Losing run

[MattR]

Question on expected longest losing runs here. If something (over a sample of 500) has a 25% chance of happening what is the longest losing run you should expect statistically speaking, and also the longest winning run?

[vegyjones]

When my losing run stops, I'll let youknow how long it is :yikes:

[mathare]

Ahh, probability questions, love 'em.

The easiest way to do this is to work out the probability of losing/winning runs of various length and then stop when you decide the probability is too small to be worth worrying about.

P(W) is the probability of a win, 25% here. P(L) is then the losing probability, so 75%. These are better expressed as 0.25 and 0.75 as we will need to multiply them up several times later and it's easier with them as decimals.

1 time in 4 (on average) you'll have a winner, with the other three being losers.

A losing run of 1 occurs 75% of the time then, yeah? Nope. A losing run of 1 only occurs when you have a loss followed by a win so the probability of a losing run of exactly 1 is P(L) x P(W) = 0.75*0.25 = 0.1875 (3/16).

Similarly a losing run of two will be in a sequence LLW so P(L) x P(L) x P(W) = 0.75*0.75*0.25 = 0.140.. (9/64)

And so on. It is common for people to forget to end the run with an opposite result so quoted figures can often be significantly out.

I suppose, technically speaking, by extension the losing run should be preceded and followed by a winner so the probability of a losing run of exactly 1 is 0.25*0.75*0.25 = 0.0468..

Something like Excel can probably help you here, let me have a play and get back to you...

[MattR]

Thanks Mat, interesting stuff. Look forward to your findings!

[Stewards enquiry]

Obviously no help. Deleted.

[mathare]

OK. Excel can be used but only in as much as it's a glorified calculator.

The probability of a losing run of length exactly N is P(L)^N * P(W)^2.

In Excel speak the formula would be:

=POWER((1-$B$1),$B$2)*POWER($B$1,2)

I will post a spreadsheet of examples when I have double-checked this as the numbers coming out don't seem right to me at the minute

[mathare]

What we are looking at here is Bernoulli trials, and a quick Googling of that might help explain the theory behind it a bit better.

Anyway, I have attached an Excel version of the numbers. Just tinker with B1 and B2 accordingly.

[MattR]

Thanks a lot for that Mat, very helpful. Some rep coming your way but it seems I have to spread some around first, (can't you just see Vegy whoring for it on here in a minute? :D )

[vegyjones]

13 minutes actually, but I'll make it easy for you

CLICK HERE (http://www.win2win.co.uk/forum/reputation.php?p=334276)

[DigbyDigger]

Here is a link to an article on losing runs, and a simple little table of the longest possible losing runs that you can expect from various strike rates.

http://www.free-bet.co.uk/betting-article-display.asp?id=22

Philip.

[Win2Win]

Now I'd usually rollick a newbie for breaking forum rules by posting alink without permission, but as it is very useful, I'll let it go.

I recommend everyone prints it off.

[Profit Seeker]

Well spotted, in time Ooo

[Win2Win]

Record :D