# Numpty probability question from a non-mathematician

Discussion in 'Mathematics' started by duncx, Nov 15, 2011.

1. ### duncx

Thanks for the replies folks - I've already considered and understand most of what's been said, I also followed about half way through answer 5 and then lost the plot (Subjectknowledge - you are clearly mad and need to get out more!).
I still think I'm right that in a truly perfect dice, 100x6s has the same probability of being thrown as any other sequence - surely this is correct?
However I have come to this conclusion as to why we might believe (other than it seems obvious common sense!) that the dice is loaded. Any sequence thrown that uses all the numbers clearly CAN NOT be the result of a loaded dice - it MUST be a good dice, but any 100x6s sequence COULD be a good dice or COULD be a loaded dice. So, the 100x6s throws shows that the likelyhood that the dice is loaded is higher than for seemingly random sequences. How's that for a layman's explanation? Anywhere near the mark?
Now, I must get those books....

2. ### bobboots

If you roll a dice 100 times it has to land on some sequence.
If that sequence has roughly 17 of each number it is probably not loaded.
If it lands on 100 6s it almost definitely is.

3. ### reilloc

I think i see where you are coming from. The thing to think about is how many ways can you throw the result. There is only one way to throw 100 6s against all the different ways that you could roll 99 sixes and 1 other number, 98 sixes and two ther numbers etc.

I think you are also mixing up the probabilities of each individual roll with the sequence in a variation of the gambler's fallacy.

If your dice is unbiased and you have however improbably rolled 99 dice, you are right that on the 100th roll the outcome of a six is equally likely, but it does not change the fact that any dice that gives 99 sixes is highly suspect!