Earlier in the thread I left a comment about my own particular conundrum on this topic and I'm honestly a little surprised that no one followed up with me given the smart statistical heads that hand around this forum. Here's my issue, we know that, as has been said above, in these sorts of games each trial is independent. However, I think we also know that increasingly long streaks are increasingly unlikely. How do we resolve these two (both valid, I think) intuitions?
i explained that here:
Look, lets say we have a 50% chance of red/black and we play 4 times, what are the chances of getting 4 blacks in a row? 6.25% what are the chances of getting 4 reds in a row? 6.25%, what are the chances of getting 1 red 1 black 1 red 1 black ? 6.25% and so on
Here are all the possibilietes :
RED RED RED RED - 1
RED RED RED BLACK - 2
RED RED BLACK RED - 3
RED RED BLACK BLACK - 4
RED BLACK BLACK RED - 5
RED BLACK BLACK BLACK - 6
RED BLACK RED BLACK - 7
RED BLACK RED RED - 8
BLACK BLACK BLACK BLACK - 9
BLACK BLACK BLACK RED - 10
BLACK BLACK RED RED - 11
BLACK BLACK RED BLACK - 12
BLACK RED BLACK BLACK - 13
BLACK RED BLACK RED - 14
BLACK RED RED BLACK - 15
BLACK RED RED RED - 16
16 Possible outcomes , guess whats 6.25% x 16 ? = 100%
Even tho getting 4 blacks in a row is unlikely (6.25%) getting 2 reds 2 blacks is unlikely aswell (6.25%) so every combination is equally unlikely
I think that does help actually. So, even though my intuition is that 5 blacks in a row is more unlikely than 4 blacks in a row, in fact, any combination of 5 is more unlikely than any combination of 4? Is that right? I think I said that very inelegantly but this does help, thanks Bardman.
