Considering they had to cancel last night and even though it's cloudy it hasn't rained today and isn't supposed to rain heavily, the play should be able to go on. But I second everything m.m said - if they must they'd make the call close to curtain/even during the show and you can bring or buy a poncho just in case!
If rain is expected they often make the call whether to go on or not pretty close to the performance. They sell ponchos, but they are expensive. Bring your own. I think there is probably a number you can call for The Public.
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