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The Wizard Himself - FAQ

A suggestion, really, O Wizard--when next you print up your book, could you make it smaller? Perhaps a pocket edition that could fit in a purse?

Maryanne S. from Redmond, Washington

My current book is 5.5" x 8.5". Sorry, but I don't plan to publish another one anytime soon.

How did you derive the house edge in blackjack?

John C. from London, Canada

I wrote my own combinatorial program which cycles through every possible event and keeping a running tally of all the possible outcomes weighted by their probability. Except in cases where re-splitting pairs is involved, my calculations are exactly right.

You take a lot of your time or space on your web site to explain that no system can beat the house edge. I'd like to know what drives you to continue to play casino games if you know that you will loose in the end?

Yvan from Quebec, Canada

The rare times that I play a negative expectation game it is for entertainment. pai gow (tiles) is the only game I find enjoyable enough to play without an advantage.

Very interesting site, do you produce your income as a gambler? Have you looked at the probabilities in stock index futures trading?

Randy from Aurora, Illinois

I am tempted to learn more about futures trading but for now I simply don't have the time. My income comes from both advertising revenue on this site (please click through the banners) and consulting fees on the analysis of new casino games.

Are the craps probability numbers with the odds taken 100% reliable. Also is the gaming industry your full time profession, and do you visit Atlantic City often? Also, how do you simulate billions and billions of hands, spins, and rolls. Is it computer generated and if so with which software?

DB from New York, USA

Well, anyone can make a mistake, but craps is an easy game to analyze mathematically so I would be very confident my odds on craps are right. Yes, gambling in one way or another is my full time self-employed profession. I have been to Atlantic City many times in the last few years but two months ago I moved to Las Vegas. So, I'm afraid I wouldn't be gracing Atlantic City with my presence much any longer. I prefer a combinatorial approach as opposed to random simulations whenever I can. Either way, I roll my own software with Visual C++. For random numbers I use a Mersenne Twister.

Are you going to tell us when you will be on the travel channel?

Gil from Saint Petersburg

I plan to tell my newsletter readers. However since you ask it should air sometime in April or May in a show titled something like "The Top Ten Ways to Win." I’ve been interviewed on radio and television before and I can never stand to watch or listen to myself afterward. I always feel I could have done better. So I don’t plan to make a big fuss over it.

What was the most money you ever won after walking away from a blackjack game?

Joseph from Shelton, Connecticut

I think about $800. I’m not a very big bettor. I once lost more than that chasing a 2 to 1 blackjack promotion at an Internet casino.

Michael, saw you on the travel channel from Vegas the other day giving your expert advice regarding house advantage. Good job. Didn’t realize you were that young. I was playing craps at the new Seneca/Niagara casino and instructed the dealer to have the odds working for a don’t come bet on the come out roll. He advised the odds are always working for that bet. Is he correct?

Gordon from Niagara Falls

Thanks for the kind words on my Travel Channel appearance. For those of you who missed it the show was titled Sucker Bets. The dealer was right. In general bets are turned off on a come out roll in which a seven would cause the player to lose. I guess they don’t want some players to sour the mood of the table by rooting against a 7 on the come out roll. Since a 7 would cause the odds on the don’t pass to win they are left on.

Your Money Management page says:

"For those who sometimes lose too much and later regret their actions some self-constraints may be in order. I would suggest setting a specific loss point in these cases, for example $200. Personally I don’t set such limits on myself. If I’ve lost too much it won’t be fun any more and I’ll step away for that reason."

But for you, what does "too much" mean? On every other web page of your wonderful site, you warn against using gut feelings. But when it comes to losing, you say you stop when it doesn’t feel good. Especially with video poker, I set a bankroll size, and I stop when I lose that. Losing always sucks, whether it’s 1 credit or 300 credits.

"Anonymous" .

You are right that I am not specific about money management. Unlike other gambling writers I do not put a lot of emphasis on how much to bet or when to walk away. For the recreational gambler there is no method of money management that can either add to or take from the house edge over the long run, so why dwell on it? So while I’m very specific on how to play your cards how much to bet is up to you. There should be some room for free will in gambling anyway. However I do say that if you’ve lost so much that gambling isn’t for fun any more then it is time to walk away.

