Misere combinatorial games.
The least absolute integer shift at which a short game has outcome N.
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The defining property of the $\mathscr{N}$-tipping point: at $\operatorname{n}(G)$ itself, either the positive or the negative shift has outcome $\mathscr{N}$.
Minimality of the $\mathscr{N}$-tipping point: below $\operatorname{n}(G)$, neither the positive nor the negative shift has outcome $\mathscr{N}$.
$\operatorname{n}(-G) = \operatorname{n}(G)$
The least nonnegative shift at which a short game has outcome R.
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The least nonnegative negative shift at which a short game has outcome L.
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Negation sends the $\mathscr{R}$-tipping point to the $\mathscr{L}$-tipping point: $\operatorname{r}(-G) = \operatorname{l}(G)$.
Negation sends the $\mathscr{L}$-tipping point to the $\mathscr{R}$-tipping point: $\operatorname{l}(-G) = \operatorname{r}(G)$.
The $\mathscr{R}$-tipping point is a witness: $\operatorname{o}(G + \operatorname{r}(G)) = \mathscr{R}$.
The $\mathscr{L}$-tipping point is a witness: $\operatorname{o}(G - \operatorname{l}(G)) = \mathscr{L}$.
Minimality of the $\mathscr{R}$-tipping point: below $\operatorname{r}(G)$, the positive shift is not $\mathscr{R}$.
For a Left-win game, $1 \le \operatorname{n}(G)$.
For a next-win game, $\operatorname{n}(G) = 0$.