What is a card worth, in cards and in life?

Practice · resources

Four decks are up for auction and the only money in the room is your own opening hand and your own life total. Bid by offering to start the game worse off.

How the auction works, and what wins it

All four decks first. Every deck is on the table before a single bid is made, and you should read them all before you bid on any: what one deck is worth to you depends on what you would be giving up by not taking another. The auction then runs deck by deck.
The currency. You bid in cards and in life: an offer of six cards and eighteen life means you would start the game holding six, on eighteen. The bigger the sacrifice, the better the offer.
Cards outrank life. This is the auction’s own rule, and it is absolute: an offer of six cards and twenty life beats one of seven cards and fifteen. Every bid sits on a single ladder, and giving up one card climbs higher than giving up every life point you could.
Every deck is forty cards. Twenty-three spells and seventeen lands, or twenty-four and sixteen when the spells are especially cheap, or twenty-two and eighteen when they are expensive — the chapter’s own shape. The lands are split between the two colours in proportion to the coloured mana the spells ask for, so a deck that wants more of one colour is given more of it.
What a deck is worth, and what a price costs. Both are measured in the same thing: games. Before the bidding starts the four decks play each other — six hundred games a pairing, at seven cards and twenty life — and a deck is worth the share it wins. A price is paid in the same coin, because starting on a smaller hand and a lower life total loses you games: one card off your opening hand costs about 13 points of win rate, one life about 2. So a deck and its price can be set against each other with nothing converted and nothing assumed.
How a deck is sold. The bidding goes round and climbs. On your turn you either raise the offer on the table or pass. Nothing is sold until one bidder is left holding an offer nobody will beat — only then does the deck change hands and the next one comes up.
Passing puts you out. Pass while an offer is on the table and you have given up that deck: the bidding will not come back to you, and you cannot step in at the end. The one exception is the opening — with nothing on the table there is nothing to concede, so you may let them start and still bid afterwards.
Raise by one rung. Every press of a stepper moves the offer exactly one rung up the ladder, and the offer always starts at one rung above the table. Beating the table by more than one wins the deck just the same, and pays for the difference.
The other three players, and the mistake they make. Each deck is worth paying for only what it gains you over the one thing you can have for nothing: the last deck in the room, which falls to whoever is left when everyone else holds one. The rivals work that out and bid up to the price it covers — but their estimate of a deck is always a quarter out, a quarter low on some decks and a quarter high on others, and you are never told which. They beat any offer below their limit and pass at it, which puts them out too.
Which is where the money is. On a deck they are low on they stop below what it is worth, and a rung more than their limit buys you more games than it costs. On one they are high on, every offer that beats them costs more games than the deck wins you. One rule separates the two without your ever being told which is which: pay up to what the deck gains you over the free one, and not a rung above. Then the decks they are low on come to you cheaply and the ones they are high on pass you by.
The floor. Bidding stops at four cards and fourteen life. The last life points cost far more than the first: at a low total the price in life stops being a price and becomes the game, so a real auction does not run to the bottom.