# The Math of It All

/ Last month, a game inventor that I met at last fall's Global Gaming Expo posted a comment on a *Linked In* message board regarding gaming math. He noted that as a relatively new inventor the first question he is always asked is if the math on his game was done and who did it. The majority of the rest of the thread dealt with the value of using a company like Gaming Laboratory Inc. (GLI) for the math given that their approval (or a company like them) is required in many jurisdictions to put a game out on the floor. GLI is a very reputable and talented company. In the end, most seemed to agree that GLI is a good answer if your game is complete and you need math mostly confirmed. If you simply have a game idea that needs a lot of back and forth, you may find GLI to be a bit costly and you might be better with a math guy/consultant, such as myself or one of several other well known analysts.

Today's column is not about the merits of GLI vs. anyone else, but rather the overall importance of having the math worked out before you get too far with any game. Many years ago, I received a call from an inventor who described a game he had sort of created on the fly for a charity even the week before. It was relatively easy to figure out the payback of the game, but the game could not easily be changed in ways to fine tune the payback. He was very excited about the game as it had performed very well at the charity event. Unfortunately, the game had a payback in the mid-60% range. This would make it illegal in most (if not all) jurisdictions. People didn't mind losing money for a charity. I doubt it would perform as well in the NOT not-for-profit arena.

And, as I said, the game was structured in a way so that changing the payback was not so easy. Fortunately, before calling up casinos, he came to me. I was able to explain to him the issues of the game from a mathematical perspective, long before he convinced some casino manager about the game. How embarrassing it might have been to get a casino all excited about a game only to find out that it wasn't really a viable game at all. If you're really hoping to invent casino games, you may find that you never get another chance to even pitch one if you make this big of a mistake!

Roger Snow, the SVP Table and Utility Products of Bally Technologies, and perhaps the most prolific inventor of table games always tells me how he is a slave to the math. If the math doesn't work, it simply doesn't matter how much fun the game is to play. When I work with Roger, we will frequently spend weeks 'fishing' as he likes to call it. We'll play with some ideas and just run some frequencies without even a betting structure. It is not always just about the payback. Hit frequencies, Fold frequencies, Play frequencies, Raise frequencies and a whole host of other numbers are critical to a games success.

Ironically, over the years, many inventors have discovered that sidebets can actually help make or break a game. The base game might be pretty good, but casinos like to see as much action as possible and Players like the higher payouts that most sidebets offer. Creating a sidebet out of a 6-card game can sometimes be challenging. If you pay for Two Pair or better, the hit frequency will be about 20% which is a relatively high frequency. If you start at Three of a Kind, then the frequency drops to about 7.5% which is a bit low. Nothing can change these frequencies. They are the distributions of a 6-card deal from a 52-card deck. If you are building a game around a 6-card deal, you have three choices. You can go with a low hit frequency like 7.5% but can offer more robust paybacks. You can choose a higher hit frequency of 20% but the payouts are going to be a bit weaker. Or, you can attempt to find a solution in the middle by paying for SOME Two Pairs. But, it can be very confusing for some Players to know what you mean by paying for Two Pairs "8 over" or "10 over" or worse yet - "8 over 4's"!

When you are dealing with a deck of cards, you are not in control of a lot of the numbers. Some exist as a result of the nature of randomly dealt cards from a deck. Many inventors - unless they are poker players - are pretty clueless to some of these frequencies. As a result, a game may sound much more appealing than the math will allow it to be.

If you are interested in inventing a game, the idea is half the battle. The other half is the equally important math that goes with the game. I do recommend that you work with someone who has knowledge both of the industry and of math and someone who can help you mold your game idea from just an idea into a viable casino game.