Math of probabilities in table games similar to sports
August 28, 2014 2:59 AM
by Elliot Frome
When I tell people I do gaming math for casinos, the usual first question is, “You mean slots?”
I’ve actually never done math for a slot machine. While I’m sure there are aspects of slot math that make it more straight forward than it might seem, I have heard people refer to slot math as a proven product.
I mean there is really nothing that stops a slot company from taking a proven machine based on one theme and merely changing the theme leaving virtually all of the math elements the same.
Further, slot mathematicians have a clear advantage over table games. They can make up all the frequencies. If they want a particular combination to occur 1.2345787674% of the time, they just make it happen. With table games, which are predominately cards, we’re stuck with whatever probabilities the random occurrences bring us.
That said, these probabilities are still completely known and finite. Even where the models are very complex, we can estimate to within a few hundredths of a percent, which is good enough. I can’t imagine what it must be like to figure out probabilities about sporting events – although it sounds like a really fun proposition (no pun intended).
The number of variables that go into the calculation must be astounding. And many of these variables are based on pages of statistics that have to include lots of assuming. In baseball, they must take into account past performance of specific hitters against specific pitchers. They have to take into account if the players are hot or cold. Essentially, I think sports gambling math is to table slot math!
This entire topic is on my mind because of a conversation on Facebook today. A friend who is a diehard Yankees fan was commenting on their chances to make the playoffs this year. He was not hopeful based on where they stood and how they had been playing lately.
A second friend agreed. A third friend, however, came on with rosy predictions of how the Yankees were about to turn things around, go on a long winning streak and take the second Wild Card in the American League. I’m a Mets fan, so I know all about being overly optimistic.
I keep an eye on the Yankees (one of two or three teams as a Mets fan I root against). Was it possible for them to make the playoffs? Sure. Was it likely? As objectively as I could look at it – no.
The optimistic friend remarked the Yankees needed to play .650 ball (win roughly 2 out of 3 of their remaining 37 games) to take the Wild Card. I ran some numbers (purely mathematical) and came to the conclusion this was no guarantee they would overtake the other four teams.
This didn’t matter to our fan. Then, of course, there is the part that says what is the likelihood a team that has been playing .500 ball for the first 125 games would become a .650 team for the final 37?
So, I did what most anyone would do it my position. I went to Google and ran a search on “probability of Yankees making the playoffs.” Now, I can’t speak to the credibility of the sites I stumbled on, but a couple I checked had relatively similar answers – 3%.
I’m going to take an educated guess and say this isn’t some fan in the room taking a guess at it. If I had time today, I could’ve checked some local sports books to see if they had any specific odds on this proposition. These guys aren’t making wild guesses either.
Somewhere, there are a team of programmers combined with some serious sports number crunchers who are putting every imaginable variable into a program and coming up with this number of 3%. With this, they can set the appropriate odds in the sports books (say 30 to 1?).
Back to Facebook, where our overly optimistic friend was virtually “guaranteeing” the Yankees will make the playoffs. He told me to come back and check with him in 2 to 3 weeks.
I remarked back to him it was his over confident attitude that had helped build the billion dollar casinos here in Las Vegas. He told me he doesn’t gamble. So, what is the cost of this over-confidence? I guess only bragging rights.
My father used to joke that you should never bet on any event where the participants have two legs. He felt this was mainly because you never know what is going on in the player’s lives that might impact performance.
I suppose horses and dogs might have bad days, but doubt they are prone to having their spouses cheat on them or need to deal with a kid’s illness. I think the second component of this is many sports bettors have favorite teams and tend to get overly rosy in their predictions of how they will do.
As a Rams fan, I know I find it hard to pick against them in my football pool (no point spreads), which can be quite costly while the team is going 2-14. It is not just a wild guess when the sports books set them up as a 10 point underdog!
The second key point is, as I said earlier, the probabilities in sports betting are a bit less exact than for table games. But, they are still very educated “guesses” when they are set. So, there might be some argument for playing a “hunch.”
Table games have no guesswork. There are absolute probabilities and they do not deviate. Table game results do not vary because of the day of the week, the weather, the pitcher, the quarterback or if the dealer is having a bad day (that might ruin your enjoyment of the game, however).
There are specific probabilities assigned to every outcome and thus the strategy of how to play is clear. There is absolutely no room for “overly optimistic” predictions or you’ll just be one of the people who contributes that much more to the next billion dollar casino.
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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. Contact Elliot at ElliotFrome@GamingToday.com.