Misère

However, for misère, open misère, and double misère a breach always occurs at 3 tricks.

Misère version The computation history of the misère version of Sprouts is very similar to that of the normal version, with the same people involved.

Neither misère nor open misère is usually permitted in this variant since it is too easy to win.

Also called Lay Down Misère and may be made at any time.

Greedy Nim Misère has the same rules as Greedy Nim, but here the last player able to make a move loses.

Grundy's game can be played as either misère or normal play.

However, the misère version is more difficult to compute, and progress has been significantly slower.

In a game that starts with heaps of three, four, and five, the first player will win with optimal play, whether the misère or normal play convention is followed.

In misère play, the goal is instead to ensure that the opponent is forced to take the last remaining object.

In misère play, the player who makes the last move loses.

In particular, in ideal play from a single heap of n objects, the second player can win if and only if : n ≡ 0 (mod k + 1) (in normal play), or : n ≡ 1 (mod k + 1) (in misère play).

In the case of a set occurring during double misère the player who touches the kitty first is not allowed to bid in the next round.

Nim can be played as a misère game, in which the player to take the last object loses.

Only tame games can be played using the same strategy as misère nim.

Open misère may be bid in a similar fashion.

The 21 game The game "21" is played as a misère game with any number of players who take turns saying a number.

The common variant is in bidding, where misère may be bid before a bid for seven tricks.

The normal play strategy is for the player to reduce this to size 0 or 1, leaving an even number of heaps with size 1, and the misère strategy is to do the opposite.

The only difference is that as a first step, before computing the Nim-sums, we must reduce the sizes of the heaps modulo k + 1. If this makes all the heaps of size zero (in misère play), the winning move is to take k objects from one of the heaps.

When played as a misère game, Nim strategy is different only when the normal play move would leave no heap of size two or larger.