As an engineering student (and a pool player) I had a healthy interest in gambling in my early adulthood. My main interest was in how it worked, how it could be beat, and ultimately why anyone would ever do it! Betting on pool and other games of skill like state fair games and crane games is different, so in this section I’ll just talk about conventional gambling like craps and blackjack.


Blackjack is an irresistible lure to a budding software engineer. It’s one of the most analyzed gambling games and can be analyzed in deep detail by computer. I grew up just as this was becoming possible and my generation were the first to be able to create our own simulations on personal computers. These were great fun and the ultimate success…. ZZzzz was to confirm the published odds. Testing systems was also fun but of course proved useless. The real fun was to come with craps.


With craps I actually did some clever work. It wasn’t unique but it involved a fairly subtle discovery that was very interesting, and it came in handy many years later.

Craps held a special allure to me because multiple bets can be made simultaneously and their outcomes made to depend of the same rolls of the dice. This uniqueness makes it very tempting to look for a system (combination and/or sequence of bets) that affect the odds of the game, hopefully even changing a negative expectation game to a positive one in the way that card counting does for blackjack.

While playing with the math of craps and trying to calculate the odds and how they were affected by systems of simultaneous bets I made a discovery that I had never read in any book.

I had become well acquainted with the different ways to calculate odds, vigorishes, house advantages, and so on with craps. I would look at all the different ways of betting and verify that my calculations matched the published odds and vigs precisely.

A “discovery”!

One day I learned some special rules about place bets. First a place bet could be made at any time. Second it could be suspended or continued on a  come-out roll. And third it could be taken back at any time! There seemed to be more degrees of freedom with this bet than with the pass/don’t pass and come/don’t come bets. That gave me the idea that maybe some combination of place bets and line or come bets could result in different odds than either alone, hopefully better, hopefully in the player’s favor. But I wasn’t naive and I knew it was an academic exercise.

I was thwarted at first. But then I had an idea. The six and eight place bets had a house advantage of 1.52%. A seven roll loses either bet. And you could place either or both at any time and take either or both down at any time. So what if you placed both bets simultaneously, then when either bet won you collected your winnings and then took both down. Both bets would be contributing to the chance of winning, but once either won, you could remove the other from risk.Would this affect the odds I wondered?

The calculation of the odds was very easy. The formula for determining the house edge was straightforward and had to be right. The math showed clearly that when both were played together in accordance to the strict rules of this system, the odds were clearly better than either bet on its own! It reduced the house odds down to about 1.04%!

I hadn’t found a way to beat the game but I had discovered a way to improve my odds simply by combining two bets in a creative way. That was a thrilling result. My first reaction was that it might just be the beginning. Maybe there was a combination that could produce odds that were actually in my favor. But that hope was short-lived. And it didn’t take much research, once I knew what to look for, to discover that of course my technique had been well known and discussed in better craps books. And most disappointing of all was learning that the true house edge of the two bets really were independent after all. The apparent reduction in the house advantage was actually a mathematical artifact of sorts. What was happening was that I was in effect creating a new bet which could be resolved in fewer rolls than either of the original place bets. By exposing the bets to fewer rolls in which they were at risk, the vigorish of the whole bet really is reduced. However, the vigorish in terms of house edge per roll was exactly the same. No actual advantage was gained. And of course the end result is that NO system of simultaneous bets could ever decrease the house advantage (but some could increase it).

Debunking a Craps System

Many years later I was talking to an old fixture in the pool hall and he described his craps system to me. He claimed it couldn’t lose. And he attributed all of his great wealth to it. He described the system to me and I found it really interesting, and compelling. I could certainly see why he believed in it. But of course I knew better, and I knew I could figure out what the catch was. I had a lot of experience with craps.

I went home and figured it out, then I returned to explain it to him. Of course he’d have none of it. He’d made up his mind. Math and reason, no matter how well explained, could never change his mind. But the system was so interesting, and the debunking of it so interesting, I decided to write it up. Maybe somebody would be interested like I was. At any rate it would be fun to try to explain in detail. Explaining something very complex to a layperson is a great and useful challenge. And I always admired people like Carl Sagan, Richard Dawkins, Brian Greene, John Gribbon, and Richard Feynman who could do it well. So it was fun to try my hand.

I wrote a long detailed article for a blog I had been working on. It took months to get right.  It was a fun project and I am proud of it to this day. I doubt anyone has ever read it in detail. However, I did write to Professor Michael Shackleford author of the top gambling web site Wizard of Odds. A couple years later, he commented on it and posted an endorsement and a link from his web site!

My blog article is here: Debunking a Craps System

The article got hundreds of comments! But to my dismay, horrible dismay. Every single one of the comments was from someone with a useless system of their own, or someone dense enough to believe in a system. It was a complete debunking, a thrashing of a purported system. It concluded and proved that all systems are garbage, marketed only to the naive and gullible. Yet those were the only people who read it! And not one seemed to reconsider their views. I eventually started deleting the dumb posts.My insightful article proving that gambling was useless appeared to end up promoting the abuses it was debunking. That experience contributed to one of my Big Three insights (see here).


I never gamble anymore. I won’t risk a thing unless the odds are in my favor.

  • I play trivia in a casino where the reward is cash but the cost is nothing.
  • I play an occasional game of pool or bags for modest sums, but only when I have a reasonable chance to win.
  • And I’ll buy a single lottery ticket on occasion.

But in general, I’ll never play blackjack or craps or slots. My fascination has subsided and my tolerance of a losing bet is gone… but I don’t rule out someday discovering a way to turn the odds.

In games of skill, turning the odds in my favor is easy. But it’s not something I’ll do in good conscience. On occasion someone will try to hustle me at pool or bags. I’ll know almost for certain I can beat them easily, but I normally won’t take advantage of them. It doesn’t feel sporty, much less right. But if they’re cocky enough and obnoxious and the stakes are small I’ll agree to play for a few bucks or a round of drinks (my soda isn’t always free). When I do I’ll tell them honestly I think I’m a much better player and they should expect to lose. And they almost always do.

Turning the tables in real gambling is a lot harder and more questionable. I read what Phil Ivey did to the Borgata. I found it brilliant, and seemingly legal, maybe even “right” in a way. But I’m not sure it’s something I’d do myself. It makes for great conversations though.

I’ll stick to gambling on myself.