What are the odds?

[CRGreathouse]

Borel's Law of High Numbers applies more or less to any completely random event.

False. This specific incarnation of Borel's Law applies only to specific observable cosmic phenomena. What's more, I don't accept it even under those conditions.

 

[Wicht]

False. This specific incarnation of Borel's Law applies only to specific observable cosmic phenomena. What's more, I don't accept it even under those conditions.

Well you don't have to accept it for it to be true

I am however curious as to what is a nonspecific unobservable cosmic phenomena?

And in any case the rolling of dice (which was the subject i was commenting on) is generally a prespecified observable random event. So in this case I would tend to think that if you threw 1x10^50 20 sided dice they would never all come up as 20's no matter how many times you threw them. You could feel free to disprove it through practical experimentation though.

 

[CRGreathouse]

So what's the chance of someone getting three 20's in a series of three rolls? Yes: 1/20^3 = 0.000125.

Now say that person rolls about 30 rolls in a session. What are the chances he gets 3 consecutive 20's? About 1 - (1-0.000125)^10 = 0.001249 (not quite correct, but close enough).

Now let's assume there's one DM and five players. What's the chance any of them get 3 20's? 1 - (1-0.001249)^6 = 0.00747.

Now let's assume you play every week for a whole year. What's the chance anyone in your party will get 3 20's in a row during that time? 1 - (1-0.00747)^52 = 32% !

Considering how long some of us have been playing, three 20's in a row doesn't seem all *that* surprising...

I'll try to work up some numbers on this tomorrow. I'm curious, myself.

 

[Numion]

Actually, this is not quite true either. After a certain point the improbable becomes in fact the impossible.

Borel's law of probability states that any event for which the chances are 1 in 1 followed by 50 zeroes (1 in 1x10^50) is an event that may be stated with certainty will never happen no matter how much time is alloted nor how many opportunities are given.

Intresting. If I had died yesterday, I wouldn't have known this. Would you mind giving an explanation for this? Mathematically speaking, I'll stand behind my previous statement

 

[hong]

Intresting. If I had died yesterday, I wouldn't have known this. Would you mind giving an explanation for this? Mathematically speaking, I'll stand behind my previous statement

http://www.talkorigins.org/faqs/abioprob/borelfaq.html

 

[mirzabah]

I'm sittin' on the couch, watching TV, and eatin' Teddy Grams. I pull out a Teddy and examine it, noticing that there are four different kinds of Teddies. So I eat this first Teddy, and pull out another. Same kind. Pull out another. Same kind. Five more teddies, all the same. The next is different, but I've pulled out 8 Teddies that were the same.

What are the chances of that?

How many of each type of Teddies did you start with?

[edit]damn! someone beat me to it...[/edit]

 

[mirzabah]

Apologies if someone else has already picked this up, but...

The probability of a sixth consecutive 26, however, is quite small.

Not quite. The probability of a "sixth consecutive" 26 is no different to the probability of a 26 at any other time. However, the probability of six consecutive 26s is, indeed, quite small.

Cheers,
Mirzabah the Pedant

 

[bondetamp]

I think you should all just convert to the Storyteller System.

 

[CRGreathouse]

So what's the chance of someone getting three 20's in a series of three rolls? Yes: 1/20^3 = 0.000125.

Now say that person rolls about 30 rolls in a session. What are the chances he gets 3 consecutive 20's? About 1 - (1-0.000125)^10 = 0.001249 (not quite correct, but close enough).

Now let's assume there's one DM and five players. What's the chance any of them get 3 20's? 1 - (1-0.001249)^6 = 0.00747.

Now let's assume you play every week for a whole year. What's the chance anyone in your party will get 3 20's in a row during that time? 1 - (1-0.00747)^52 = 32% !

Considering how long some of us have been playing, three 20's in a row doesn't seem all *that* surprising...

I can't figure the exact probabilities, but they're considerably higher than what you have here - around 2% per session, or 60% per year.

 

[Wicht]

http://www.talkorigins.org/faqs/abioprob/borelfaq.html

I like the discussion on this site a little better