I'm glad that a consensus is forming about the data dependence/independence issue.
However, the more I think about it, the bigger the selection bias issue appears to be. Let's analogize a SNG to a basketball game or a football game. If we take a look at the score at halftime or the start of the fourth quarter, I'll bet that the team with the greater points is more likely to win the game. But that lead is due, at least in part, to a difference in skill between the two teams and their coaching staffs.
Now, if we take a look at the chip count in a SNG anytime after the starting position, we have to recognize that at least some of the difference is due to relative differences in skills. After all, it's a fact that some players have higher ITM%s/ROIs than others. That's one of the "shortcomings" of ICM and why eastbay has considered modifying ICM with a
skill factor.
If we use chip counts from the middle of actual HU tourneys, I cannot see a way to get around selection bias. The same applies with even greater force if we use chip counts once a SNG has become heads up. After all, the two players accumulated their chips at least in part through their relative skill over their opponents and those skill differences had more time and chips with which to express themselves.
As a result, the only way that I can see to use data from live tourneys to negate the null hypothesis (i.e., that the equity function is linear in a HU freezeout) is to use random starting chip stacks. That way the differences in the initial condition don't reflect skill differences. Of course, that pretty much rules out using data from traditional online tournaments.
If data from actual SNGs were used, the results may not be sufficient to negate the null hypothesis, but if that data, notwithstanding the selection bias, was still consistent with the null hypothesis, it might tend to make the hypothesis more likely. Given the difficulty of data collection and selection bias issue, it seems to me that the most fruitful approach at this point is to double-check
gumpzilla's argument.
The Shadow (who's more impressed by gumpzilla's argument than David Sklansky's proof)