Hello. My friends and I are going to have a battle royale with the express purpose of having our characters be as rulebreaking as possible. We all get a level 20 character, 20k gold, 1 legendary, 2 v rare, 3 rare, and 4 uncommon magic items. 

The arena is a 250ft radius sphere. Would the following tactic function?

Level 20 wizard
Learn the spells Arcane Gate and Wish
Use my 1 legendary item for a Ring of 3 Wishes
Buy a Sphere of Annihilation for 20k gold (The price on the list we're using for buying magical items)
Get to the center of the battlefield and cast Arcane Gate to the very edge of it. Wait for everyone else to get within 180 feet of the center. Put the sphere of annihilation in the center. Go through the gate and then bring the sphere with.

When a SoA passes through a portal of some sort, you roll to see what happens: 1-50, it's destroyed. 51-85, it goes through. 86-100, it teleports itself and everything within a 180 foot radius to the astral plane.

So, I pass the sphere through. If I roll 1-50, I use wish to undo it. If I roll 51-85, I put it back through and use wish if that also ****s up. If I roll 86-100 while in the center, it nukes everything and wins me the game. With 4 casts of Wish, this should leave me with a relatively high chance to win.

Is this a winning, workable tactic? Is there any better way to create a nuke of the same sort?

Other tactics that may work:
Use a Bag of Holding plus Mage Hand instead of the Arcane Gate in order to trigger the nuke.
Have a hireling (Yes, for some dumb**** reason we're allowed to bring hirelings) teleported to the center and have him use a bag of holding while I sit comfortably and just wish away his bad rolls.

I don't see how everything being teleported to a random plane is "nuking" anything. It doesn't do any damage. Just seems like it would change the battlefield to a new plane.

The other thing I'd warn is that you're kind of assuming everyone is going to politely move into your 180 radius and wait as you cast and recast Wish until you get the effect you want. Never assume you can have multiple setup rounds in a PvP situation.

Quote from scatterbraind >>

. Never assume you can have multiple setup rounds in a PvP situation.

 That being said, as a level 20 Wizard, they could potentially take "Time Stop" and get a few rounds that way. 

With four casts of wish, I don’t know why you’d go through all that other stuff. Just wish your enemies were all dead or wish you win the fight or something. 

Quote from Kaboom979 >>

Quote from scatterbraind >>

. Never assume you can have multiple setup rounds in a PvP situation.

 That being said, as a level 20 Wizard, they could potentially take "Time Stop" and get a few rounds that way. 

 Well that's your 9th level slot, so you're down to 3 wishes. If my math is correct that leaves you with a 39% chance to actually pull it off, assuming you get the Time Stop off. 

Non-basic use of wish = 1/3 chance of never being able to cast wish ever again. That includes through magic items.

Wish for Simulacrum
Both you and Sim use Shapechange into Ancient Brass Dragons. Use Sleep Breath to incapacitate and your fly speed to keep distance from attacks.
You can cast spells using Shapechange as a dragon so cast spells like Cloudkill or Sickening Radiance. One of you readies a Forcecage spell to be triggered when the other uses the AoE. You've trapped them into a death box. And one of you would still be a dragon, readying a firebreath against any that escape.

Seems a better option that betting on non-basic wishes.

Should wish your target to gain and attune to a Cursed Scarab of Arcane Cancelation ;)