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Hey chainsaw , try it yourself .
The first problem has been solved .
Work it out for n=3 , then n=4 and you'll see a pattern emerge .
The final list Nicho provided is accurate .
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No it isn't. See the thread in probability. The list Nicho provides is an approximation, but isn't accurate at the edges.
probability thread.
In particular, Nicho says that you want to push on turn two with K3o+. This is because K2o is below his 50% hand list. But this is silly as we know that if you go to the last round where both people are forced to push then you will win 50% of the prize pool as you have equal equity with the opponent. But K2o gives you 50.5087% equity against a random hand so you'd be a fool to fold it if that meant next hand you both pushed blind.
The basic point that joeq is trying to make is that you can't just say what is the probabiliy that I get a better hand next time, but rather what is the probability my equity is better next time. Because equity doesn't scale exactly with hand count the pick the top 1/n-th hands on turn n is not correct, although it is a reasonably close approximation for the early turns. On turn 2 Nicho is missing 22, K2o, Q2s, Q5o, and J6s all of which have greater than 50% equity versus a random hand (50.3340, 50.5087, 50.1690, 50.1201, 50.6059 respectively).