I enjoy your site a great deal. This morning I was reading your reviews of online casinos and your experiences with them and it seemed you inevitably lost everything on your deposits. I found this discouraging. Then I saw that you requested donations and now understand why you do so!

"Anonymous" .

Since I started gambling on the Internet four years ago I am up about $20,000, about half of which is thanks to the Golden Palace. What you’re seeing in my reviews is just my most recent experiences, and like everyone else sometimes I lose for a month or two. However I just won $786 at Casino.Net and $2317 at Casino Kingdom. So I don't ask for donations to subsidize a losing gambling habit. Donations simply help me to keep offering this site to the public for free. Although in fact the donations come in through PayPal which I then usually use to buy things on eBay.

Does "cracking your knuckles" result in larger knuckles?

"Anonymous" .

Contrary to popular belief I think cracking your knuckles is totally safe. My chiropractor has cracked my back and neck lots of times and I’m better for it.

Many senior managers in casinos today have an educational background similar to yourself rather than coming up through the gaming floor. I was just wondering if, with your interest in gaming you had ever considered going to the dark side and making a move into casino management.

"Anonymous" .

I’m tired of professional gamblers referring to those who work in or for casinos as the "dark side." Casinos provide thousands of jobs across the country, revenue to government, and a source of entertainment to millions. I don’t remember the source but I read that something like 90% of visitors to Las Vegas leave with a gambling loss, yet 95% leave happy. The other side is quick to argue that casinos contribute to the problem of compulsive gambling. Yes, there are some compulsive gamblers who abuse what should be done in moderation. However I believe that the majority should not be denied the opportunity to place a bet because of the problems of a minority. In other words I believe that the benefits that come from legalized gambling far exceed the costs.

I fully admit I consult for casinos and gaming businesses. I have to because this site doesn’t make enough money to support my family. My bankroll is not large enough to make a living as a professional gambler. However I make no apologies for what I do. To answer your question, yes, if the right offer came along I would consider employment in casino management.

Have you ever received any dumb questions?

"Anonymous" .

Don’t get me started.

Boxers or briefs?

"Anonymous" .


Hi Mike, Just to lighten the mood a little, I remember watching you play roulette on a special Vegas Challenge show a while ago. Obviously you knew your expected value wouldn’t change regardless of strategy. I remember you playing only one number, but I forgot if you changed after a win. Not sure what I’d do in your situation, but out of curiosity, did you play the single number as opposed to an outside bet like red/black to maximize the variance? That way if you get "lucky" you’ll be ahead by the most? Anyway, I enjoyed the fact that you played a really conservative and boring strategy.

"Anonymous" .

You accessed my strategy quite well. I intended to bet the minimum through most of the hour to avoid the house edge grinding me down. The producer was not happy with such a boring strategy so I tried to act more excited than I normally would be. The reason I picked a single number as opposed to an even money bet is that I wanted volatility. I knew if I ended close to my starting point of $10,000 I would probably lose. So I wanted a bigger shot at getting ahead. I stuck with 23 the entire time, although towards the end I added 5 as well. I’m Glad you liked the show.

Since you are very well-known and respected for your expertise on gambling, statistics, house odds, etc, do local casinos still allow you to play at their Blackjack tables, since you obviously are an experienced counter?

"Anonymous" .

It is my policy not to count in Las Vegas. Since I live here I don’t want to make any enemies out of prospective clients. So I am allowed to play blackjack at all but two casinos locally. However last January I went to Reno and Lake Tahoe for a few days and was told not to play blackjack at four different casinos.

Recently, I was watching an episode of the new a "high-roller" playing, I believe, blackjack. Apparently started to lose more and more, he would tear up the cards! I would have thought this a severe breach of etiquette, if not some actual gaming commission regulation, but when asked to stop, he was insulted that they would ask him! Is this sort of thing generally tolerated and I've just never seen it, or is this guy just used to being allowed to get away with that sort of thing because he's losing tons of money, or something else entirely?

"Anonymous" .

