In this naive model, one would expect each share to be worth $2.
If the company spends all its liquid assets buying out 25 shareholders at $2 apiece (prices respond to demand for shares, of course, so this toy model doesn't hold at these ratios, but ignoring that for a second), we now have 25 shareholders, each owning 1/25th of a company that's now worth only the company's EV of $50, i.e., each share's still worth $2. So no value was created, it was a waste of time.
In practice, many many companies' cash holdings are not valued at par by the company's existing investors. That is to say, if the company spends their cash on something that isn't value destroying (surprisingly difficult! Many an acquisition is value destroying!), they can actually increase the value of each share by spending the money in a way that investors like.
Share buybacks thus have the counterintuitive impact of raising the value of each share not by transferring money to the remaining shareholders, but by reducing existing shareholders' risk that management will misuse the company's liquid assets on some ego-driven vanity project.
Buy back doesn't create value (nor destroy value) - it just shifts the dollars from the company to shareholders, who could decide to sell to retrieve the money at a later date.
Of course, buying back at a time when the share price is lower than expected (given a company's inside information) means they actually do gain value (lost from those shareholders who did the selling at the time of the buyback). Market participants who believe Amazon not to be irrational would also start buying as soon as they hear the news, assuming that there's inside info that the company is acting on resulting in such a buyback.
I suppose it's a matter of if they are favoring their future share holders or the ones selling.
Some guys just have it all figured out, huh?
I don't see how buybacks can help in the long term a company that is not issuing dividends.
They are burning real money to buy a potentially higher valuation that can evaporate in an instant (think of Meta)