## On Fruitful Opals – student

Recall that the Baron’s game consisted of guessing under which of a pair of cups was to be found a token for a stake of four cents and a prize, if correct, of one. Upon success, Sir R----- could have elected to play again with three cups for the same stake and double the prize. Success at this and subsequent rounds gave him the opportunity to play another round for the same stake again with one more cup than the previous round and a prize equal to that of the previous round multiplied by its number of cups.

## Fruitful Opals – baron m.

Greetings Sir R-----. I trust that I find you in good spirits this evening? Will you take a glass of this excellent porter and join me in a little sport?

Splendid!

I propose a game that is popular amongst Antipodean opal scavengers as a means to improve their skill at guesswork.
Opals, as any reputable botanist will confirm, are the seeds of the majestic opal tree which grows in some abundance atop the vast monoliths of that region. Its mouth-watering fruits are greatly enjoyed by the Titans on those occasions when, attracted by its entirely confused seasons, they choose to winter thereabouts.

## On The Hydra Of Argos – student

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.

## The Hydra Of Argos – baron m.

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.