Baccarat (at the big tables) is the only casino game in which players are allowed to damage the cards. An explanation I heard is that Asian players bend the cards anyway as they slowly peak at them that they only use each card once. Therefore as long as the dealer is replacing the cards after one usage the casino may as well let the players do anything with them. Being able to identify cards is of little value to baccarat players anyway because the dealer doesn't take a hole card (as the dealer does in blackjack) and the player has no choice as to whether to hit or stand. However, there are also gaming regulations that stipulate that the tapes must show all the cards in case of a dispute, which isn’t possible if the player tears them up first. In the show you mention the player didn’t know this and I think both parties handled it badly, which led to the hard feelings that the show captured. Had I been the casino manager I would have explained what I just said and then asked the player to lay the card face-up on the table before ripping it into tiny pieces.

On a related note yours truly will be on The Casino sometime this season. The story is some college students try to parlay $1000 into $5000 as quickly as possible. They seek my advice on how to do achieve this goal.

Update: That episode never aired. Probably because of me.

Do you have any new TV appearances soon? I seem to recall something about a blackjack team, so I’m wondering if it is next week’s show. (As an aside, American Casino on TLC is much much better than The Casino on Fox! Gambling and T&A don’t mix, in my book).

"Anonymous" .

Yes, I’m going to be on an upcoming episode of The Casino. I do not know the air date. In the show I serve as an advisor to some college students on how to parlay $1000 into $5000. About American Casino, I agree, it is a better show.

In general, how much time do you actually spend in casinos? Of that, watching/observing (as in your recently disclosed craps experiment) versus playing?

"Anonymous" .

It varies a lot but not very much to be honest with you. Some weeks I spend a lot and others none at all. However if forced to give an average I’ll say 2 hours a week. About 90% of that is actually playing. Rarely do I just observe. In fact for the dice setting experiment I was betting too, hoping the dice setters would win me some money.

Since you seem to be driven by house advantage, do you actually play for fun anywhere (whether floor games, machines or poker), or do you only do blackjack counting and/or video poker with progressives over a target amount? Or do you not actually play at all? I think a lot of your "readers" would be interested in that, but you may not want your hosts to know!

"Anonymous" .

The only time I might play for fun is if I am entertaining somebody visiting Vegas and am just out gambling with them. Otherwise I always look for an edge. I also play new games sometimes just to ensure that I understand the rules correctly. I don’t want to give away all my secrets but card counting and positive expectation video poker are definitely two games in my bag of tricks.

Quit gambling.

"Anonymous" .

But it is so much fun.

I would like to know if you put your real name, address, phone number, date of birth when you sign up in online casinos.

"Anonymous" .

Yes, to all of those things. If some of the shadier casinos find you provided false information they will use it as an excuse not to pay you. Besides, these pieces of information are not that hard to come by for someone looking to abuse or steal your identity. Recently Crazy Vegas casino asked for my Social Security number, which I thought was going too far. I gave them a phony one. When asked for my mother’s maiden name, by anyone, I give the name of my cat.

In one of your old columns, you mention a manuscript for a book that you wrote, that you were unable to publish. What was the book about? Is the manuscript available anywhere? I’m curious because about 20 years ago, I wrote a draft of my own book about odds and gambling, a sort of condensed and simplified version of Allan Wilson’s book. I wrote to Stanford Wong, asking him if he would look at my manuscript. He replied yes, but he would have recommend that I not bother to write the book in the first place. There were already too many gambling books. So I gave up on the idea of trying to publish my book.

"Anonymous" .

Yes, I wrote a gambling book manuscript four years ago. I shopped it around and only Huntington Press agreed to publish it. However three years and four revisions later and it still isn’t out. There is already a glut of gambling books on the market so I agree with Stanford to not waste your time. Since I wrote my original manuscript I have learned that the name of the author is much more important to selling books than the content of the book itself. A no-name has almost no hope of publish a book on gambling, or anything. If you want to publish a book you should do something else to become famous first.

[Update: The Wizard’s book Gambling 102 was published in Spring 2005.]

