Hot numbers in roulette

I'm not gonna name the site but I was looking at yet another person peddling their roulette strategy based on tracking numbers (no genuine advantage play).

Basically, you stick in the last 6 numbers and voila, it will tell you where to bet.   If the wheel spins 3, 4, 5, 14, 15 and 17.   You should probably bet on 19-36, cause those numbers are due....

Just for fun, let's see how that looks in the Excel Simulator

The Random Numbers

This is what my Excel Random Number generator produced (feel free to replicate this experiment yourself)

3, 14, 9, 9, 3, 21, 35, 3, 29, 0, 19, 36, 4, 9, 5

The distribution

Oh look the number 3 came up 3 times (surely that's a hot number)????  BTW, that was sarcasm.   We know enough about random numbers now to know that that can easily happen.  However this could be an interesting blog post in the future.   Hot numbers.

What might be more interesting is the ranges, which is what they were betting on in this system.

Their system was either avoid betting on 1 to 12 because it's hot.  but it might have been bet on 1 to 12 because it's hot.

There is no hot....  It's just some random numbers.   nothing is due or not due....

The kicker

And here was the kicker.  Don't worry, if you lose, just martingale and it'll recover your losses.

And we know how that ends...

Anyways, you know my thought on this sort of thing already.  I could type up their system into Excel and formally disprove it.   But you can always do that yourself if you want.

We know enough about random numbers, streaky numbers and martingale to know this is a silly strategy.

For more info on Martingale, read my martingale post (and feel free to download the excel tool)

For more info on streaks, read my post on streaky coin tosses

For generating roulette numbers in excel, read my post (or look at the martingale one)

How to calculate streaks in excel

So in my last post, i showed you how to look at streaks for coin tosses in Excel

In this post, i'll show you how i calculate the streaks in Excel (or google docs).   You can use the same technique to calculate streaks in anything (i.e. roulette).

What is a streak?

For coin tosses would be the same coin be thrown X times in a row.  e.g. 7 heads in a row would be a streak.

What does this look like in Excel?

First thing we need to do is track the length of a streak.   This is how it looks for me in Excel.

1) In the left hand column is the result of the coin toss (heads or tails),  you can generate this randomly using the technique described in my blog post, generating random coin tosses in excel

2) The right hand column tells the length of the streak.   As you can see in the image above, every time the streak ends, the count gets reset to 1.  If the latest coin toss is the same as the previous it increases

How do I calculate this in Excel (or google docs)?

I've used the following formula to calculate this.  I put this in each cell in the B column

=IF(A2=A1,B1+1,1)

Column A is the column with the result of the coin toss

Column B is the length of the streak.

This formula basically says, if the current coin toss is the same as the previous coin toss then increment the streak count by 1.   If the coin toss is different from the previous, reset the streak count to 1.

Summarizing the Data

Now that we've got the streaks.   We want a summary of the data.  This is how it looks in Excel

And this how we calculate it

1) Left column is a just count of the streaks (just enter 1 to 15)

2) Right column is calculated by the following formula

=COUNTIF(Sheet17!B2:B20001,A2)-B3

This formula counts up all the entries in the range that meet the IF condition.  In our case, we look at our 20,000 coin tosses that we've held in Sheet 17 in cells B2 to B20001.   The condition it needs to meet is the value in the A column (i.e. the length of the sequence, in this case A2).   So for row 10, it will count up all the sequences of length 9.     Now obviously a sequence of 9 will also count all the sequences of 10's.   So we subtract that number that's next in the sequence.   We don't want to count all the 10's in the 9 sequence count (that's the -B3 bit).

And then we can generate a chart against the distribution, i used a nice bar chart

Anyways, i hope this is useful.  This technique is pretty useful for predicting monte-carlo predictions of betting patterns and proving how bad things like martingale are.   And if you develop some advantage play system in blackjack, roulette, sports betting then this technique will allow you to calculate streaks.

Hope it helps.

Streaky coin tosses

In the previous post we looked at how the data distribution gets closer to the real probability as the number of samples increase.   And we showed this happened in our excel generated random coin tosses.   What we didn't look at was how streaky the coin tosses were?

A streak is considered as the same coin toss in a row i.e. Heads, Heads, Heads, Heads.   Would be a streak of 4 heads.

So what happened in our 20,000 coin tosses?

As we can see above, we get lots of long streaks.   Actually we get 14 tosses of the same side in a row.    That's quite a streak.   

And that curve looks quite appropriate.  It's a binomial distribution and one that looks like it should for a 50/50 probability.

At another time, we'll discuss binomial distributions and the probability of coin tosses.   But for now, lets just say, a streak of 14 is quite normal.   :)

Loss Recovery betting plans aren't looking so good now.

Do we really wanna talk about Martingale / loss recovery betting patterns?   Really?  Ummm ok, we can.   Are you sure you're expecting a black just because the last color was a red?   Are you sure you're owed a black.   Are you sure 10 reds in a row is unusual?  Looks pretty normal to me.

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.