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I’ve made no secret of the fact my columns are targeted to the average player. I mean absolutely nothing bad about this.

While some people can take exception to be considered average, in this case, I mean that vast majority of people who go to a casino to play. They don’t have advanced math degrees. My father, Lenny Frome, thought the same way. That is why he called his strategy Expert Strategy as opposed to Perfect Strategy. He knew in some cases the strategy he presented was not perfect. Instead, it was one that could reasonably be learned by the average player.

Strangely enough, most casino game inventors aren’t overly skilled in math either. It really isn’t surprising to me. Inventing a game takes a certain level of creativity that not all math minds have. We tend to be overly analytical and thus creativity is not always a strong point. At the same time, creativity without some analytical thought around it can lead to a disastrous game design.

I recently met with a game designer who had a brand new idea for a game. (Obviously, I cannot discuss any of the aspects of the game itself at this point). His idea for a sidebet was fairly novel and it was not necessarily obvious how often the winning event(s) would occur. For simplicity he assigned a payout of 20 to 1 for a single winning event. If his guesstimate was correct this would mean the event would have to happen about 4.5% of the time.

This would create a payback of 94.5%. This would also mean the event would happen about 1 in 22 hands. The game is dealt so all the cards are community cards (like baccarat). So, all the players who make the sidebet win or lose at the same time. He didn’t see a problem with this win frequency.

In a blackjack setting it might be a little low, but doable. There are six or seven players at a full table and thus, someone will win (or at least have the winning event even if he doesn’t make the sidebet wager) on average every three or four deals around the table. But, if the game is dealt with a single hand applying to all, a frequency of 1 in 22 means a winning hand 1 in 22 deals around the table. This is about half an hour on average.

For most situations, it is rather easy to calculate the probability of the number of deals between the sidebet hitting. I can give a long chart to the inventor explaining what this means. But, I’ve found it easier to simply use a rule of thumb that has proven to be quite useful, which I call the rule of three. It is meant to be just a guide to help either an inventor or player. For the inventor, it is used to make him realize his sidebet, which should occur on average 1 in 22 hands, will very likely happen between 7 (22 divided by 3) and 66 (22 multiplied by 3) hands.

If a game is dealt at a rate of 40 hands per hour, it now means there could easily be a gap of more than an hour and a half between wins. This could be problematic to the inventor. How likely will a player play a sidebet if he sits down for an hour or two and sees it maybe once?

Now, this doesn’t mean it will take an hour and a half, only that it will not be considered the least bit odd or some form of outlier for it to take this 90 minutes. It might also hit seven hands a part and thus hit three to five times in an hour, which might make it the most popular game in the casino. The inventor can use this information to help guide him in developing his sidebet.

A player can use this rule of thumb to help guide him when he plays. A similar frequency exists for hitting Quads from Trips in video poker. When we use this guide we find, about 68% of the time, a player will go between 8 and 70 occurrences of Three of a Kind before hitting Quads. Ironically, a good deal of the remaining 32% is actually the ones between one and seven, but it is really the high end I’m more concerned with.

This is the end that tends to bother players. No one complains when they hit Quads three out of seven times from Trips. But, if you go 30, 40 or 50 hands you start to get antsy. The reality is, it is not unlikely to go 70 hands without hitting one (seems like I’ve gone about 200 lately!).

The specific likelihood would be impacted by the actual volatility of the outcome. As the examples I used here were not very uncommon events, we find there are a large number of times even more common than the 1/3 of the time measure. If we were talking about something more rare – i.e. a Progressive, we would find a more even distribution.

Knowing what to expect is a key component of Expert Strategy and this is one of those rules of thumb that can help. It is not perfect math, but it something that can help you play expertly.

About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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