Generator

Hackenbush from LLRL and RRRL — and who wins

Two Hackenbush stalks with the total stated before anybody moves. Left cuts blue, Right cuts red, and everything no longer joined to the ground falls off. The total is negative, so Right wins whoever starts, and every reply the machine makes was worked out in advance from the same recursion the essays describe.

1 essay calls play-hackenbush. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

The positions it draws

3 distinct positions, harvested by running this generator again at the options each essay passed it.

Position	Worth	Outcome	Drawn in
`LLRL`	`7/4`	L	Hackenbush is a numeral
`LLRL + RRRL`	`−3/4`	R	Hackenbush is a numeral
`RRRL`	`−5/2`	R	Hackenbush is a numeral

It plays back

The winner is named before a move is made, and every reply was worked out in advance.

Hackenbush is a numeral — Hackenbush from LLRL and RRRL — and who wins, worth −3/4, R, 10 positions solved before the page was served.

Where it is called

Changing this generator changes every one of these figures.

The picture is the numeral. Blue-red Hackenbush strings and their values. Left may cut a blue edge, Right a red one, and everything above the cut falls. The value of each string is a number, and reading the string from the ground upward gives the binary expansion of exactly that number.

Particular games

Hackenbush is a numeral

Draw a stalk of coloured edges. Read it as a string, blue for one and red for zero, and the string is the binary expansion of what the position is worth. Not approximately — exactly, and the site computes it both ways and refuses to build if they disagree.

The whole library · The position index · The figures that play back