I think the conclusion is that 'expected value' calculated this way is a bogus metric, even for a single toss (what is the 'average' of a single toss, it alread

I think the conclusion is that 'expected value' calculated this way is a bogus metric, even for a single toss (what is the 'average' of a single toss, it already makes no sense). You can't simply take the mean average of summed probability-outcome products, or at least, it does not mean 'expected value', it means the 'probable limit' of the total. In the $60/$150 bet the 'expected value' is $105, but no-one is getting $105. What is that number? It indicates a 'probable limit' to the total money in the system, but says nothing about what any individual should expect, or about the actual total size of the system, which will obviously tend towards the aggregate individual outcomes. And that is clearly exposed when you start repeating the bet. In fact 'expected value' is quite clearly 0.6 * 1.5 = 0.9, ie $90, or I think more generally: (outcome-1 * probability-1 * ... outcome-n * probability-n) / (probability-1 * ... probability-n) It's maybe counter-intuitive that the 'limit' of the system should keep growing, while the 'actual' size of the system tends toward the 'real' aggregate expected value, but I think it's much less counter-intuitive than what I think is claimed here, that repeating a bet turns it from being a 'good' bet to a 'bad' bet. It was always a bad bet, just measured wrong.