The Setting: Two wizards both ready the Polymorph spell targeting each other. They both choose the same trigger. In this example let us say the trigger is someone shouting “now.”
What happens?
Does the reaction casting of Polymorph from each wizard happen at the same time resulting in both wizards being transformed? Or no?
If not, why?
Xanathar's Guide to Everything includes an (optional) rule for exactly this situation. On page 77, it contains a section entitled "Simultaneous Effects":
In rare cases, effects can happen at the same time, especially at the start or end of a creature's turn. If two or more things happen at the same time on a character or monster's turn, the person at the game table - whether player or DM - who controls that creature decides the order in which those things happen.
So, if it was the person who shouted now's turn when they shouted it, then they get to decide who goes first. The spells would not hit simultaneously.
A few years prior to Xanathar's Guide to Everything was published Jeremy Crawford offered a different piece of advice:
Q: If two creatures Ready on simultaneous triggers, do they act simultaneously or in initiative order?
Crawford: It's up to the DM. As DM, I'd have those creatures act in initiative order.
So, in the end it is up to the DM either way. If you are using the optional rule I listed above then there is your answer. Otherwise, the DM can choose whatever method seems best to them with initiative seeming like a good candidate.
My group used initiative as the deciding factor for months of play before XGE came out and it worked really well. It was simple and intuitive. After the release, we switched to the optional rule because it was more general and could be applied even to things that don't have initiative (different spell effects for example). This rule has worked just as well if not better for us.
While there's no "hard and fast" rules on this kind of event, I've found two sources that address similar events.
The question How are simultaneously-triggered Readied actions resolved? does address this in the highest voted answer (32 points, and the only positive answer).
The answer being that the creature with the highest initiative will "get the jump" on everything else and to utilize their enhanced reaction time to act before those with lesser reaction times.
In this instance, it would come down to whoever has the highest initiative acting first. Coincidentally, this is also the character who Readied first. Even in the event of a tied initiative, there are stated ways of determining who goes first in a draw (from comparing dex scores, to players deciding who goes first, down to random chance).
Even if your Wizards plan on casting at the same time, reaction (aka Initiative) is still a factor. Just because you say or think you have an infinitely accurate reaction time doesn't mean you do.
In a different question, What order do Opportunity Attacks that trigger simultaneously happen in?, the person who's turn it currently is decides in what order the triggers occur. Since these are readied actions that indicate that initiative (and turn order) has been decided, there will be a single character's turn who can decide. Better hope he's on your side.
Keep in mind, this is based on an optional rule listed in Xanathar's Guide to Everything, and your DM may have other plans for your "Reaction" time.
These two options are built off of either assumptions or optional rules, so the best source for a question like this is whatever your DM says. Considering events like this don't happen without DM's supervision, it's a reasonable assumption that he may have plans for how he wants to determine a contest of this nature.
