A buyback doesn't inherently increase the price of the shares. A buyback works like this: Start with a company with an operating business valued at $750M and a pile of cash in the amount of $250M. You own 100 shares out of 1000 (10%). Your shares are worth $1B * (100/1000) == $100M. The company now does a buyback of $50M. They buy 50 shares from other shareholders and cancel them. You now own 100 shares out of 950 of a company with an operating business valued at $750M and a pile of cash in the amount of $200M. Your shares are worth $950M * (100/950) == $100M.

That doesn't mean the share price won't change in practice, but not because of the math, rather because of what investors make of the decision.