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Author Topic: "Odds" question  (Read 3861 times)

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Flip5ide

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"Odds" question
« on: August 17, 2015, 04:10:49 pm »
0

If I have played 5000 games with all the cards (not counting Adventures), what are the odds that I have played the same kingdom twice?

I think for starters, I should try to recall how many kingdom cards there are altogether (not counting Adventures).

As an added bonus, at what point (after how many games) does it become a 50% chance that I have played 2 games with an identical setup?
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XerxesPraelor

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Re: "Odds" question
« Reply #1 on: August 17, 2015, 04:12:06 pm »
+1

Pretty high, if you use the preset kingdoms.
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Flip5ide

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Re: "Odds" question
« Reply #2 on: August 17, 2015, 04:17:02 pm »
+1

Pretty high, if you use the preset kingdoms.

So in other words, basically 100% after the first 2 games of playing the "First Game"? Dang I had no clue haha

I suppose I should add that you are picking a set of 10 from a set of 180 or however many kingdom cards there are. I guess you could throw in YW's bane card but I'm guessing it's negligible.
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liopoil

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Re: "Odds" question
« Reply #3 on: August 17, 2015, 04:32:22 pm »
+6

I'd be willing to wager a lot that every single full random game played with all the pre-dark ages cards had a different kingdom. That is, NO kingdom has been generated more than once randomly.

Reason: 155 choose 10 is a lot. It has 15 digits, while the number of games that have been played has ~7 digits. (12 million were played on isotropic. How many on Goko/MF?). This puts the odds at around 10% that it's happened at all.
« Last Edit: August 17, 2015, 04:47:51 pm by liopoil »
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qmech

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Re: "Odds" question
« Reply #4 on: August 17, 2015, 04:53:22 pm »
+3

As an added bonus, at what point (after how many games) does it become a 50% chance that I have played 2 games with an identical setup?

You would have to play on the order of 100 million games.
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SCSN

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Re: "Odds" question
« Reply #5 on: August 17, 2015, 05:03:19 pm »
+9

If you're playing "full random" casual/unrated on Goko and you're not overly careful, you should expect multiple duplicate kingdoms per day.



#DefyingTheOdds
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Flip5ide

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Re: "Odds" question
« Reply #6 on: August 17, 2015, 07:55:57 pm »
+1

I feel like maybe this idea comes into play at some point?

https://en.wikipedia.org/wiki/Birthday_problem
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liopoil

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Re: "Odds" question
« Reply #7 on: August 17, 2015, 08:08:45 pm »
+3

I feel like maybe this idea comes into play at some point?

https://en.wikipedia.org/wiki/Birthday_problem
This is exactly what Qmech and I are talking about, and where our estimates come from. Specifically, I used the estimate 1 - e-n2/2m, where n is the number of games you play and m is the number of possible kingdoms.
« Last Edit: August 17, 2015, 08:13:10 pm by liopoil »
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Witherweaver

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Re: "Odds" question
« Reply #8 on: August 26, 2015, 03:50:24 pm »
+1

I feel like maybe this idea comes into play at some point?

https://en.wikipedia.org/wiki/Birthday_problem
This is exactly what Qmech and I are talking about, and where our estimates come from. Specifically, I used the estimate 1 - e-n2/2m, where n is the number of games you play and m is the number of possible kingdoms.

-1 for ambiguous fraction notation. 
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liopoil

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Re: "Odds" question
« Reply #9 on: August 26, 2015, 04:01:44 pm »
+3

What, do you really think that the m might not be in the denominator?
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Kirian

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Re: "Odds" question
« Reply #10 on: August 26, 2015, 09:27:47 pm »
+1

Never tell me the odds.
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Dingan

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Re: "Odds" question
« Reply #11 on: September 03, 2015, 06:25:33 pm »
0

Related thread:
http://forum.dominionstrategy.com/index.php?topic=13647
(I really do want to answer that question, just haven't had the time to sit down and do the math lately.)
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