Why Do Options Deep OTM/ITM Have Low Gamma Regardless of Implied Volatility?

Options deep Out-of-the-Money (OTM) or In-the-Money (ITM) have very low Gamma because their Delta is already stable, close to 0 or 1/-1, respectively. The option is either highly unlikely or highly likely to expire ITM.

Changes in implied volatility primarily affect the uncertainty around the strike price (ATM options), not the certainty of deep OTM/ITM options. Therefore, their Delta is already saturated, and Gamma is near zero.