The Daniel Rainsong challenge made good reading. However after some thought I can only conclude that: 1. Daniel wanted a professional analysis of his system, to confirm for himself whether or not it had a positive expectation 2. Daniel concluded that risking $2000 for $20000 was clearly preferable to simply paying someone [like yourself] to analyze his ’procedure’. I don’t know what you charge to analyze a game, but I am confident it would be more than $2000 in this case. If so, using the Wizard’s Challenge was a very smart choice -- no matter how small the chance of success. Nevertheless, your decision to accept the challenge and decline the surrender was an even smarter choice! The final irony is that this story will probably result in MORE ill-conceived systems. What do you think?

"Anonymous" .

I offered a straight no-bet analysis to Mr. Rainsong for $1000 but he declined. He felt very strongly that he would win. The less evidence there is for anything, the stronger the faith of the believers. I charge more than $2000 to analyze most games but this was just a simulation. All I had to do was modify my existing blackjack simulator to fit the rules of this procedure. Not surprisingly Mr. Rainsong has had lots of interested buyers in his system despite the fact that it failed my test. All I can do is tell the truth that systems don’t work over the long run. Whatever the masses do with my advice is up to them.

If you were playing $50 per play, what would you personally chose between these two games of video poker (assuming both games have the same pay schedules and you bet the maximum of 5 coins for each hand): single-play at $10 or ten-play at $1 per hand? Thanks for your time and consideration.

"Anonymous" .

Mathematically they of course have the same expected return. However I would play the 10-play because the volatility is less and I think it is more fun.

Thank you for the education! I appreciate it. One thing you must get asked a lot, but is absent from your site is... How much have you made from gambling? With such a life's dedication, has it paid off? Or is there still an edge to the house, even with your experience and knowledge? Or do you make money but your winnings are still not enough to produce a significant cash flow (i.e. enough to happily live on)? Further, if you had all the money you desired, would you still teach, consult and educate?

Kelly B.

I spend a lot of time analyzing bets and do okay at it but it isn't enough to live on. Last year for example bets I made won $26,843.14. However I lost $9,491.50 backing other gamblers where I thought I had an advantage. I'm working on increasing my bankroll and more research in profitable areas to hopefully making gambling a greater portion of my income in years to come. It should be emphasized that gaining an edge over the casino is possible but requires a lot of hard work for fairly small advantages. Assuming I do reach the day where I can live off of gambling I still plan to keep the website going and teach my casino math class at UNLV. However I'm trying to phase out of consulting and hope to give that up completely as soon as other income replaces it.

I read about how your Ties Win Blackjack is on field trial in Laughlin, Nevada. What kind of permit is required and how much did it cost?

"Anonymous" .

A new game trial period permit was required. This is opposed to a "variation" permit, which is less expensive. For a new game the cost is $3000, I had to fill out lots of forms, including an employment and residence history going back 20 years. The waiting time was six months, which was shorter than what I was expecting.

I’ve finally accepted a job in Vegas, and the family will be moving in less than a month. What areas of Vegas are nice to live, what areas are undesirable?

"Anonymous" .

For family living the nicest areas are indeed Henderson and Summerlin. Personally I live in a master planned community called Peccole Ranch, which borders Summerlin. In my opinion the west side, where I live, is better because:

  1. It has an Orange County, California, look and feel to while much of Henderson looks like it was made from a cookie cutter.
  2. The west side is higher in elevation and thus cooler in summer.
  3. Henderson suffers from the noise of landing airplanes.
  4. The west side is right next to the mountains, which offer outstanding hiking and climbing.
  5. The future growth of the west side seems to be better planned.

If you ask someone from Henderson they will claim Henderson has less traffic, but there are two sides to that issue, and I think the west side is better in that area too. I’m sure I will hear from somebody from Henderson over this, and am happy to print a rebuttal in the future, because I believe in presenting both sides.

The worst parts of Vegas are around downtown, gradually getting better as you move further away. For something in the middle there is lots of growth on the south side of town along the I-15 and the north side along the U.S. 95.

Are you a Packers fan at heart? I am. It looks like you are betting with your heart and the packers are killing your great NFL picks. Great percentage even with the packers not coming through for you. Just thought you might like the observation.

