WIFOM (Game)

WIFOM (Game) is a game developed by Who and Zaicon via the MafiaScum Site Chat.

The standard version of this game is 2-player, although a 3-player version of this game is playable.

The Setup

One player will pour the wine; the other player will be the drinker. Turns alternate after every round.

The pourer must first choose whether to poison the drinker or not. Then, the pourer can place either an antidote, some poison, or nothing in each glass (all combinations are allowed, one per glass).

After that, the game can begin. If there is a mod, the pourer should notify the mod of his/her choices at this point.

The Play

Typically, the drinker will ask questions to help determine what to drink (if anything). The drinker can choose to drink from neither glass, one glass (the drinker must specify whose glass to drink from), or both glasses.

The drinker wins if he/she is still alive. One dose of antidote will cancel out one dose of poison (being poisoned to start with counts as one dose of poison). However, the antidote by itself is also harmful and will kill the drinker if there is no poison to cancel it out.

Scoring

If the drinker lives, the drinker gets points equal to the number of wrong choices there were. If the drinker dies, the pourer gets points equal to the number of right choices there were.

Right/wrong choices refer to the different options available to the pourer (drink from no glasses, drink from glass A, drink from glass B, and drink from both glasses). A "right" choice is a choice that allows the drinker to live.

Example

Let's say Player A is the pourer and Player B is the drinker.

Privately, Player A decides to poison Player B and put a dose of antidote into each glass. Once the decision has been made, Player B can start asking questions of the pourer. Eventually, Player B decides to drink from both glasses.

Since Player B has a dose of poison and two doses of antidote in his/her system, he/she dies (one of the antidotes does not cancel out). Player A gets a total of two points because there were two options available to Player B that would have allowed him/her to live (by drinking either glass, but not both).

Theory

There are a total of 18 possible combinations for the poison and antidotes (including whether or not the drinker starts poisoned). They are listed below.

Letter Code	Drinker	Glass A	Glass B	Points for Drinker	Points for Pourer	How to win
NAA	Not poisoned	Antidote	Antidote	3	1	Do not drink
NAN	Not poisoned	Antidote	Nothing	2	2	Do not drink / Drink B
NAP	Not poisoned	Antidote	Poison	2	2	Do not drink / Drink both
NNA	Not poisoned	Nothing	Antidote	2	2	Do not drink / Drink A
NNN	Not poisoned	Nothing	Nothing	0	-	Any action
NNP	Not poisoned	Nothing	Poison	2	2	Do not drink / Drink A
NPA	Not poisoned	Poison	Antidote	2	2	Do not drink / Drink both
NPN	Not poisoned	Poison	Nothing	2	2	Do not drink / Drink B
NPP	Not poisoned	Poison	Poison	3	1	Do not drink
PAA	Poisoned	Antidote	Antidote	2	2	Drink A / Drink B
PAN	Poisoned	Antidote	Nothing	2	2	Drink A / Drink both
PAP	Poisoned	Antidote	Poison	3	1	Drink A
PNA	Poisoned	Nothing	Antidote	2	2	Drink B / Drink both
PNN	Poisoned	Nothing	Nothing	-	0	none
PNP	Poisoned	Nothing	Poison	-	0	none
PPA	Poisoned	Poison	Antidote	3	1	Drink B
PPN	Poisoned	Poison	Nothing	-	0	none
PPP	Poisoned	Poison	Poison	-	0	none

If we ignore all combinations where one player is guaranteed to win and earn 0 points (and therefore have no reason to be chosen), there are 13 combinations. Of those 13, four of them are effectively duplicates (such as NAA and NPP), leaving us with a total number of 9 unique combinations, listed below:

Letter Code	Drinker	Glass A	Glass B	Points for Drinker	Points for Pourer	Do not drink	Drink A	Drink B	Drink both
NAA NPP	Not poisoned	Antidote Poison	Antidote Poison	3	1	Win	Loss	Loss	Loss
NNA NNP	Not poisoned	Nothing	Antidote Poison	2	2	Win	Win	Loss	Loss
NAN NPN	Not poisoned	Antidote Poison	Nothing	2	2	Win	Loss	Win	Loss
NAP NPA	Not poisoned	Antidote Poison	Poison Antidote	2	2	Win	Loss	Loss	Win
PAP	Poisoned	Antidote	Poison	3	1	Loss	Win	Loss	Loss
PPA	Poisoned	Poison	Antidote	3	1	Loss	Loss	Win	Loss
PAA	Poisoned	Antidote	Antidote	2	2	Loss	Win	Win	Loss
PAN	Poisoned	Antidote	Nothing	2	2	Loss	Win	Loss	Win
PNA	Poisoned	Nothing	Antidote	2	2	Loss	Loss	Win	Win

Four of those nine combinations are won by not drinking anything (those of which the drinker is not poisoned will always be won by not drinking). Four of those nine can be won by drinking Glass A. Four of those nine can be won by drinking Glass B. Three can be won by drinking both glasses.

Note that three of the combinations carry less reward to the pourer and more to the drinker by having only one correct choice, whereas the other six have two correct choices. Statistically both have the same expected value assuming random choice by the drinker, though this only matters after a reasonable number of rounds.