There are only two reasons to travel to Las Vegas. Gambling and Las Vegas Showgirls! Both, it must be said, pretty good reasons. It was during my last such visit to ‘glitter city’ that following a fair amount of success at the former I had a chance encounter in the street with one of the latter.
I was doing the normal tourist thing, you know, walking down ‘The Strip’, looking up. When I bumped (quite literally) into the most awesomely beautiful woman I had ever seen. I mean this girl was amazing, the poise and grace of a ballet dancer (although at 5’11” considerably taller) long slender legs that seemed to stretch all the way to her armpits and masses of gorgeous auburn hair that cascaded over her shoulders like brightly coloured bracts of bougainvillea.
It was at this point that I said what any well bred Englishman would say under similar circumstances. “Excuse me madam, I do beg your pardon!” You have to understand I was in awe. Well, instead of being mad (as you might expect after some big lump has just trodden on your million dollar toes) she merely smiled sweetly and said, “you’re English aren’t You?” “Yes, that’s correct, how very perceptive of you. Was it my accent that gave it away?” I replied. “No, it’s the fact that you’re clumsy and you’ve got bad teeth!” With that she disappeared down the strip, in a mass of auburn locks and Chanel Number 5. As I stared after her open mouthed, a strange thought came over me. How do I get this girl to marry me?
Now I know what you’re thinking, what has all this got to do with the National Lottery? Well, I’m glad you asked.
Because I was still pondering this titillating question two hours later in the Sports bar at the Aria Resort & Casino with my mate Rob, when he turned to me and said. “You’ve got as much chance of marrying any of those Las Vegas Showgirls as of winning the National Lottery.” Then he turned away, took another sip of his ice cold draft beer and we sat there, in silence, pondering which of these two scenarios actually offered the greater odds.
So let’s start with the National Lottery. Basically in order to win the jackpot you are required to pick 6 out of 49 numbers (or you were when I first wrote this.)
If we say that the amount of combinations I could set for any amount of numbers is N (n!). For example, the amount of times I can set 6 numbers is 6x5x4x3x2x1=720 or simply 6!
We will assume therefore, that I have a total of N objects and I have to choose from them K objects, the number of times that I can do it is subject to the fact that I have to select the same numbers more than once each time. Meaning…
It doesn’t matter in what order I choose these numbers that increase my winning option by 720 times because I have k!
So, the final formula to work out my winning chances (according to Rob) would be…
If I implement this formula in order to get 6 numbers out of 49, my chances would then become…
49*48*47*46*45*44* / 720
We managed to work out then that the chances of winning the National Lottery were (at that time) 1:14,000,000. If though, the lottery was made up of only 45 numbers then my chances would be…
This example shows you that if we were able to take out only four numbers my chances of winning the lottery would be nearly double.
Now it took me and Rob the best part of three and a half hours to work all this out. All the while we were quaffing deliciously cold beers being served to us by the Aria’s genial barman Lenny. Needless to say we never actually got around to figuring out the true odds of my marrying any Las Vegas Showgirls. One thing I can be sure of though. My odds in that department may not be all that good, but it’s pretty damned sure there isn’t 14 million of them!