What do random coin tosses look like?

In my last post, I showed you my attempt at faking 40 coin tosses.

Let's take a look at what happens if we generate the coin tosses in excel

Excel Generated Data Run 1

Here is the data

Tails,Heads,Tails,Heads,Heads,Heads
Heads,Heads,Tails,Tails,Tails,Tails
Tails,Tails,Heads,Tails,Heads,Tails
Tails,Tails,Tails,Tails,Heads,Heads
Heads,Tails,Tails,Heads,Tails,Tails
Heads,Heads,Heads,Heads,Heads,Heads
Tails,Tails,Heads

Fun facts about this data set.

• Longest Tails Sequence is 6
• Longest Heads sequence is 6
• 44% Tails vs 56% Heads

And this distribution looks like this:

There are a few points to be noted on this:

• Sequences are quite long (6), in the fake random data we only generated sequences of 3
• The distribution is not 50%, more heads were generated (eventually over time, it'd be closer to 50-50, we'll prove this later

Excel Generated Data Run 2

Just for fun, i thought, i'd do another run and this is what it looked like

Tails,Heads,Heads,Tails,Heads
Tails,Tails,Heads,Heads,Tails
Tails,Tails,Tails,Tails,Tails
Tails,Tails,Tails,Tails,Heads
Heads,Tails,Heads,Tails,Tails
Heads,Heads,Heads,Tails,Tails
Heads,Heads,Tails,Heads,Tails
Tails,Heads,Tails,Tails

Fun facts about this data set.

• Longest Tails Sequence is 10
• Longest Heads sequence is 3
• 62% Tails vs 38% Heads

And this distribution looked like this

Again the point is, with very small datasets, the data won't be evenly distributed 50/50.
Eventually over a large sample it will eventually become statistically correct.

As I said in a previous post.  Random data doesn't necessarily look like random data.

There are a few points to note though.

• If I set my excel to say Red or Black (for roulette), how many of you would think that Black (tails) was a hot color?   
• How many people would say after 6 tails, well we're due a head?
• Do you really want to play a doubling up betting pattern such as martingale (discuss in a future post) when we have sequence of 10 tails.

We'll discuss a lot of these concepts later but it's thoughts to think about.

In the next couple of posts:

• We'll look at generating longer sequences (and see the stats regress towards the mean (i.e. end up around 50%).
• We'll also look at what happens with physical coin tosses

Don't worry, we'll get to roulette and other games.  But these concepts are important to understand before we get there and get blinded by the games.