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Suppose someone could drive the ball well using a left or right handed driver? Could this give them big advantage? Downside is they would have to give up a club in order to carry 2 drivers.

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TL;DR - Yes, it would be an advantage, but likely a very small advantage.

The biggest advantage of being able drive from both sides of the ball comes from shot shaping. I'm going to assume our standard golfer is right handed.

For a right handed golfer, a slice would be an extreme left to right movement off the tee, a fade would be a slight left to right, a draw would be a slight right to left, and a hook would be an extreme right to left.

Certain holes are considered "dog-leg" holes, and feature a very distinct change in direction. Off the tee, PGA players usually want to hit their shot in a shape that matches the direction of the hole. A dog-leg right would be played with a fade from our right handed golfer, ideally landing in the fairway, "around the turn" from the tee box.

A perfect golfer wold be equally capable of hitting fades and draws(slices and hooks almost always mean that a player made a mistake, and the ball was not ideally hit). However, no golfers are perfect, and most will be more successful at either hitting a fade or a draw. If a switch hitter was better at hitting a fade, they would hit right handed on a dog leg right and left handed on a dog leg left. If they were more adept at draws, they would do the opposite.

An assumption I'm making is that the player has the same exact swing from both sides. If they do not, they might be better at fades from one side of the ball and draws from the other, meaning the flight of the ball will the same from both sides, not mirrored, providing little if any advantage.

The versatility of having easier shot shaping off the tee is certainly an advantage for anyone who cannot already hit excellent draws and fades. How much of an advantage is another question.

Realistically, from the tee, a golfer would only hit the opposite hand drive ~5 times per round(Though this can vary by course/ conditions, for PGA golfers it may not even be that much). The advantage per shot is likely only a half shot on average. A ideal shot shape will not save you a shot over a straight ball shape every time. Being 30-40 yards closer to the hole on a par 4 or 5 will not always translate to a better score, but it often will.

So ~5 times per 18 holes, gain ~2-3 shot per 18. That sounds great! Except for in order to use another driver, you must lose a club as well. So where you gain ~2-3 strokes, you might lose a couple strokes as well; Which club to replace depends entirely on the golfer and course, but by replacing any club, you will be forced to play shots with a sub-optimal club. So where you make up on the drives, you will be forced to hit a 4 iron when you should hit a missing 3-wood, or a 9 iron when you should hit a pitching wedge. These drawbacks would likely outweigh the advantages, but that depends on the skill of the player and the course they are playing. A long course with lots of fairway bunkers may call for the extra driver, as shot shaping to avoid hazards would be very beneficial, where a short course with deep green side bunkers and small greens would mean that an extra wedge would come in handy more than a driver.

Overall, it is conceivable that it would be an advantage for a PGA pro, but most peoples time would be best spent practicing putting.

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    Good point about the opportunity cost of practice - an ambidextrous golfer will have to spend time practicing both their left-handed and right-handed shots, but a "unidextrous" golfer could spend that time improving the weaker of their draw/fade, so the difference between them will be even smaller. A more fair comparison might be between a golfer who hits equally well lefty/righty and one who hits equally well draw/fade, in which case there'd be little difference - otherwise the ambidextrous golfer is just more skilled than their counterpart, so they'd clearly have some (small) advantage. – Nuclear Wang Jul 24 at 18:48

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