Get the Largest Count of Consecutive Value
First of all, you can't trust that table to work.  A table, by definition, is unordered.  SQL is free to return the ones and zeros in any order.

So...  You need to have another column that can be used to sort on -- a date or a game-number, or something.

Then you can ask the question because you can do a SELECT ... ORDER BY ....

The rest is messy.  You should consider, instead, writing the algorithm in your favorite programming language other than SQL.


Add an AUTO_INCREMENT column and index it.
Do a self join on a.id = b.id-1 to find where the transitions are (0 to 1 or 1 to 0)
Extract only the transition ids.
Repeat the auto_in game, but instead of finding transitions, subtract the old ids.  This gives you the run lengths.
SELECT ... ORDER BY .. LIMIT 1 to find the longest run, together with some of the history of where it came from.