Salutations Sir R-----! I trust that this fine summer weather has you thirsting for a flagon. And perhaps a wager?
Splendid! Come join me at my table!
I propose a game played as a religious observance by the parishioners of the United Reformed Eighth-day Adventist Church of Cthulhu, the eldritch octopus god that lies dead but dreaming in the drowned city of Hampton-on-Sea.
Several years ago, the Empress directed me to pose as a peasant and infiltrate their temple of Fhtagn in the sleepy village of Saint Reatham on the Hill when it was discovered that Bishop Derleth Miskatonic had been directing his congregation to purchase vast tracts of land in the Ukraine and gift them to the church in return for the promise of being spared when Cthulhu finally wakes and devours mankind.
When the Baron last met with Sir R-----, he proposed a wager which commenced with the placing of twenty black tokens and fifteen white tokens in a bag. At each turn Sir R----- was to draw a token from the bag and then put it and another of the same colour back inside until there were thirty tokens of the same colour in the bag, with the Baron winning a coin from Sir R----- if there were thirty black and Sir R----- winning ten coins from the Baron if there were thirty white.
Upon hearing these rules I recognised that they described the classic probability problem known as Pólya's Urn. I explained to the Baron that it admits a relatively simple expression that governs the likelihood that the bag contains given numbers of black and white tokens at each turn which could be used to figure the probability that he should have triumphed, but I fear that he didn't entirely grasp my point.
Ho there Sir R-----! Will you join me for a cold tankard of ale to refresh yourself on this warm spring evening?
And, might I hope, for a little sport?
I should not have doubted it for a moment sir!
This fine weather reminds me of the time I spent as the Empress's trade envoy to the market city of Argos, famed almost as much for the remarkable, if somewhat fragile, mechanical contraptions made by its artificers and the most reasonably priced jewellery sold by its goldsmiths as for its fashion for tiny writing implements.
Recall that the Baron and Sir R-----'s most recent wager first had the Baron place three coins upon the table, choosing either heads or tails for each in turn, after which Sir R----- would follow suit. They then set to tossing coins until a run of three matched the Baron's or Sir R-----'s coins from left to right, with the Baron having three coins from Sir R----- if his made a match and Sir R----- having two from the Baron if his did.
When the Baron described the manner of play to me I immediately pointed out to him that it was Penney-Ante, which I recognised because one of my fellow students had recently employed it to enjoy a night at the tavern entirely at the expense of the rest of us! He was able to do so because it's an example of an intransitive wager in which the second player can always contrive to make a choice that will best the first player's.
Sir R-----, my good friend! Come shake the snow from your boots and join me by the hearth for a draught of warming spirits!
And will you also join me in a wager whilst you let the fire chase the chill from your bones?
Fine fellow! Stout fellow!
I have in mind a game that reminds me of my raid upon the vault of Heaven, which I mounted in order to make amends to the Empress for my failure to snatch the Amulet of Yendor from the inner circle of Hell.
When last they met, the Baron challenged Sir R----- to evade capture whilst moving rooks across and down a chessboard. Beginning with a single rook upon the first file and last rank, the Baron should have advanced it to the second file and thence downwards in rank in response to which Sir R----- should have progressed a rook from beneath the board by as many squares and if by doing so had taken the Baron's would have won the game. If not, Sir R----- could then have chosen either rook, barring one that sits upon the first rank, to move to the next file in the same manner with the Baron responding likewise. With the game continuing in this fashion and ending if either of them were to take a rook moved by the other or if every file had been played upon, the Baron should have had a coin from Sir R----- if he took a piece and Sir R----- one of the Baron's otherwise.