In ring games, yes. In tournaments, he can sit back and wait on a good hand and be right one time and get everything.
Depends on the stack sizes involved.
Yes, of course. If he’s got a healthy stack, wait and pounce. If he’s got a short stack, much or shove and pray.
Yes, of course this ignores ICM considerations; we’re talking cEV rather than $EV. The principle still applies.
Variance is part of statistics, which is part of math. If you flip a coin 100 times, there’s a possibility that you’ll get exactly 50 heads and 50 tails, but 92% of the time you won’t. A big part of succeeding in poker is understanding not just EV, but variance as well, which gets fed into areas of poker as diverse as bankroll management and ICM distortions for tournament play.
Poker is a game built on discrete statistics. Differential calculus won’t get you far here - it’s an entirely separate branch of mathematics. Statistics feed into range analysis and decision trees to determine optimal play. Certainly, observation is important, but what you’re observing and how that influences your actions should be driven by the underlying math. Psychology, storytelling, pressure, and all other non-math-driven considerations should be entirely irrelevant, because they introduce distortions that are exploitable and will lead to suboptimal play.
Also, lawl at PvNP.