Page 8 - February 2003 • Southern California Gaming Guide

SOUTHERN CALIFORNIA GAMING GUIDE
Column: Video Poker with Bob Dancer
Page 8
February 2003
Evaluating Ace$ Bonus PokerTM by Bob Dancer
Aces Bonus Poker is the same as 8-5 Bonus Poker, with one addition. Usually when you end up with four aces, the game pays you 400 coins. But if you end up with, in order, X A♠ A♥ A♦ A♣, or A♠ A♥ A♦ A♣ X (where “X” represents any other card in the deck), then you get paid 4,000 coins rather than 400.
The question becomes: How do you gure out how much this is worth? And, if you do play the game, what strategy variations should you use?
This will be a math lesson. For some of you, this math is much too hard or boring. Fine. Skip this article and come back next month when the discussion won’t be so technical. But many of you will be able to follow along and apply the lesson to other games, too.
Bridge players will nd the speci c order of the suits easy to remember, as will those who can gure out “reverse alphabetic order,” but most people will ignore the suits themselves and concentrate on the big yellow letters A, C, E, and S, that IGT has super- imposed on top of the card images. I’ll talk about just the superimposed letters because they are simpler to deal with.
The critical thing to realize in order
to make the problem manageable is
that it is really two separate problems.
The rst problem is: Once we have
four aces, what are the chances that
they are exactly in order ACES? The second problem is:Oncewehavetheacesinorder,whatarethechances that the “X” (i.e., the fth card) will either be to the far left or the far right? Once we’ve answered each of these questions, we will multiply their probabilities together. (Those of you who’ve had some probability theory back in school somewhere will remember that when both probabilities have to happen at the same time, multipli- cation is the correct procedure.) What we will end up with is how many four-ace hands qualify for the bonus.
So, the rst question. Given we have four aces, what are the chances that “A” comes rst. Obviously, 1 in 4. Now, once we have four aces with the rst one being
“A”, what are the chances of the second one being “C”. Again, not too hard. It’s 1 in 3. And we have only two aces left, so it’s 50-50 (i.e., 1 in 2) that they’ll be in the right order. Multiplying these together (1/4 times 1/3 times 1/2) we see that, if we have four aces, it’s 1 in 24
that they are in order ACES. To prove this to yourself, youmightwanttowriteouttheother23.(ACSE,AESC, AECS, etc.). Do that and you’ll become convinced that
1 in 24 is correct.
Now the second question. Once they’re in ACES
order, what are the chances that the “X” will be at one end or the other? If you look at ve side-by-side boxes (representing the ve spaces that the ve cards can be in), you’ll see that the “X” can be in two good spots (one at either end) and three bad spots. In other words, 2 out of 5 times we have the sequence ACES correct, we also have an “X” on an end. Multiplying 1/24 by 2/5, we get 1/60. That is, one in sixty times that we get quad aces will we receive the bonus.
So how much is this worth? Assuming that 4,000 provides a bonus of 3,600 every 60 times (because we’ll get 400 the other 59 times), we see the bonus adds an average of 60 per set of aces. (That is, 3,600/60 = 60)
Receiving 460 per ve coins means receiving 92 per coin. Now we need to plug this number into a computer program.Ilike“BobDancerPresents WinPoker.” Click on ‘Bonus Poker,’ and change the value of four aces from 80 to 92, and one minute later the computer will tell you that the game is worth 99.4%.
Not bad. Certainly better than 8/5 Bonus Poker by itself (returning almost 99.2%), but not as good as 9/6 Jacks or Better (returning over 99.5%). And the 99.4% is correct if we make no strategy changes
whatsoever to take advantage of the 3,600 coin bonus. Actually one strategy change is appropriate. Let’s see what it is.
Normally when we start with a pair of aces, it is about 1 chance in 360 to complete the 4-of-a-kind. But that’s when we don’t care which speci c position each ace
ends up in. When we are dealt two aces in ACES order, it is 2,163 to one against getting the bonus. This is a long enough shot that there are no strategy variations to make. If it comes, it comes. When we are dealt three aces in ACES order, however, we now are getting close. It is only 46 to 1 against getting the 3,600-coin bonus, so we certainly should break up a full house and go for it. 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 reports, strategy cards, videos, and the award-winning computer software, Bob Dancer Presents WinPoker, and a brand-new book Million Dollar Video Poker. Dancer’s products may be ordered at www.bobdancer.com.