Page 10 - November 2005 • Southern California Gaming Guide

SOUTHERN CALIFORNIA GAMING GUIDE
How Often Do Things Happen? by Bob Dancer
This month’s article is on simple video poker mathematics. Let’s assume you are playing a game where, on average, you hit a quad (i.e., a four-of-a-kind) every 400 hands. Further, let’s assume you play for a total of 1,200 hands. I’ll arbitrarily say that it takes you two
hours to complete the 1,200 hands. How many quads can you be expected to end up with over that number of hands?
It appears obvious that the answer should be three times, but this is the wrong answer. To get the correct answer, we need to look at the binomial distribution, the results of which
e distribution, of course, is the same as rst given. Just because we had a bad day says absolutely nothing about what our score will be the next day. ere is no tendency to either “once you start running bad you keep running bad because you’re an unlucky player” or“you’ll get more quads the next day to make up for the shortfall.”
Now let’s assume we change machines halfway through. Now the distribution of the quads expected over the 1,200 hands is:
Is this distribution beginning to look familiar? It should. Changing machines has nothing to do with changing the distribution.
In this discussion so far, we’ve said nothing about skill. We are assuming players are playing perfectly. If players play imperfectly, the distribution will change. For example, on a hand like K♥ K♠ 4♦ 4♣ 5♥, it is correct in almost every game to hold KK44, although many seat-of-the-pants players playing games where two pair only returns even money, incorrectly hold just the pair of kings. Making this kind of mistake systematically will improve your chances for hitting quads, but cost you overall. e reduced number of full houses you get by holding only one pair usually far more than compensates for the increased number of quads.
Bob Dancer is America’s best-known video poker writer and teacher. He has a variety of “how to play better video poker” products, including Winner’s Guides, strategy cards, videos, and the award-winning computer software, Bob Dancer Presents WinPoker, his autobiography Million Dollar Video Poker, and his recent novel, Sex, Lies, and Video Poker. Dancer’s products may be ordered at www.bobdancer.com
appear here:
What this says is that 5% of the time you won’t hit any quad, 17% of the time you’ll hit four, 2% of the time you’ll hit seven, etc. These numbers don’t tell you which quad you’ll
hit. Just how many.
the probability of getting one fewer quad than typical is virtually the same—actually 22.4135%, which is slightly less.
We could, I suppose, call getting either zero or one quad as “bad luck,” getting two, three, or four as “typical luck.” and getting five or more as “good luck.” It doesn’t change anything by assigning terms dealing with luck to the results. To me when some-
body asks me “how much skill and how much luck was involved” in describ- ing whatever happened yesterday, my answer is often, “I have no idea.”
Let’s assume that on this particular day in question, we don’t hit any four-of-a-kind. Definitely worse-than- average luck, but it happens about one day in twenty. It’s slightly rare, but not extraor- dinarily so. Now the question is, since you’ve just gone through worse- than-average luck, what will be the distribution of quads for your two-
hour session tomorrow? For this, the following distribution will hold:
“One of the interesting accurate, but not really features of this distribution
These numbers are
precise. For example, the chance to get exactly three quads could more precisely be written as 22.4322%, but that is far more precision than we need for today’s discussion. It looks like they only add up to 99%, but that’s rounding error and also not important for today.
Another typical feature of the distribution is that
One of the interesting
features of this distribu-
tion is that the number
of quads that we think
we “should” get, namely
three, actually occurs less than one time in four.
is that the number of quads that we think we ‘should’ get, namely three, actually occurs less than one time
in four. Another typical feature of the distribution is that the probability of getting one fewer quad than typical is virtually
the same.”
Page 10 November 2005
Video Poker with Bob Dancer