Math in the casino isn't always simple
December 01, 2015 3:00 AM
by Elliot Frome
I’ve always been good at math. Well, at least for as long as I can remember.
When I was 8 or 10 years old, this meant I could quickly add numbers together. When I got to my pre-teens, it meant I could quickly multiply numbers together. I still have these skills.
I don’t expect everyone to be able to multiply two two-digit numbers together, but the number of times I hear someone ask something like what’s 500 divided by 25 and not be able to do the math in a split-second is mind boggling.
I’ve always been willing to take the time to try and explain any concept to anyone who wants to listen and/or asks the question. This past week, I dealt with something like this twice.
The first person had a question about Royal Flushes at a full-table of Texas Hold’em. Was the frequency altered because the players used five community cards? In short, the answer is no. The long-term frequency is not changed, but the volatility is.
While the odds of two players getting a Royal Flush in a 7-card deal (without community cards) are quite rare, it goes to absolutely impossible in a Texas Hold’em game. The only exception is if the community cards form a Royal, in which case all nine players will have a Royal, not just two.
One out of 21 Royals at a Texas Hold’em table will form this way. At that very moment, nine Royals will happen simultaneously. How does this not affect the overall frequency? Well, because of all the other times.
As I just said, there is zero possibility only two players get one in the same hand, and unless the community cards contain at least three to the Royal, there is zero chance. In essence the Royals will clump together a bit more than with no community cards (when these cards form a Royal) and they will be a bit more rare the rest of the time. The long-term result is that the frequency of a Royal will be the same, they’ll just group together at times.
Unfortunately, the other situation was a bit more exasperating. I received an email expressing concern that a particular game with two independent sidebets had a problem. Each of the sidebets on their own was fine, but if the player wagered on both of them, then he transformed the game so there was a player advantage.
My very first reaction was not a chance! First, if this was the case they wouldn’t be independent sidebets by their very definition. To make matters worse, the email contained an attachment both explaining the issue in words and a spreadsheet walking through the math. A casino was frantic and we needed to confirm that, in fact, there was no player advantage.
This was one of those cases where a little bit of knowledge is a dangerous thing. This was not someone merely inquiring about the possibility of something. Instead it was someone who hit the fire alarm button and made everyone panic for a few minutes until cooler heads prevailed.
Somehow the author of this faulty analysis came to his conclusion because sometimes the player wins both sidebets with the same hand. Further complicating the matter, he decided that wagering one unit on each was the same as wagering two units on a “combined” paytable of sorts.
I’m guessing if I showed the spreadsheet that was attached to most people, they’d look at it and say it makes perfect sense and there must be a player advantage here. Fortunately, this issue finally made it across my desk where I was able to untangle the web that got created.
Lost in the analysis were the situations where the player won one of the sidebets and lost the other. In these cases the player would win the payout indicated and have the one unit wagered on that sidebet returned (payouts were TO 1). But, he would lose the other wager.
By combining the paytables and the wager, the math was now altered. If he won either of the two wagers, the entire two units bet were returned to the player. This led to a significant increase in the payouts to the player and the belief there was an advantage.
I would’ve preferred to deal with this second situation as a simple inquiry rather than a casino in full panic mode. Nothing scares a casino like the potential of having a game with a player advantage. This is one of those cases where it would’ve been better to leave the math to a professional.
Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Email: ElliotFrome@GamingToday.com.