amazing odds

[PieceOfMind]

Hey it's all good. It's not about being offended it is about understanding the results that you get. I'm trying to think of something that can explain what does the ~60% result represents in practice. Needless to say I still have big issues with the way the problem is worded (4 or more wins out of possible 5). It's like you come into a room when someone is playing Civ and find out that 4 battles were just won at 90% odds and there is one more battle left at the same odds and for some reason the equation tells me I only have 60% chance to win?

edit: or rather based on the wording of the question this should be in the past tense. Someone who just had 5 battles at 90% odds tells me that 4 were won, and asks me to guess the outcome of the fifth. If I say Win then I only have 60% of getting it right? This just doesn't sit well with me.

I thought you wouldn't have been offended. Yet another person who values learning more than being correct

Yes, a similar sort of counter-intuitive result is the Monty Hall problem which I think you'll find just as interesting. This one is very famous.

Your comment in the EDIT describes the situation well. I agree it doesn't sit well, but it is certainly correct, and that's why it's fascinating.

 

[vale]

That link about the Monty Hall problem explains it pretty well and the part about "Increasing the number of doors" is exactly the way I like to help others get a more intuitive grasp of conditional probability.

 

[PieceOfMind]

I'm sure some of you will be interested in seeing this. This is a spreadhseet I compiled which experimentally verifies the results I've been claiming. Hopefully the data in the spreadsheet are self-explanatory, but if you download it you can fiddle with the (blue) numbers in it.
If you download it, extend the data down to more than 100 trials. At least 1000 preferably. I kept it to 100 trials so it is small to download. You then need to change the cell W2 from

=SUM(O8:O107)/SUM(Q8:Q107)

to

=SUM(O8:O1007)/SUM(Q8:Q1007)

or however far you extend the trials. In fact you can set it to any large number, eg. =SUM(O8:O60000)/SUM(Q8:Q60000)

Spreadsheet

Sample data:

Spoiler :

 

[Winston Hughes]

Last night I won three consecutive fights at 20%, 21% and 26% (Impis attacking hill-city Archers). I put this down to the ritual sacrifice I conducted before playing, rather than any of your fancy calculations. The RNG gods are especially fond of chicken.

 

[popejubal]

Last night I won three consecutive fights at 20%, 21% and 26% (Impis attacking hill-city Archers). I put this down to the ritual sacrifice I conducted before playing, rather than any of your fancy calculations. The RNG gods are especially fond of chicken.

Interestingly, you can sacrifice any meat product to the RNGods since it all tastes like chicken to them anyway.