Continuation of: "Sub-puzzle: Master and Slave versus Bob the Violent but Honest Psychopath" and "Master and Slave versus Bob: easy version"
The hard version is identical to the easy version (see link), except: the Prologue has only 2 Red/Black rounds, but Bob only grants them 2 Mulligans.
(So, when the games are chained together, you have a game where they have to get 3N rounds correct out of 4N+1. In particular, 9 out of 13, so this finally completes the answer to "Strategy to beat the Casino reversed". I will post my own answer later. Actually, my own answer is pretty messy, maybe you will come up with something nicer...)
Your task is, as before, to come up with a Deck, and a definition for Large and Small amounts of information, and GUARANTEED (not probabilistic) survival strategies for the Main game, Prologue, and Epilogue.
Tiny hint:
You may wish to start from a solution to the previous puzzle first, and see what needs to be patched.
Medium hint: the Deck I plan to use in my answer is
the top four ranks from a standard deck (16 cards). These correspond to the odd parity cases (3-1 split). The colour of the card is the majority colour, and the rank of the card is the position of the minority colour. I have no nice description for the difference between clubs and spades, and between hearts and diamonds. It is a patch to make things work. You may wish to start by coming up with an unpatched solution based on this, and see where it needs to be patched.
A larger hint: in my Deck, a Large amount of information means
knowing 1 of 10 overlapping cases: you know the rank and colour of the card (8 cases), but you don't know the suit; OR you know the next card is a Q/K of spades, OR you know the next card is a Q/K of hearts. In the last two cases you don't know the gender.
And a Small amount of information means
knowing 1 of 2 overlapping cases: either you know the card is not a spade; or else, you know it is not a heart.
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