**Edited by Thalia, 08 December 2010 - 01:15 AM.**

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### #21

Posted 08 December 2010 - 01:14 AM

Come check out Mafia in the Games Forum**Trainer's Manual Mafia XII: Bugs Mafia **is in signups

Other games:

**The Green Glass Doors**

**Telephone**

### #22

Posted 08 December 2010 - 01:38 AM

**Edited by phillip1882, 08 December 2010 - 01:40 AM.**

### #23

Posted 08 December 2010 - 01:55 AM

firstly there are 15 players, not 16, and secondly..

Spoiler for

Yes, that's what I got but

### #24

Posted 08 December 2010 - 02:00 AM

### #25

Posted 08 December 2010 - 04:10 AM

### #26

Posted 08 December 2010 - 07:32 AM

A fair coin toss would follow the binomial distribution for probability of a predefined pattern in successive tosses.

So, let's say what are the odds of seeing 7 reds and 7 blues? Coz that's the only 50-50 possibility for the chosen leader to guess wrong.

Whenever this balance is tilted in favor of one color, the leader should chose the other color, to account for balancing nature of binomial distribution.

### #27

Posted 08 December 2010 - 09:18 AM

It seems all the respondents here are treating the coin toss as random event.

A fair coin toss would follow the binomial distribution for probability of a predefined pattern in successive tosses.

So, let's say what are the odds of seeing 7 reds and 7 blues? Coz that's the only 50-50 possibility for the chosen leader to guess wrong.

Whenever this balance is tilted in favor of one color, the leader should chose the other color, to account for balancing nature of binomial distribution.

"The colour of the cap is determined completely arbitrarily, e.g. by coin toss."

Coin toss is only an example of random event that may be used to determine the colour on each cap independently of the other colours. Thus, all configurations from RRR...R to BBB...B are equally probable.

### #28

Posted 08 December 2010 - 09:22 AM

**Edited by Kornrade, 08 December 2010 - 09:27 AM.**

### #29

Posted 08 December 2010 - 09:26 AM

Spoiler for OK, I'll get the ball rolling at 75%

Well done so far!

### #30

Posted 08 December 2010 - 10:52 AM

Spoiler for OK, I'll get the ball rolling at 75%

We have to be careful with how we calculate probabilities on this. If each individual cap colour was decided by a coin toss as per the OP, then these probabilities would work. However, Kornrade has since clarified that "all configurations from RRR...R to BBB...B are equally probable." If we start from this position, then the chance of any 3 caps having the same colour is actually 50%. If the chance of each distribution was based on binomial probabilities (i.e. in the coin toss scenario), then your result would be correct, as the chance of 3 caps of the same colour would only be 25%. Attaching a spreadsheet just to illustrate the difference:

#### Attached Files

**Edited by rajat_magic, 08 December 2010 - 10:55 AM.**

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