Without knowing more specifics about the game itself, it is very difficult to establish a correlation between data and confidence. but I will try to give you an upper bound for a broad class of games. That is games with the condition that there is some factor of your bankroll that you cannot make more than in any given iteration. (there are many games that do not truly satisfy this condition),
more specifically, if we assume that your friend is a martingale (that the expected value between his bets doesn't change, and is always zero), we can then invoke the Martingale Central Limit Theorem on the logarithm of the values in his data.
This link give some bounds on the rate of convergence of a martingales bankroll to a normally distributed bankroll.
So for "sufficiently large N (dependent on the maximum factor by which we can lose or make money)" our log-scale data is approximately normal, and our measured standard deviation is close to the actual deviation, and that allows us get a probability that your friend is a martingale based on the logarithm of his profits.
this is insufficient though, because you have to consider your own selection bias. This is generally very hard to correct for, but you may always assume that your sample size is the population of earth, and you are simply looking at the most extreme case. More likely though, you aren't considering people that you don't know. and you only have to consider a sample size of all of your friends who play such games, but there is a lot to consider in order to make that claim. If you want to determine whether the wealthiest poker player is/isn't a martingale, you should treat your sample size as the total number of poker players since the choice of "the best poker player in existence" is not a uniformly random one, in fact if the best poker player in existence is just lucky, it is probable that he will be at least 5 standard deviations from the mean (log scale). 6 standard deviations is 1 in a billion, and more than this is evidence of non-martingaleness no matter how large your selection bias is.
but ultimately you need a big N, and a big profit. just how big depends on the game.