the regular buy bet is called the Pig Vig. Here are the details.

In the Pig Vig wager, the player wagers $21 on either the 4 or 10 (or both). Let's use the 4 to illustrate. If the shooter makes the 4, then he is paid $60. Effectively this means that the player's $21 is returned along with $39. The player has, therefore, won $39, had $20 of his $21 returned, and paid $1 in vigorish. If the seven occurs the house simply collects the player's $21; the player loses $20 and pays $1 in vigorish.

In the Fig Vig game, the player wagers $20 on the 4. If the shooter rolls a 4, then the player receives his $20 wager back plus $39 rather than $40; essentially he is charged $1 in vigorish. If the seven occurs the house collects the player's wager of $20.

To compute the house edge for each game, we first calculate the player expected loss per game and then divide this figure by the wager per game. This produces the following tables.

Pig Vig:

Event

Prob

Payoff

Product

Win

1/3

39

39/3

Loss

2/3

-21

-42/3

Totals

1

--

-3/3

As you can see the expected return per game is -1, so the expected return per dollar waged is -1/21. This means the house edge is approximately 4.76%.

Fig Vig:

Event

Prob

Payoff

Product

Win

1/3

39

39/3

Loss

2/3

-20

-40/3

Totals

1

--

-1/3

The house edge here is 1/60, which is approximately 1.67%. I hope these simple calculations clear up things for you, Michael.

I should point out that the above two wagers are not the only buy bets involving the 4 and 10. There are a slew of buy wagers involving these two numbers. For example, some casinos offer the player a chance to buy the 4 or 10 for $25, pay 2:1, and collect $1 vig on winning bets. If you check this out the house edge is only 1.33%. You can find a list of these various wagers in the new book Casino Craps, Shoot to Win by Frank Scoblete with Dominator. I'll be reviewing this book next month.

Finally, as I mentioned in my last article, I had both a broken computer and a broken back during much of June and July. These annoyances resulted in my not receiving some of my email during that period. If you wrote to me this past summer and I didn't answer you please write again; I should get your letter this time. See you next month.


Don Catlin can (hopefully) 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