Stan from Coconut Creek

The reason has nothing to do with team loyalty. My program rated them the fifth best team at the close of the 2004 season, and that I carry that power rating over into the 2005 season. However maybe it is too slow too react to recent history. Something for me to think about.

Dear Wizard, you go to great lengths to explain the odds and why they are always in the casino’s favor. This being the case, why would anyone gamble?

Mike from Miami

Because it is so much fun!

You have made it known that you use card counting in casinos. Why do casinos let you still play in their casinos?

Jason from Boston

I was recognized in Reno when counting once, although it may have been by dealer who knew me personally and tattled. It is a long and bizarre story. Aside from that I don’t play often, nor for high stakes, so the threat I pose is fairly small and not worth the fuss of memorizing another face.

As a dealer, I hear a lot of "Fuzzy Math" from players and always come to your site when I have a question about the odds of a game. I only offer advice when asked because in my view, it’s their hard earned money and they can play however they see fit. My question is, when you sit at a table and hear someone say something mathematically incorrect, do you cringe but keep silent, or do you correct them?

Mike from Vegas

I cringe and keep silent. It is my policy to not offer unsolicited advice. Why pick an argument? Also, I’m not trying to convert everybody to proper strategy. The casinos need some bad gamblers to subsidize the good ones.

I’m a long-time fan. Thanks for keeping it fresh. I just watched a show on CGTV (Canadian Gaming TV) called "Casino Life" that dealt with Caribbean Stud Poker. The host of the show gave kudos to you and your site and your strategy for this game was presented on the show. Later, I saw that you were credited. Does this generate income for you or is it just good press?

Peter from Ottowa, Canada

Thanks for the kind words. Yes, I gave Casino Life permission to use my material. I’m happy they gave me a good plug. No, they didn’t pay me. I also have never been paid for my appearances on the Travel Channel here in the United States. I do it for the fun and the publicity.

On the ’Vegas FAQ’ show on the Travel Channel, you recommend the 9-6 Jacks or Better machines. However, the machine that you showed was a short pay 9-6 machine because two pair only paid 1 instead of the normal 2 giving the house an extra 5% advantage. Changing the value of two pair from 1 to 2 is a common trick by the casinos to increase the house edge.

"Anonymous" .

I knew somebody would eventually write about that. It wasn’t I who showed that machine. The producers didn’t understand I was referring to 9/6 Jacks or Better. Later in the editing room they showed somebody pointing to a 9/6 Double Double Bonus Poker game, which has a return of 98.98%. That is much worse than 9/6 Jacks or Better, at 99.54%. An embarrassing moment for me, much like the many incorrect edits I had no control over, in my old Casino Player articles.

Do you have any opinions about presidential futures? I.e., betting on which candidate will win his/her primary or the general election? Is there any way of calculating the house edge? Would you ever consider making such wagers for real money? Personally, I think that watching the current betting lines may be better than polls to predict election results. Do you think there’s any validity to them?


Yes, I do indeed bet on elections. In 1996 I made my biggest bet to date on Clinton over Dole at even money. That was also one of the best bets I ever made. I have been betting every election ever since, most of the time against friends. At major online sites that take political bets, I think it is a close to efficient market. In other words, I think the market is basically right, and the odds can be used to estimate the probability of each candidate winning. Currently I think that TradeSports is a good source for election odds. As I write this, on September 29, 2007, the odds given equate to the following probabilities of victory.

Republican Primary

Candidate Probability
Giuliani 40.0%
Thompson 8.4%
Romney 28.5%
Paul 6.7%
McCain 7.0%

Democratic Primary

Candidate Probability
Clinton 71.0%
Obama 12.3%
Gore 8.2%
Edwards 4.9%

Party to Win

Candidate Probability
Democrat 63.0%
Republican 35.8%
Other 1.2%

You can use my sports betting appendix 5 to calculate the overall house edge of any type of futures bet. For politics, my hunch is that betting on the favorites is probably the better way to go, in general. For example, I would be happy to buy a contract on Hillary Clinton if I had an account at TradeSports. Just my two cents.

