## 0.4107

Aaron Siegel has found many more wild misere game solutions amongst the four-digit octals, including this amazing one, for 0.4107.

## Amazing misere quotient

### Misere game solution, or extraterrestrial transmission?

Aaron Siegel writes:

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0.4107 has period 24, preperiod 66, and quotient order 506 – the largest yet discovered! Its quotient has a minimal set of 34 generators (!!) It’s quite neat to look at; there are many irregular values among the smaller heaps, until finally a pattern suddenly emerges. This behavior makes me wonder how many other super-complicated-looking games nonetheless settle down fairly quickly. I can’t resist including the pretending function for 0.4107 ðŸ™‚

Phi = 1 1 a a b b ab c c d e f g h b i ab2 j k l m n o p q r abo anq b3 s t abm cq2 u cjk v w x b3 y agt z b2i A B b3 C D b4c bco abF E b3 F ab3c grx G abF abF b3 ab3c H b3 b4c ab4 cfH b4c ab3c ab3c b3 b3 ab4 b4c b4c ab4 ab3c b3 b3 ab3c b4c b4c ab4 ab4 b3 ab3c ab3c b3 b4c ab4 ab4 b4c ab3c ab3c b3 b3 ab4 b4c b4c ab4 ab3c b3 b3 ab3c b4c b4c ab4 ab4 b3 ab3c ab3c b3 b4c ab4 ab4 b4c ab3c ab3c b3 b3 ab4 b4c b4c ab4 ab3c b3 b3 ab3c b4c b4c ab4 ab4 b3 ab3c ab3c b3 b4c ab4 ab4 b4c ab3c ab3c b3 b3 ab4 b4c b4c ab4 ab3c b3 b3 ab3c b4c b4c ab4 ab4 b3 ab3c ab3c b3 b4c ab4 ab4 b4c ab3c ab3c b3 b3 ab4 b4c b4c ab4 ab3c b3 b3 ab3c b4c b4c ab4 ab4 b3 ab3c ab3c b3 b4c

Just look at that cluster of anomalies – “j k l m n o p q r” – that all smooth out in the end . . .