Dominated Ace

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When I got my first computer back in 1996, I wondered where the huge number-crunching ability all computers were supposed to have could be found. I somehow envisioned myself figuring the value of pi to 7 million decimal places, but had no idea if the computer could do it, or even how to go about making such a calculation, even if my machine was capable of doing so. Well, of course computers can do stuff like that. For me, it's done in the amazing program called Excel by Microsoft and now that I (finally!) know how to use Excel, it crunches all kinds of numbers, far beyond my imagination.

Although this article is about Poker, you're going to see an entire series of articles eventually appear here that will fall under the umbrella of "Excel For the Advantage Player". Most people don't like the mathematical aspects of casino gaming as much as I do, but by showing you how to use Excel, most of the pain associated with the math will hopefully be eliminated. Calculations like standard deviation, variance, combinatorial analysis and other mathematical functions are performed by Excel in literally the blink of an eye, if you know how to program it correctly.

And that's what I'll show you here: how to program Excel to give you the answers you seek. For starters, I thought it would be interesting to see just what the chances are that your hand of Ace-whatever is "dominated" by another A-x hand (the "x" means any other card). By dominated, I mean that you and an opponent share the Ace, but his kicker - the second card in his hand - may be higher than yours. Of course, if you already have an A-x hand, the probability that your opponent also has an A-x hand is reduced because the deck contains only three Aces at that point, instead of the usual four. But, it's still possible for him to have it and if you have any experience with the game at all, you know players will hold on to their Aces with a death grip. I wrote about that in Lesson 22, "Playing With Ace Huggers" and this lesson will supplement that by giving you some solid numbers as to the probability your hand is the best when comparing A-x hands.

Knowing the probability that your A-x hand is best is important at anytime, but I think it's crucial to know this once you get to the point in a tournament where you're facing just one other opponent. Needless to say, in a heads up situation, any hand with an Ace in it is capable of winning the match, but there's still the possibility that your opponent has you dominated, so before you go all-in at least know what your odds are.

Before I get into the specific chart, let me show you a few simple calculations that Excel can do when it comes to Poker hands. The vast majority use the combination function, which is COMBIN in Excel programming language.

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