Are some randoms more random than others?

Peter Ebbesen · #1 March 12th, 2004, 02:37 AM

Equal distribution as far as my observations indicate.

The odds of NOT getting an extra water on a S&A Celestial Master would be ~76.6%. In other words, you can expect almost 1 out of 4 Celestial Master's to get at least 3 water, which certainly leads to the feeling that a lot of Celestial Masters get this bonus.

However, it should be noted that the number of mages of the same type recruited in a single game are often too low to use for any sort of statistics. I player a S&A game where 3 out of 5 Celestial Masters recruited in the first ten turns 1 blood, and by the end, 7/17 recruited had 1 blood - which are too few to use for a good statistical analysis, really, and certainly fall within the range of an "equal distribution" hypothesis. (It was fun though)

tinkthank · #2 March 12th, 2004, 02:46 AM

Quote:

Originally posted by Peter Ebbesen:
Equal distribution as far as my observations indicate.

The odds of NOT getting an extra water on a S&A Celestial Master would be ~76.6%. In other words, you can expect almost 1 out of 4 Celestial Master's to get at least 3 water

Thanks much sir. Suspected as much.
I know too little about statistics to remember standard deviance and what not, but may I ask an unqualified question?

- If 1 out of 4 CMs gets at least 3 water, then isnt the chance also that 1 out of 4 CMs gets 2 Fire, Astral or Air? (Chance of getting +1 water = chance of getting +1 to anything else they already have, right?)

Peter Ebbesen · #3 March 12th, 2004, 02:57 AM

Quote:

Originally posted by tinkthank:
- If 1 out of 4 CMs gets at least 3 water, then isnt the chance also that 1 out of 4 CMs gets 2 Fire, Astral or Air? (Chance of getting +1 water = chance of getting +1 to anything else they already have, right?)

Depends on how you phrase the question

If you ask, what are the odds of a Celestial Master to get at least 2 Fire, it is indeed ~23.4% under the equal distribution hypothesis. [And likewise if you ask specifically about 2 Air or 2 Astral]

If you ask, what are the odds of a Celestial Master getting at least 2 Fire or at least 2 Air or at least 2 Astral, the odds are much, much, higher. Since the chance of getting NO extra fire, air, or astral would be 5/8*5/8 ~ 39.1%, you can expect 60.9% of Celestial Masters to have at least 2 picks in one of the minor default paths.

tinkthank · #4 March 11th, 2004, 03:20 PM

Heh thanks.
I always wondered: If there is a 1% chance of an event happening, and you looked at 100 possible event-worlds, what are the chances of it happening once? If it is 1/100 + 1/100 ..., wouldnt that make it 100/100? Does that mean there is a 100% chance of it happening? That just sounds absurd to me. Obviously, "chances are" that it will happen, but what the heck does that mean? (Is my question clear or must I be more precise?)

Endoperez · #5 March 11th, 2004, 03:22 PM

Happening once or atleast once? That is a world of difference... Interesting question, anyway.

PDF · #6 March 11th, 2004, 03:50 PM

Quote:

Originally posted by tinkthank:
Heh thanks.
I always wondered: If there is a 1% chance of an event happening, and you looked at 100 possible event-worlds, what are the chances of it happening once? If it is 1/100 + 1/100 ..., wouldnt that make it 100/100? Does that mean there is a 100% chance of it happening? That just sounds absurd to me. Obviously, "chances are" that it will happen, but what the heck does that mean? (Is my question clear or must I be more precise?)

eheh, probabilities... Your additive method only works with very small chances/small number of occurences, but in this case it's faulty.
A 1% chance event has an *average* chance of NOT occurring (at all) of (1-0.01)^100, that's 33.6%, so chance of occuring *at least once* is 66.4 %
However the average *number* of occurence is 1 (ie it will sometimes occur 0 time, other 1 time, or more, but average still is 1%*100 = 1)

tinkthank · #7 March 11th, 2004, 03:51 PM

I dont know.
I'll put it this way.
If you flip a coin, there is a 1/2 chance it will come up heads. If you flip it twice, there is a 2/2 chance you will get heads in one out of those two times -- right? So I think that means "once"?
But it would be absurd to say there is a 100% chance of you getting heads, so I must be confused somewhere, or maybe it is a language thing.