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Timeline for 5 people each have 5 equal cards

Current License: CC BY-SA 3.0

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Nov 4, 2016 at 11:50 comment added kaine @2012rcampion Thank you. That was the concept I was aiming for but I didn't want to use that term unless I was certain it was appropriate. I'm an chemical engineer so that isn't quite in my normal vocabulary.
Nov 4, 2016 at 11:04 comment added 2012rcampion The technical term for the solution you found is a Nash equilibrium. I calculated it using a different method and got the same result, so I'm fairly certain you have the right solution.
Nov 3, 2016 at 18:15 history edited kaine CC BY-SA 3.0
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Nov 3, 2016 at 18:06 history edited kaine CC BY-SA 3.0
added 62 characters in body
Nov 3, 2016 at 17:59 comment added kaine @Jik just for you (sarcasm) I removed the (P1+P2+P3..) from the equations, calculated the probability of a draw for each one which is $P_d_x = P_x^4+6P_x^2( \sum (P_o^2))+4P_x( \sum (P_o^3))$. multiplied that by .2 and added it to each win. My previous answer did bias it further towards the 4s and 5s. The numbers in the answer will be edited shortly.
Nov 3, 2016 at 17:43 comment added kaine @JiK I originally using the divide by (P1+P2+P3...) to take care of that. Realized that was wrong later. You are correct. My method aimed to maximize win percentage for each round instead of improving win to loss ratio.
Nov 3, 2016 at 17:36 comment added JiK It seems to me that your formulas don't take into account the fact that the round is replayed if there is no clear winner.
Nov 3, 2016 at 15:28 comment added corsiKa "A single idiot at the table changes everything" - just like in real cards. Some idiot being opening with 2 9 suited under the gun and calls a 3 bet... you can't beat stupid players with logic!
S Nov 3, 2016 at 15:25 history suggested Shufflepants CC BY-SA 3.0
spelling: probability
Nov 3, 2016 at 15:16 review Suggested edits
S Nov 3, 2016 at 15:25
Nov 2, 2016 at 22:35 comment added ffao I'm surprised we have P5>0, but the math is sound. Upon further thought, it makes sense, because lower numbers are more likely to tie, so it's easier to be a loner with a 5.
Nov 2, 2016 at 19:05 history edited kaine CC BY-SA 3.0
edited body
Nov 2, 2016 at 18:36 comment added kaine Mistake corrected and got updated results. Did another type of simulation where actual games were run and results were within 0.1% in value.
Nov 2, 2016 at 18:35 history edited kaine CC BY-SA 3.0
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Nov 2, 2016 at 16:26 comment added kaine Note, I have found a mistake in caculations. I did not take into account 3 people having a single number....damn
Nov 2, 2016 at 15:35 history edited kaine CC BY-SA 3.0
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Nov 2, 2016 at 15:27 history answered kaine CC BY-SA 3.0