On random numbers

Let’s start with a quick quiz.

  1. Pick a number under 10
  2. You throw a die 5 times. What’s a more likely outcome? 1 2 3 4 5 or 2 1 4 3 3?
  3. You flip a pure coin three times. The outcome is H H H – what are the chances of the next flip being heads?
The ultimate in random numbers - a die

The ultimate in random numbers – a die

So, what did you pick?

  1. 7? Congratulations, you’re not alone. About 45% of the people asked about a number “between 1 and 10” will pick 7.
  2. Did you say “they are both equally as likely?” Congratulations!
  3. A pure coin, not a weighted one, will have a 50% chance of heads, every single time. Yes, there’s a 1/16th chance of having heads four times in a row. But that’s when you start out with nothing. After three times heads you’ve already weeded out 14 of 16 permutations… giving you a chance of 50% to make it H H H H.The problem with random numbers is (a) it’s really hard to get truly random numbers, and (b) if it doesn’t “look” random people won’t believe that it is. Throwing 1 2 3 4 5 with one die is not more or less likely than a “random” sequence of numbers, or five sixes (or five ones, for that)

Does it matter?

Well, if you play online games that depend on chance, it does. Consider Backgammon. A double in backgammon counts double. So a double six is really four sixes and getting two or even three in a row can turn the game quite around.

Now, how do you play backgammon online? Do you trust your opponent? “Dude, believe it or not but I totally just threw double six. Again.” Of course you wouldn’t. I wouldn’t.

Enter a service like Games By Email where you can play various games, at your own pace, against opponents. Including games that rely on random things like dice throws. As a neutral party, one can expect Games By Email (hereafter called GBE) to be a neutral party in this, right?

Well of course, unless your opponent does get those three of four doubles in a row. Obviously there’s some sinister scheming going on! “But I’m using a Mersenne Twister to generate dice throws!” Well then, never mind that the chances of getting four doubles in a row are only 1 in 1296 and you’re producing thousands of dice throws per day… Obviously your algorithm is wrong!

A brute force solution

So, what do you do then? You build the dice-o-matic, a Rube Goldberg contraption that can generate a freakish 1.3 MILLION dice throws per day. And you post a video of that machine to prove that your dice rolls are actual dice rolls, to quiet the critics.

Then you read the youtube comments. “LOLZ ur an idiot. Dont u know u can use the mersenne twister 4 that? lolz”

Sometimes you just can’t win.

DISCLAIMER: I’m not affiliated with Games By Email nor the Dice-O-Matic. Stumbling on the Dice-O-Matic on youtube my first reaction was “why?” but after reading the description I could totally understand it. Given the many comments about “a computer can do this just as good, dude!” one can only conclude that understanding math is apparently a lot easier than understanding the human mind.