Who Said Maths Can’t be Fun

It is weird to think that gambling is usually seen as a light and easy activity, not heavy on the mind and exercised by not the smartest bunnies out there. At least that’s the general overall impression. But if you stop for a second and think, most of the games of chance (and even more so the ones that require some skills, like poker) are based on pure mathematics – probabilities, chance, chaos theories – that’s all science and it can be really fascinating if you look into it. So for today’s post I’ve decided to look at maths from a bit of a different angle than the usual boring one and uncover some really interesting things about numbers. Check it out.

You Think You’re Special? Not as Special as a Deck of Cards

Now you may have heard the bizzare fact that when you shuffle a deck of 52 cards, you will end up with an order that no one else has ever had before. Ever. In history. No kidding. Now, you may think it’s crazy but hear me out. Let’s start with the first card in the shuffled deck – it has 1/52 chance of being a particular card, right? Then the next card behind it has a chance 1/51 of being any of the remaining 51 cards. Then you add another one. And another one. So the odds add up and to save you the calculation – you have 132,600 possible combinations of just the first three cards of any deck. Adding the fourth card takes that up to 6,497,400. So for the total of 52 cards that’s 8.0658X10⁶⁷ (phew! That’s 62 digits of a number. Fancy!). And to put things in perspective, we can’t really assume how many times cards have been shuffled in human history (we exclude the possibility of aliens playing to make life easier), but let’s make the odds obscenely in our favour and say everyone (and by everyone I mean every single person in the history of Earth) has been shuffling decks of cards full time, all life long, still, the number of times is not matching the number of possible combinations. So, if ever you want to feel unique and special – shuffle a deck of cards – it’s the only combination like the one you end up with for all times!

What on Earth Monty?

If you haven’t heard of the Monty Hall Problem…well, you’re lucky and I am just about to ruin it for you.
That paradox really bugged me for quite some time. Now, it is said to originate from some American TV show. Imagine you have 3 doors. Behind one of them there’s a prize, the other two hold nothing. You can pick one. Now, logically, your chances to grab the prize are 1/3. So off you go, you take a pick. The TV host (or whatever) then opens one of the remaining 2 doors – it turns out empty. So suddenly, there are just two left, one of which is your choice already and one definitely has a prize behind it. The question is – should you change your choice? Before you go bananas, rest assured there have been quite a few scientists being skeptical and in disbelief about what I am about to say. And it took convincing them with computer models replaying the situation until it is statistically confirmed. So, point is, you do actually have better odds if you change your choice.

Most people (me included) would think that once an empty door is out the way, your chances have increased to 1 in 2 automatically. Wrong. Your door still has the 1/3 chance. It’s the remaining other one that has shifted its chances to 2/3. I know, sounds crazy but it’s true.

The Mandelbrot Set

I am going totally geeky here but hear me out. You know those crazy people that would tell you maths and numbers are beautiful? I know, you wonder how. Well this might just give you an idea and a sort of a sneak peek into the way how scientists see the subject of their interest – we see dry numbers on a screen or a piece of paper. They see this:

You probably wonder what this is. The so called Mandelbrot set is a collection of numbers with the use of a simple formula (z -> z² + c). The crazy video above is a graphical representation of that – it is not created or designed by anyone– it is just those numbers going on forever, visually represented. Life suddenly makes more sense, right?

So there. Now you can go and have a deserved rest, spin some roulette or something, I don’t know, just try not to think of the numbers behind it all, hey!