If SirPrimalform's going to pick someone I think ZFR's a good choice. If it goes wrong we'll have two people going "see, I told you not to trust him!" which is unfortunate, but that's basically what would happen anytime an F comes up, isn't it?
supplementscene: Yea go on
ZFR: This is slightly counter-intuitive:
zeo shuffles the remaining cards and starts dealing them out one by one, face-up (i.e. we can see whether it's L or F). At any time we can say STOP, at which point the next card that's not yet dealt is passed as a policy. If zeo deals all the cards without us saying STOP, the last card is automatically passed as policy.
What's the best strategy we can adapt (as to when to say STOP) to increase our chances of passing an L policy?
FFFFFFFFFLLLL
If we shout stop immediately, there's a 4/13 chance we'll hit L. Not insignificant.
But if we let one card go there's two outcomes -
outcome one (9/13 chance) - 1/3 chance the next card is an L
OR
outcome two (4/13 chance) - 1/4 chance the next card is an L
So each at each card we're going to double our outcomes, meaning there are, I think, 2048 individual outcomes. No. that's not right because after 4 cards have been passed, one branch ends with a big printed FAILURE. (the possibility of LLLL having being turned over,) then several of the next set of branches (LFLLL for example.)
This is interesting to think about but I can't see a clear way into it. I think my first question is - is 4/13 chance greater than a 9/13 chance of getting a 1/3 chance but a failure leaves us with a 1/4 chance. I don't know how I'd work that out - how would you do that ZFR?
Does letting all the card play give you the same chance as saying stop immediately? Immediately I think yes, because there's a 4/13 chance that the bottom card is L, just as there's a 4/13 chance the top card in the pack is L.
I think the best strategy is to first sneak a look at the pack - if we can see what the bottom card is we'll have a lot more information to work with :)