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[Titandrake]

All I can say is, this site is pretty cool and run by cool people, and that is a very big number.

[Davio]

I would guess ~1 million of those are from me.

You're welcome, guys. 

[greatexpectations]

in a sort of related note, isotropic should cross the 10 million games played threshold about a week from today.

[Davio]

in a sort of related note, isotropic should cross the 10 million games played threshold about a week from today.

Still not even 1% of all possible kingdoms played. 

[TWoos]

in a sort of related note, isotropic should cross the 10 million games played threshold about a week from today.

Still not even 1% of all possible kingdoms played. 

Hm.  I'm getting 0.00000000534%.  That assumes that every single game had a unique kingdom.  Which, given the staggering number of possible combinations, is possible.

[jonts26]

in a sort of related note, isotropic should cross the 10 million games played threshold about a week from today.

Still not even 1% of all possible kingdoms played. 

Hm.  I'm getting 0.00000000534%.  That assumes that every single game had a unique kingdom.  Which, given the staggering number of possible combinations, is possible.

Even if it was 100% it would still be possible. I think you mean highly probable.

/pedantry

[TWoos]

in a sort of related note, isotropic should cross the 10 million games played threshold about a week from today.

Still not even 1% of all possible kingdoms played. 

Hm.  I'm getting 0.00000000534%.  That assumes that every single game had a unique kingdom.  Which, given the staggering number of possible combinations, is possible.

Even if it was 100% it would still be possible. I think you mean highly probably.

/pedantry

Yes, that is what I should have said.

[theory]

The forum made it past 10MM views recently too

[AJD]

in a sort of related note, isotropic should cross the 10 million games played threshold about a week from today.

Still not even 1% of all possible kingdoms played. 

Hm.  I'm getting 0.00000000534%.  That assumes that every single game had a unique kingdom.  Which, given the staggering number of possible combinations, is possible.

Even if it was 100% it would still be possible. I think you mean highly probable.

/pedantry

It's not highly probable that every game on Isotropic had a unique kingdom. It's highly probable that someone at some time played a game on Isotropic, said "that was an interesting kingdom", and then re-played the same one.

[Captain_Frisk]

in a sort of related note, isotropic should cross the 10 million games played threshold about a week from today.

Still not even 1% of all possible kingdoms played. 

Hm.  I'm getting 0.00000000534%.  That assumes that every single game had a unique kingdom.  Which, given the staggering number of possible combinations, is possible.

Even if it was 100% it would still be possible. I think you mean highly probable.

/pedantry

It's not highly probable that every game on Isotropic had a unique kingdom. It's highly probable that someone at some time played a game on Isotropic, said "that was an interesting kingdom", and then re-played the same one.

The paralyzed experiment guaranteed it.

I also definitely replayed a few games with theory.

[Schneau]

It is 100% certain that the same kingdom has been played at least twice on Isotropic.

[jonts26]

Fair enough, but what about ranked games? i.e. pure random. Well the biasing makes the math a little trickier, but I'm almost certain no two ranked games by the current method are identical.

[Davio]

Fair enough, but what about ranked games? i.e. pure random. Well the biasing makes the math a little trickier, but I'm almost certain no two ranked games by the current method are identical.

The probability can be surprisingly high.

It's the same as the birthday analogy.
If you get 23 people in a room, there's a 50-50 chance of two of them having the same birthday.
Get 57 people together and there's a 99% chance of a shared birthday.

I don't know if the order of magnitude for different kingdoms is that high that the probability is still low with 3 million.

[greatexpectations]

the probability of this occurring will also vary by date. if you jump back to when we had 2-3 less expansions we have less potential kingdoms. yes, there were a lot less people playing on isotropic but id guess that the change in kingdom totals is more significant than the change in games played.

[jonts26]

Fair enough, but what about ranked games? i.e. pure random. Well the biasing makes the math a little trickier, but I'm almost certain no two ranked games by the current method are identical.

The probability can be surprisingly high.

It's the same as the birthday analogy.
If you get 23 people in a room, there's a 50-50 chance of two of them having the same birthday.
Get 57 people together and there's a 99% chance of a shared birthday.

I don't know if the order of magnitude for different kingdoms is that high that the probability is still low with 3 million.

Yes but the birthday problem you have 20 or so people out of 365 total dates. That's a completely different ballpark than 10^7 games and 10^20 or whatever it is total possibilities.

[DStu]

Fair enough, but what about ranked games? i.e. pure random. Well the biasing makes the math a little trickier, but I'm almost certain no two ranked games by the current method are identical.

