# What is the smallest territory in go that can be successfully invaded?

Let's stay one player has a corner of the board totally enclosed, but with no stones in it, like this:

``````\$\$ ------------------
\$\$ | . . . . . . X .
\$\$ | . . . . . . X .
\$\$ | . . . . . . X .
\$\$ | . . . . . . X .
\$\$ | . . . . . . X .
\$\$ | . . . . . . X .
\$\$ | X X X X X X X .
\$\$ | . . . . . . . .
``````

How big does this space have do be before the other player can successfully invade it? Successfully invade here means build an alive structure despite the owner of the territory defending it move-for-move with expert play on both sides. The defender's surrounding stones should be assumed immortal.

It seems obvious that 4x4 and smaller is not invadable, and I strongly suspect a 5x5 space isn't invadable either.

This page on Sensei's Library suggests that a 6x6 space is not invadable under optimal play, but there is some dispute. Is that true? How about 6x7 or 7x7?

• Am I right to think you mean the invader has to create a pass-alive shape, while the defender’s stones are presumed immortal? Commented Dec 19, 2020 at 21:58
• For clarity, the board image should be extended to the right and downward, including the implication that the black stones cannot be killed. A question to Zags: will black defend the space? Commented Dec 20, 2020 at 1:51
• @PJTrail. Yes, exactly. I'll add that clarification
– Zags
Commented Dec 20, 2020 at 15:41
• @fred_dot_u Assume black will defend the space move-for-move.
– Zags
Commented Dec 20, 2020 at 15:41