I read that Warren Buffet (the world’s third richest man) complained that he only paid a 17.7% federal tax rate, while his secretary paid 30%. This seems outrageous to me. Can you comment?

Joe from Nashville

Normally I would say this is out of my area. However, as a former government actuary for eight years, I know a thing or two about taxes. From what I’ve read, most of Warren Buffet’s income is defined as capital gains, which is taxed at only a 15% rate. Like it or not, the tax laws allow it. What puzzled me is why his secretary was paying as much as 30%. According to this video, he was counting “payroll and income taxes.” By “payroll taxes” he obviously meant Social Security and Medicare taxes. Let’s see if 30% is a reasonable total federal tax rate for his secretary.

In 2007 the highest tax bracket was taxed at 35%, but that only applies to income above $349,700. The income up to that point is taxed much less. Let’s assume his secretary is single, with no dependent children, and her salary was $100,000. First, let’s subtract the minimum deductions. In 2007 the standard deduction for single filers was $5,350. The personal deduction was $3,400. So, we’re left with $100,000 - $5,350 - $3,400 = $91,250 in income subject to income taxes. For single filers in 2007, the tax rate was 10% on the first $7825 in income, then 15% up to $31,850, then 25% up to $77,100, and 28% up to $160,850. So, her income tax would have been =0.1×$7,825+0.15×($31,850-$7825)+0.25×($77,100-$31,850)+0.28×($91,250-$77,100) = $19,660.75. That is only 19.7% of her income. All my assumptions like her income, filing status, and not itemizing worked against her, or for a higher tax rate.

Now let’s do Social Security and Medicare. In 2007, the Social Security tax was 6.2%, up to incomes of $97,500, when it completely shuts off. The 2007 Medicare tax rate was 1.45%, with no cap. So, her combined Social Security and Medicare tax would have been 6.2%*97,500 + 1.45%*100000 = $7,495. Counting those taxes, her overall tax rate would have been ($19,660.75 + $7,495)/$100,000 = 27.2%. Still we’re 2.8% short of 30%.

My best guess is that she is also considering the fact that ultimately she is the one paying the employer’s matching Social Security and Medicare tax. For those who don’t know, Social Security and Medicare taxes are really double that deducted from your checks. The employer pays the other half. However, some, including me, would argue that ultimately it is the employee who pays both. If the employer didn’t have to pay that tax, he would have more money to pay his employees. It is easy to feel that way when you’re self-employed, like I am, and have to pay both shares. If you double the Social Security/Medicate tax, the rate is now ($19,660.75 + 2×$7,495)/$100,000 = 34.7%. I assume the 4.7% difference is because she makes less than $100,000, is married, has dependents, itemizes deductions, or some combination.

The Social Security and Medicare taxes would not apply much to Warren Buffet. First, the Social Security cap of $97,500 would be insignificant to him. Second, those taxes apply to wages, not capital gains, as he defines most of his income to be.

So, that is my best guess as to the math behind Mr. Buffet’s statement.

Update: Shortly after this column appeared I received the following response. In the interests of fairness, I present the following argument that Mr. Buffet is paying too much in taxes.

I read with interest your answer to the ’outraged’ person who thinks it is so unfair that Warren Buffet pays less percentage in taxes than his secretary. I was disappointed in your answer, which does not correct the misinformation that implies that Mr Buffet pays less tax than his secretary.

First, as you noted, investment income is indeed taxed at 15%. This is in effect double taxation as the earned income that Mr. Buffet invested was taxed at his marginal rate of 36%. Comparing apples to oranges (work income vs investment income).

Second, one should not look at the percentage. In gambling terms, one should look at the ’payout’ instead. I am very certain that Mr. Buffet paid millions of dollars in taxes in the same year that his secretary paid thousands of dollars. Shouldn’t your reader be more outraged that one citizen of the country is paying 1000’s of times more than other citizens for the same government services? Once could just as easily say "I heard that Warren Buffet paid 1,000,000 times more taxes than his secretary, that is outrageous!"

Just thought I’d point out that only looking at "percentage" and not "actual payout" is a fallacy. Similar to many of your gambling fallacies.