The probability can be surprisingly high.

It's the same as the birthday analogy.
If you get 23 people in a room, there's a 50-50 chance of two of them having the same birthday.
Get 57 people together and there's a 99% chance of a shared birthday.

I don't know if the order of magnitude for different kingdoms is that high that the probability is still low with 3 million.

Yes but the birthday problem you have 20 or so people out of 365 total dates. That's a completely different ballpark than 10^7 games and 10^20 or whatever it is total possibilities.

But the principle is the same. Probability scales first order like the number of pairs, which scales like the square of the games which is 10^14 We have 202 cards linked as Kingdom cards on the wiki including 10 knights (something else I've forgotten?) so 193 kingdom cards (including DA which is not on iso, so say 150). 150 chose 10 is ~10^15, so it's somewhere in the realm of possible but not very likely.

[eliegel34]

This question is just a larger version of the birthday problem.  Let t=the total number of kingdoms (1.17*10^15) assuming 150 kingdom cards; and g=the number of games played.

The probability of each game adding a unique kingdom to the set is p=(t-g)/t
for i =1:g
p(i)=(t-i)/t

Taking the product of each of these g terms for how many games have been played gives you the probability that for g games played that a all kingdoms are unique.
pn(1)=p(1)
for j=1:g-1
pn(i+1)=pn(i)*p(i+1)

This leads to a probability of 4.19% that we have played the same kingdom twice after 10 million games.  If we keep playing there will be a 50% chance after 40 million games.

[jonts26]

Yeah, I'm was using the DA in my first calculations which brings the probability down to like .3%. Which is significantly less likely than ~4% without DA.

Actually, my first, first set of calculations was the 10^20 I pulled out of my faulty memory which is in fact about non-existent chance.

[jonts26]

This question is just a larger version of the birthday problem.  Let t=the total number of kingdoms (1.17*10^15) assuming 150 kingdom cards; and g=the number of games played.

The probability of each game adding a unique kingdom to the set is p=(t-g)/t
for i =1:g
p(i)=(t-i)/t

Taking the product of each of these g terms for how many games have been played gives you the probability that for g games played that a all kingdoms are unique.
pn(1)=p(1)
for j=1:g-1
pn(i+1)=pn(i)*p(i+1)

This leads to a probability of 4.19% that we have played the same kingdom twice after 10 million games.  If we keep playing there will be a 50% chance after 40 million games.

Are you iterating 10^7 times to figure that out? That's a lot of computation. You can just use the poisson approximation to binomial. P=1-exp(-g^2/(2t))

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[Davio]

Still, looking at the exact same kingdom is pretty useless.

I mean, replacing a card that isn't bought by another card that will not have been bought has 0 effect on the actual game. Can you say that these people played a different kingdom? Yes, but you could also say they played the same interesting subset.

Now I'm sidestepping on a road where it's pretty hard to quantify stuff, but I think two different kingdoms where the exact same subset of cards has been purchased has been played.

Obviously, you can play Big Money in any kingdom,, but that's a bit lame. The skill of the players is also a factor. I think good players are better at deciding which cards in the kingdom should and shouldn't be bought. So if a newbie always buys Talisman, does it really count?

It's still an interesting discussion point I think.

[eliegel34]

Are you iterating 10^7 times to figure that out? That's a lot of computation. You can just use the poisson approximation to binomial. P=1-exp(-g^2/(2t))

Yea did run 10^7 calculations since i wanted to plot games vs. probability.  It only takes 30 seconds to run in MATLAB.  Extremely inefficient, but marginally more accurate.

[jonts26]

Are you iterating 10^7 times to figure that out? That's a lot of computation. You can just use the poisson approximation to binomial. P=1-exp(-g^2/(2t))

Yea did run 10^7 calculations since i wanted to plot games vs. probability.  It only takes 30 seconds to run in MATLAB.  Extremely inefficient, but marginally more accurate.

Here you go. Wolfram Alpha FTW

[greatexpectations]

it is looking like iso will hit 10 million games played in the early afternoon tomorrow pacific time. i vote that someone sifts the logs to find out which game ends up being the big one. then maybe we can all analyze the kingdom and put together a strategy article about the kingdom as a [[Tribute]] to isotropic.

[jonts26]

Guess I'm skipping work tomorrow and playing iso all afternoon.

[Davio]

Guess I'm skipping work tomorrow and playing iso all afternoon.

For me it's the other way around.