Probabilistic Chess

Inspired by sleeplessness and reading NN Taleb's "Fooled by Randomness".

Backstory: Apparently Taleb had Russian PhDs who used to play chess against MBA interviewees at his firm who had "proficient/expert in chess" listed on their CVs. Of course, this was mostly superficial on the candidate's part, since they were taught that it gave the impression of intellectual sophistication, when in reality they knew only the rules and nothing else. 

However, in reading the book and getting into the Taleb-esque mentality of appreciating the role of randomness, I propose a new variant of chess that fundamentally changes the dynamic between players of any strength, and emphasizes the role of risk attitudes alongside actual chess skill. I'm not sure if this style of chess has been proposed before, but to me it seems relatively novel. 

Idea: Essentially, the right to play your turn is determined by a coin toss (or any other unbiased method that yields a binary outcome). What this means is that it allows individuals to actually make multiple consecutive moves and at the same time have that possibility stacked against him on equal terms. Thus, the winning ability of players lies both in their ability to play well, but also in their ability to accurately calculate risk and their strategy based on their risk tolerance.

(e.g. Should I go for a scholar's mate pattern in the first four moves because I like to gamble on my odds of getting 4 coin-flips in my favour, or should I play so conservatively and build walls, exploiting only weaknesses that arise every marginal move?) 

Interested in hearing your thoughts.