Best Regards,

Kevin A. (Dallas)

Hello, I am a seventh grader from Hawaii. I am doing a science fair project on poker and shuffling. I am using your charts about the win percentage of pocket Texas Hold ’Em hands, according to the number of players in the game. I was hoping you could answer a few questions that would help me with my project:

  1. How did you come up with the percentages found in the charts?
  2. If you used a computer program, how did you develop it and how long did it take?
  3. You stated that you started the Wizard of Odds as a hobby. Did experimenting change as your site became more well-known? Why or why not?

"Anonymous" .

  1. The two-player table was done by a brute-force looping program, that cycled through all 1225 possible opponent cards, and 1,712,304 possible community cards. For three to eight players, looping would have taken a prohibitive amount of time, so I did a random simulation.
  2. I write almost all my programs in C++, including both programs I just mentioned. The rest are in Java or PERL. I mostly copied and pasted code from other poker-based programs. The new code only look about a day to write.
  3. Yes, I started my site as a hobby in June 1997. It wasn’t until January 2000 that I accepted advertising, and tried to make a business out of it. It has gone through three different domains over the years. Here is what it looked like in May 1999. The purpose of the site has always remained the same, a resource for mathematically-based gambling strategy. Through the years, I have just been adding more games and material. One experiment was providing my NFL picks for the 2005 season, which was an abject failure.

Hi, I understand you’re busy so no worries if you can’t find the time to respond. I’m currently a math major at UNLV and am looking for some kind of direction relating to what to do with my life once I graduate. I’ve searched quite a bit for this information, and have definitely come up short. It seems the general idea here is that a math bachelor’s degree is quite useless, and that I should have been an engineer instead of a mathematician. I’m not very interested in being an actuary, because I don’t want to take additional time to pass the exams. Since I will probably stay in Vegas after I graduate, it seems that a great idea would be to work for the gambling industry, which you seem to have much experience with. Could you offer me any advice or direction?

Christina from

I can sympathize with your dilemma. When I graduated in 1988 with a bachelor’s degree in math and economics, I had no idea what to do with it. The actuary exams looked daunting at the time, because I didn’t study statistics deeply at UCSB, and somehow I didn’t feel actuarial work was my calling in life. However, after accomplishing absolutely nothing for a solid year after graduation, I gave a second look at the actuary exams. With the help of a tutor, I gave the exams the old college try, and passed the first three with high grades in a little more than a year. That eventually led to nine years of actuarial work at the Social Security Administration, where I finished the rest of the associate exams. That said, I offer the following advice.

First, don’t dismiss the actuarial field lightly. If you are smart enough to get a math degree, you are smart enough to pass the exams. Maybe you’ll need to teach yourself some statistics, but I think you can do it. Actuarial work may not seem terribly exciting, but the profession is consistently highly rated for good working conditions and compensation.

Second, at least consider the National Security Agency. They hire lots of mathematicians to analyze a sea of chatter gathered from listening in on phone calls all over the world. If you take their screening test, don’t volunteer too much information or let them fluster you. This comes indirectly from people who flunked it.

Third, most mathematicians in the gaming business work for the big slot machine companies. There are not a lot of jobs in that field, but not that many people know such jobs exist either. Contrary to what many people think, the casinos don’t hire designated mathematicians. Overall, I think actuarial work is better paying and more interesting.

Finally, don’t put down a math degree. You’ll probably never use what you learned in the more advanced math classes, but the accomplishment itself shows you should be able to learn what you’ll need to for an entry-level position in any one of the fields I mentioned.

Thank you for the opportunity to win an autographed copy of your book by predicting the exact score of the Super Bowl. However, isn’t the expected value pretty low? I figure the probability of winning is about 1 in 300.


I think the odds are better than that with a good educated guess. Here is my basic strategy for picking the exact outcome of any NFL game.

  1. Using the total and spread, estimate the total points of each team. For example, if we use a total of 57 and a spread of -5 for the Super Bowl, letting c=Colts points, and s=Saints points then...

