03-02-2016, 07:22 AM
(This post was last modified: 03-02-2016, 07:23 AM by Apocalipsis.)
I was actually waiting for your answer xD
Just to clarify what I posted in the previous page: If we assume that each one of the 364 possible distributions of 11-citizen-3-mafia tags on the 14 'slots' of the list have the same probability of happening, then that means that there are 84 favorable cases in which (at least) the first five slots have the citizen tag. That means that each time we start a new game with this specs, there are 23.08% chances of having at least 5 citizens in the first five slots.
While it would be correct to use the information from the current experience like you said, there are 2/7 chances of getting a Mafia in Bamboori's slot, or any other place for that matter, and that wouldn't help me decide whom to kill (which is what I'm trying to do now). Is it that bad to decide using the a priori probability of having a mafia there at the start of the game?
(03-02-2016, 06:19 AM)A-Man Wrote: I think what TheNave was trying to clarify with that example is that Apocalipsis's use of probability would've only been valid at the beginning of the game. So you say the probability there exists a mafia in every set of 5 players (from 15 for simplicity) is 1/5 since there are 3 mafia players in total. It stands that 3 mafia players can be in the same set, though less likely at first (since # of ways they can be like that is less as you explained). However, as nature makes her choices, whether they were the more expected ones or the less expected ones, these become current and the probability resets.
What is the probability 2 coin flips yield tails? 0.5 * 0.5. But if you've already tossed the first coin, and it landed as tails, then the probability shrinks to becoming "the probability 1 lands tails", which is 0.5. If you've already scored 3 sixes with a dice, the probability you score a 4th 6 is 1/6. The probability there is 1 mafia in every set of 5 players is great, but as the game progresses and things become determined, all of this resets to match the new numbers.
Just to clarify what I posted in the previous page: If we assume that each one of the 364 possible distributions of 11-citizen-3-mafia tags on the 14 'slots' of the list have the same probability of happening, then that means that there are 84 favorable cases in which (at least) the first five slots have the citizen tag. That means that each time we start a new game with this specs, there are 23.08% chances of having at least 5 citizens in the first five slots.
While it would be correct to use the information from the current experience like you said, there are 2/7 chances of getting a Mafia in Bamboori's slot, or any other place for that matter, and that wouldn't help me decide whom to kill (which is what I'm trying to do now). Is it that bad to decide using the a priori probability of having a mafia there at the start of the game?