You asked " How many sets of pool balls SHOULD one have?"
Key word I highlighted is SHOULD
As many as you want.
As many as you have room for.
As many as your budget allows for.
Depends on the games you play.
Is ball collecting (like cue collecting for many) one of your hobbies or passions?
If you like the game of Baseball, you SHOULD really have the Aramith Premiers because that's the only modern ball design that matches the baseball set of balls 16-21 that is still available to buy.
If you like to practice with the same balls that your local club uses for the 14.1 league you play in, then you'd need the Aramith Crown Standards if you lived here in Fort Worth --- which is one of the best formulations Aramith ever worked IMO for the price - they resist scuffs and wear marks fantastically well.
If you love the everlasting and classic design of the many, many decades of continuous production of the ever popular Brunswick Centennials, you surely SHOUKD have those.
If you follow current trends in the tournament arenas, you should make room for the 2 Cyclop sets available.
Do you have a daughter or wife or girlfriend that loves to play? You SHOULD have the Vigma HOT PINKS! and watch them get a little more enthusiastic knowing that you got those especially for them
You loved the short Bonus Ball season and sprung for your favorite retro jersey? You SHOULD get out the official Bonus Ball set and let the cameras roll.
Perhaps you created your own amazing and unique pocket billiards game around those crazy musings you have here and there - you SHOULD use your created combination set of 2.25" ball colors you obtained directly from Saluc to commemorate your genius.
You can't play American Snooker on your 9' GC without having either one of the numbered or unnumbered Aramith Snooker sets. You should get both I say.
Are you a huge sports fan during football season and your brother loves the Steelers and you are a diehard Cowboys fan and like to play some 8 Ball as part of your at-home tailgate party? Well, you SHOULD have the complete sets of both teams then to offer up a rematch of that famous Super Bowl pairing.
Oh - and don't forget the Aramith Continentals or the Premiums or the Super Pro's or the neat Great Whites for the pool shark in you. Collecting every set of Aramith's should prove interesting - and you can play with your collection.
If you only have room or the budget for one set - I'd say you should get the Aramith Tournaments if you have $350 on average to drop - or the Aramith Crown Standards at a reasonable $100.
SHOULD have. I should have stopped collecting after two sets according my wife
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