At the gate, your purses, backpacks and cooler type bags must all be open and must fit into a container on the inspection table. That container won't permit anything larger than a 16×16 square. They say nothing over 8 inches high, but I've seen plenty of people drop a full sized day pack in there and they allow them through. You may not bring any glass or metal containers, only plastic. They may ask that you remove bulkier items like jackets which keep them from seeing everything in your bag. You cannot bring knives or other weapons, obviously. You must pass through a metal detector and possibly be wanded if you set it off. The folks at the gates are pleasant and super polite. Entry to the park is amazingly fast even with bag checks and scanning. There is even a "no bags" express lane.
Everyone answered your question however the reason is for it to fit under your seat.
All items permitted into the ballpark will be inspected. No bags or items exceeding the maximum size of 16" x 16" x 8" are allowed into the ballpark. Permitted items must easily fit into a 16" x 16" x 8" container. Bags on wheels are prohibited.
My wife had a very small purse and it was checked. Best to not take any bags and you can go through the faster security line.
A reasonable size is allowed and will be inspected.
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