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Ask the Wizard #236

A 60 Minutes interview of Steve Wynn featured the following exchange:

Charlie Rose: You have never known, in your entire life, a gambler who comes here and wins big and walks away?

Steve Wynn: Never.

CR: You know nobody, hardly, who over the stretch of time, is ahead?

SW: Nope.

I find this hard to believe. What are your thoughts?

Andrew from Fort Wayne, IN

I personally know lots of professional gamblers up on the Wynn. However, I’m sure that none of them have met Steve Wynn personally. I would imagine that only the super whales are granted an audience with him, and such whales are usually superstitious (i.e. losing) baccarat players. Most heavy recreational gamblers do lose over the long run. However, if Mr. Wynn believes that nobody is up on him, I would invite him to repeat the triple-points promotion he ran Labor Day weekend 2007. Even if the promotion loses money, surely the foolish players will give it back eventually.

One of the casinos in my town is paying 36 to 1, for a straight up bet, on a single-zero roulette wheel, on a specified number for that day. For example, the specified number is 8 on the 8th of the month. How does that change the house edge? Thanks for your help.

A. Carter from Derby

The house edge on the specified number would be exactly 0%.

What is the average sum when rolling four six-sided dice after subtracting the lowest result (known as 4d6-L)? What is the standard deviation for this roll?

Aaron from New York

The following table shows the number of combinations for all possible totals from 3 to 18.

Combinations in 4d6-L

Outcome Combinations
3 1
4 4
5 10
6 21
7 38
8 62
9 91
10 122
11 148
12 167
13 172
14 160
15 131
16 94
17 54
18 21
Total 1296

The mean result is 12.2446, and the standard deviation is 2.8468.

How does the house percentage change when I buy the 5&9 for $50 if I "pay the vig after I win"? If I place them for $50, then I get $70 in return. If I throw the same $50 out to the dealer and say "buy it," then I’ll win $75 minus the $2 vig, for a $73 win. It seems that buying the 5&9 in this manor would lower this house edge. Paying after you win on buy bets is a very common practice these days. The player could buy the 5&9 for as low as $20 and still have a little edge. Place for $20, win $28. Buy for $20, win $30 minus the $1 vig =$29. Thanks for any insight.

Leo from Fort Worth

Comparing buy bets to place bets, on points of 6 and 8, the place bet always has the lower house edge. On points of 4 and 10, the buy bet always has the lower house edge. On points of 5 and 9, it depends on whether the commission is always paid or only paid on wins. If the commission is paid up front, as is usually the case, then place bets are better; otherwise, buy bets are. To be more specific, the house edge placing the 5 and 9 is 4.00%. The house edge buying the 5 and 9, when the commission is paid up front, is 4.76%. When it is only paid on wins, the house edge is 2.00%.

I need to buy an official felt. What kind do most casinos use? When I was looking for one, one of them was velveteen. Is there any difference?

Kaitlin from Preston

To be honest with you, I don’t know much about it. Casino felts are generally much better quality than those for home use. For my home poker games, we put a home-use roulette felt on top of my dining room table. By the end of the evening, there are little green felt balls everywhere. In Macau, the felts are much smoother and harder than those in Vegas. I see you can buy casino felts on eBay for about $90.

I will soon be graduating with my math major, as well as an economics minor. I am even considering actuarial science as a potential career. I recently finished the required mathematical statistics course that covers the first seven chapters of John E. Freund’s Mathematical Statistics. Where can I look to find more material on gambling mathematics? I want the technical details on how you produce your odds. Are their any books or journals I can look in? Also, are there any other nonconventional career paths for actuaries other than what you’ve chosen?

Samuel from Miami, FL

I always encourage math majors to consider the actuarial profession. The best book on casino math, in my opinion, is Practical Casino Math by Robert C. Hannum and Anthony N. Cabot. However, I think you would find it below your level. Most blackjack and poker-based games are done by computer, looping through all the ways the cards may fall and making the play with the highest expected value at every decision point. If you can’t write such a program from scratch, a book about it probably wouldn’t help much.

To answer your last question, there are a number of nonconventional areas for actuaries. I know a self-employed actuary here in Las Vegas who specializes in splitting up pensions in divorce cases. The possibilities are endless.