Answer:
"With 2 or 3 players, name your first player (=player which gave the first clue of the game) the 'captain'.
With 4 or 5 players, name the third player the 'captain'.
Count the number of no 5 NOT played.
Substract the number of bombs.
Advance by one slot from the 'captain' for each number you got (0=captain, 1=next player, 2=second next player...), and you get the player which will start the last round if no more bombs or no-5 are played (else it goes to his previous player for each card of this type played)."
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Full explanation:
Ok after 4 evenings, I finally get it.
Everything here will be for 6 suits of 10 cards (60 cards).
I will first assume all cards from 1 to 4 are played before the last turn.
This formula tell the number of turns (before end game) if all clues are used, and all no-5 are played:
p+(k-p-1)*2+s
It can be simplified on 2k-18 (or even just -18 or 42 since 60 is a multiple of 2/3/4/5).
k is the number of card in the deck (k=50/48/45/44/40/45 for 2p5c/2p6c/3p/4p/5p4c/5p3c)
k-1 is the number of card in the deck which will be used before the last turn.
p (=24) assume all no-5 have been played and correspond to the turn where a no-5 is played. Since it's not always the case, there is an extra step at the end for when it's not.
k-1-p is the number of discard + number of 5 played. Since you gain one clue out of them, i multiply them by 2.
s (=8) is the number of starting clue.
Then, take the modulo of number of players.
So:
- it give 0 for 2 and 3 players game, so I will name the first player the 'captain'
- it give 2 for 4 and 5 players game, so the player two slot after the first player will be the 'captain'
Then, for each missing no-5 card (the turn where the deck goes from 1 to 0 card doesn't count), you advance by one slot the captain.
Then, for each bomb, you step back the captain by one slot.
And you get the last person to start.
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What tell this formula?
If A is the captain, it mean if all 4 and below are played before end turn, he will be the one which will start last turn. Which is pretty unlikely.
But for make the next player of the captain start the last round, you will need to have one 4 not played in the board (or (number of players) extra clues, which is a lot). This happen frequently and are easy to do.
But now, if you want the second next player of the captain to start, you will need 2 differents no-5 cards to be played during the last turn, which begin to be very annoying.
If you want the third next player, you will need 3, which is impossible without careful planification, which is possible.
