Page 25 - April 2013 • Southern California Gaming Guide

Bill Burton: About Gambling
PLossibilities and Probabilities
ast night I met my friend Rich at the casino. We hadn’t gotten together for a while, so we decided to play video poker so we could talk and catch up while we played. We had been playing about twenty minutes when Rich let out a yell. I
looked over and saw that he had a Royal Flush on his screen.“It’s a natural! It was dealt to me. at’s the rst time that I was ever dealt one. What are the odds?” he said.
I told him the odds of being dealt a natural Royal Flush are one in 650,000 hands. is is only the mathematical probability of being dealt a natural. It does not mean that you will be dealt a natural every 650,000 hands. e mathematical probability of drawing to a Royal Flush is much better at one in every 40,000 hands. ese gures are based on playing computer optimal strategy with each draw giving you the best mathematical return.
Standard Deviation
Of course, nobody will get a Royal Flush in exactly 40,000 hands. It may happen in a fewer number of hands or it may take a longer number of hands. e easiest way to illustrate this is with the simple coin ip.
three standard deviations covers 99.7% of what can happen.
e formula for calculating standard deviation uses square roots and other algebra equations. e main reason to have a general understanding of standard deviation is so you will have a more realistic expectation of what you might encounter when playing a game like video poker.
When you ip a coin 1,000 times, the odds are 50/50. But instead of ipping 500 heads, we look at the standard deviation to get a truer range of the outcome. One standard deviation is about 68%, so we can expect that we will ip
casino sessions. I know about how many hands I play per hour, so I can get an estimate of the hands that I have played.
I estimated that I played about 285,000 hands without a Royal Flush. is placed me in the upper end of two standard deviations away from the norm, and since the majority of this play was at the same casino, had I not had an understanding that this was just a normal part of the distribution curve, I could easily had jumped to the conclusion that the machines were rigged. I often hear this from some skeptical players when I explain that droughts are not as uncommon as they think.
Lightning Strikes Twice
After Rich and I talked about the odds of his drawing a natural Royal Flush, I told him that the one thing I miss with coinless machines is hand-paid jackpots (unless I win $1,200 or more). Although I don’t miss waiting for a hopper ll when I’m cashing out, I do miss having slot attendants counting out hundred dollar bills. Maybe this is because the time spent waiting to get paid gave me more time to savor my win. Now, with ticket machines, it just adds your winnings from your Royal Flush, and you’re free to play your next hand. I no sooner said this, than Rich yelled again. is time he had held two cards and drew his second Royal in a matter of 20 hands. He just looked at me and said,“If I had to wait for a hand-paid jackpot, I never would have gotten my second Royal!”
Point taken. I couldn’t argue with him there.
Until next time, remember: “Luck comes and goes... Knowledge Stays Forever.”
Bill Burton is the author of 1000 Best Casino Gambling Secrets and Get the Edge at Low Limit Texas Hold’em available online at billburton.com. Burton is also an instructor for Golden Touch Craps: thecrapsclub.com.
e odds of ipping a coin and having it land on heads are 50/50. However, if you ip a coin 100 times, it would be rare to come up with exactly 50 heads and
50 tails. You could possibly come up with 75 heads and 25 tails. is is because the sampling of only 100 ips is very short, and anything can happen. If you ip a coin 1,000 times, it is still unlikely that you will have the same number of heads and tails.
“The formula for calculating standard deviation uses square roots and other algebra equations. The main reason to have a general understanding of standard deviation is so
you will have a more realistic expectation of what you might encounter when playing a game like video poker.”
somewhere between 452 and 548 heads.
Now we can use standard deviation to calculate the range of drawing a Royal Flush based on the number of hands we play. If you were to play 200,000 hands of video poker and the probability of drawing a Royal Flush is one in 40,000, you would expect to get ve Royal Flushes. But due to the standard deviation, your actual number of Royals will uctuate.
We can illustrate this by taking 100 players who will each play 200,000 hands of video poker. At the end
e reason for this is
a mathematical principle
called standard deviation.
Standard deviation is a
statistical value used to determine how spread out the data in a sample is, and how close individual data points are to the mean — or average. Some of you may remember in your high school days seeing a demonstration of ping-pong balls being dropped down a board similar to the Plinko game on e Price is Right television show. e majority of the balls group in the center, while others bounce to the left or right of the center forming a bell curve.
of that time, 68 of the players will have drawn between 2 to 6 Royal Flushes which is 1 standard deviation; 26 players will have drawn 0 to 8 Royals, which represents 2 standard deviations; and the other 6 players would have drawn from 0 to over 8 Royals. Since we can’t have a partial person I have rounded o the number of players in this example.
Droughts Happen
I have gone over a year between Royal Flushes. Although I didn’t count the exact number of hands I played, I do keep a log of the amount of time that I play during each of my
One standard deviation will cover 34.1% of the curve to the left and right of the center line, or a total of what will happen about two-thirds of the time. Two standard deviations cover what will happen 95% of the time, and
APRIL 2013
SOUTHERN CALIFORNIA GAMING GUIDE
PAGE 25