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Estimate a future option price given greeks and a 1$ move in underlying
It's not that straightforward, even though your gamma will change your delta on the fly, you likely won't see the full $.48 after such a small move.   If the vega drops due to lack of volatility while the stock is moving up, those few percentage points up might help your delta (2% gain $50 to $51 in your example) but will be partially negated by volatility going down. I mean, don't be surprised to see it at closer to $1.33 or something.  The market is out to make money, not to make you money.