    (1) c+s=57
    (2) c-5=s
    Substituting equation (2) in equation (1):

    The problem with stopping here is sometimes you get values that are unlikely to be scored by a single team. For example, the probability of a single-team total of 24 is 6.5%, but the probability of 25 is only 0.9%. The table below shows the single-team total probability, based on the 2000-2009 seasons. So we’re going to estimate the total points for each team based on realistic combinations of field goals and touchdowns.

  2. Assume the favorite kicks 2 field goals.
  3. Assume the underdog kicks 1 field goal.
  4. Subtract the field goal points from each. In the Super Bowl example, this would leave Colts = 25 touchdown points, Saints = 23 touchdown points.
  5. Divide touchdown points by 7, to get estimated touchdowns. c=3.57 TD, s=3.29 TD
  6. Round the estimated touchdowns to the nearest integer. c=4, s=3.
  7. Following this method, we get for total points c=(4×7)+(2×3)=34, s=(3×7)+(1×3)=24.

Using this method on all 6,707 games from the 1983 through the 2009 seasons would have resulted in 69 correct picks, for a success rate of 1.03%. The last time it would have been right was the Titans/Colts game in week 13 of 2009. That game had a spread of Colts -6.5, and a total of 46. The score was Titans 17, Colts 27.

One critic thought a better and simpler strategy would be to pick the nearest significant one-team total for both teams. Using such a method resulted in 51 wins only, for a win rate of 0.76%. In my opinion, splitting the field goals 2 and 1 between the stronger and weaker teams is important.

Single-Team Totals in the NFL2000-2009 Seasons

One-Team Total Total in Sample Probability
0 93 1.75%
1 0 0.00%
2 0 0.00%
3 148 2.79%
4 0 0.00%
5 2 0.04%
6 114 2.15%
7 210 3.96%
8 9 0.17%
9 76 1.43%
10 316 5.96%
11 9 0.17%
12 49 0.92%
13 289 5.45%
14 238 4.49%
15 55 1.04%
16 170 3.21%
17 373 7.03%
18 33 0.62%
19 92 1.73%
20 368 6.94%
21 234 4.41%
22 64 1.21%
23 218 4.11%
24 347 6.54%
25 47 0.89%
26 103 1.94%
27 282 5.32%
28 159 3.00%
29 52 0.98%
30 127 2.39%
31 242 4.56%
32 23 0.43%
33 57 1.07%
34 164 3.09%
35 76 1.43%
36 27 0.51%
37 68 1.28%
38 108 2.04%
39 11 0.21%
40 21 0.40%
41 62 1.17%
42 31 0.58%
43 6 0.11%
44 24 0.45%
45 33 0.62%
46 1 0.02%
47 7 0.13%
48 28 0.53%
49 15 0.28%
50 1 0.02%
51 5 0.09%
52 7 0.13%
53 0 0.00%
54 2 0.04%
55 1 0.02%
56 4 0.08%
57 1 0.02%
58 1 0.02%
59 1 0.02%
Total 5304 100.00%

This question was raised and discussed in the forum of my companion site Wizard of Vegas.

Congratulations on your 50-mile unicycle ride challenge for your 50th birthday! Now that you can cross that one off your list, what are some other challenges still on it?

"Anonymous" .

Thank you for asking. For the benefit of other readers, I challenged myself to ride a unicycle 50 miles within eight hours by my 50th birthday. I am proud to say that I achieved it! In fact, 53 miles in 7.5 hours. I have a very long and boring video about it.

To answer your question, high on my list is to do the Fargo Street challenge on a unicycle. For those who don't know, Fargo Street is the steepest street in Los Angeles and second steepest in the United States. I already easily did it on a bicycle on July 18 as a test run and made a video of that.

Besides that, here are some other challenges on my bucket list:

The next to be completed should be Mount Rainier and Pico de Orizaba after that. Here are some peaks I have already climbed.

I saw that that YouTube video where you allegedly solved the Rubik's Cube on a unicycle. However, I submit for your consideration that you faked it. I think you used two Rubik's Cubes and had a solved one in the pocket of your hoodie. When your back was turned to the camera, you switched them. Fraud!

"Anonymous" .

I'm never offended by a healthy degree of skepticism. To satisfy those skeptics, I created this follow-up video. Enjoy.