^ It's mathematically "right", but the reason it doesn't really work is because the average contestant isn't going to get to that point in Grandy and think, "Okay, I'll go for the $10K and if I don't get it on this 1-out-of-3 shot, I'll just try again next time I play this game." For the contestant playing the game, you either get it right and get the $10K, decide to walk away with the $1K, or get it wrong and get nothing. No trying again, no playing the game multiple times to accumulate $1K multiple times, just a one-and-done decision that you might end up regretting later.
Really, it's not even all that "right" from a mathematical perspective, because what you're trying to do is to statistically evaluate a probability distribution... with a sample size of one. The standard deviation on that is going to be incredibly large, and as a result, almost any statistical analysis on "is doing X a better choice" is going to return "data inconclusive". This applies to pretty much any game on Price; probability analysis isn't bad, but for the contestant playing the game, there's far more than just the raw numbers involved.