Ed Wynn introduced Conjectures in Winking World 68. Here follows a transcription of his account (by permission of Ed).
Conjectures is a new drinking game.
The game hase been found to work well for groups of around eight players. In an initial burst of enthusiasm, it has been played by groups of a dozen or more. It probably wouldn't work so well for small groups. The game is intended for the Famous Winkers Cards, but until they arrive (and they are like the days of the Son of Man, "the time will come when you will long to see one..., but they will not come") normal playing cards will do.
The cards are in a strict order of superiority: all Aces are higher than all Kings, and so on, and the suits are in the order of bids in Yogi's Whist: Clubs are higher than Hearts, Spades and Diamonds, in that order. For a typical group, a standard 52-card pack is shortened by removing all cards lower than a Six - the intention being that the chance of at least one Ace (for example) being held is fairly high but not very high. Different numbers of cards are necessary only for extreme numbers of players.
The terminology of the game has a sexual theme, hence the name "Conjectures" (as in Liz Baggage - verb. sop.).
Each player is dealt one card face down, and may immediately look at its face. In a typical game, there will be several rounds of so-called Exposure, of which each player can join only one. The basic aim of the game is to win the round that you join.
The player who has the highest Exposed card in a round has won and is not fined; he may be said to be Well-Endowed. Every other player in that round is fined according to the Shortcoming between his card and the Well-Endowed player's. To announce a round, a nominated player calls out "Three ... two ... one ... BID!". Ot the instant of the "B" in "BID!", all players with their cards touching their foreheads (still face down, or rather face-to-face) have joined that round. They show their cards, and the fines are allocated and drunk in a more or less self-policing way.
The fines already mentioned (and quantified below) make it undesirable to join a round and not win it. Why then should you ever join the first few rounds? Why not just wait until all the high cards have gone, so that you are definitely Well-Endowed? The reason is this: if there is a round in which the Well-Endowed player's card is lower than yours, you will be said to be Softly Spoken and you will be fined more heavily than players who Expose their Shortcomings. So, there's a balance between Exposing earlier than the ideal round (and revealing a Shortcoming) and not Exposing until it's too late (and being Softly Spoken, also known as Staying In The Closet). If you skilfully wait until the ideal round, then you are said to have demonstrated Anal Retention, which is apparently desirable.
The fining system now described is compatible with standard playing cards and sturdy constitutions. Fines are measured in Pencils. (A Pencil, as you probably know, is half a Finger, which is one eighth of a pint of beer.) The fine for a Shortcoming is (1 + denominator difference); for example, if you Expose an Eight but the highest Exposed card is a Ten, your denominator difference is (10-8) and your fine is 3. The fine for being Softly Spoken is (1 + 2 × denominator difference); for example, if you fail to Expose a Ten when the highest Exposed card is an Eight, your fine is 5. If you are Softly Spoken, it is in your best interest to admit it, because you will not be allowed to profit from concealing it. The players who have joined the roud or are Softly Spoken do not participate in subsequent rounds. If only one player remains, he shows his card (to demonstrate that he hasn't been Softly Spoken) and then drinks a single fine for being Asexual; the game is over.
It may happen that no-one joins a round. In this case (known as Mass Buggery), only the player with the lowest card escapes; all other remaining players are fined according to the formula of (1 + denominator difference), and the game ends. If you were holding a King, and someone else the Six of Diamonds, you are subject to a half-pint fine. This is (arguably) bad. However, if that player with the Six were the only player to join a round, then you would be subject to the higher Soft-Speaking fines - in this case, a short head away from a pint. He would have shafted everyone; he would be a Stud. This is a popular ambition, but a would-be Stud runs the risk of Exposing a significant Shortcoming if someone else joins the round.
The player announcing the round should not vary the pace of calling, and should be particularly careful not to hesitate before "BID!". To join a round, your card must be toughing your forehead at the instant of "B". To clearly not join, your card must be touching the table (or your knee if no table is to hand). To be anywhere in between is to be Unsure of One's Orientation; you are given a single fine, and you have not joined the round. This calls for a careful judgement, preferably agreed among the other players. It can be important to see who else is Exposing himself, so it is forbidden to "cabbage" (i.e., to move an empty hand in semblance of Exposure). It is perfectly acceptable to change your orientation during the countdown, though. The face-down cards that are still in the game should remain visible (so that it is clear how many there are); cards that have been used should be put in a central face-up pile. To give players a chance to wake up and check their cards, the announcer may count down from "Five" on the first round of a game.
Game should follow game as quickly as possible, so anyone can deal. The cards don't have to be shuffled too often (except that all the Aces and Kings eventually bunch together). The dealer and the announcer shouldn't be fined for venial mistakes, except when the announcer hesitates for his own good. As with many drinking games, a player should make an effort to drink the fines from one game before the next game's fine arrives. If this is completely impractical, he should announce this and sit out for the minimum period to catch up. However, no-one should drink so much that they do themselves permanent physical or spiritual harm. I should know.
Note that in recent times, it is normal for cards played with to be discarded separately from cards which have yet to be played, and to continue playing until the pack is exhausted before shuffling. This offers some opportunity for the competent to count cards.
Now that Famous Winker cards are available, this variation should also be documented: Rather than playing on the card suit and rank, the categories of the cards are alternated in order for each game, with the card of highest number in that category winning. Fines are a pencil for every difference of ten in that category, rounded up, and doubled for being softly spoken. Before showing a card (which should be done in turn), it is traditional to attempt to impersonate the person on the card (or at least the picture on the card, or otherwise give an identifying phrase), and to give others the chance to guess the person. Jokers are in, and the player of a joker should impersonate another card, before drawing another card from the top of the deck; the drawn card is treated as the player's card, and must in turn be impersonated, with the player drinking any fine necessary if that card was misplayed.