max pain changes as the stock price changes.
last week, amzn was around 273 and at that time the max pain for the options expiring today was much higher.
also, look at the open interest. to say that small number of option contracts influences the stock price of a 120 billion company is a bit far fetched.
You can't compare to the market cap, you have to look at money flow for the day vs. the money made on the expiring contracts out of the money in the both directions. Amazon has very low daily money flow vs. its mkt cap, making it an easy stock to hedge against a firm's option position (or manipulate). Today's $260 max pain had about a$50M payout on a day of $2.4M in money flow.
You find it a coincidence that the max pain this morning at open was $260 for the day, and then it magically bounced up and down around that (clear hedging) from 1pm on? It can be confirmed on Monday as well, as the hedges are unloaded. It works on AMZN about 80% of time (Friday move to max pain, with Monday reversal).
It doesn;t always work out, but it is in option writer's and holder's best interest to maximize their gain each week and Q .. if they have the money to move the stock, why not.
Until AMZN has a higher daily volume % (right now it is only 0.7% of outstanding - very low) - it can be moved with ease by big money (especially on Fri where overall volume is lowest of the week).