I've played indoor cricket twice a week for the last 9 years, and I've always just used my current bat/batting gloves. The indoor cricket we play doesn't allow padding etc, the gloves are actually more so you don't lose grip on the bat more than anything. A lot of people use either the provided woolen gloves or specially made indoor gloves, but I personally just use my regular outdoor gloves, the bat feels so much nicer in my hands and I feel way more in control of shots. As for bat weight, most people tend to use a lighter bat, but also stick to your own strengths and what feels comfortable for you. I tend to just naturally like a heavier bat than most indoor bats, so I use my regular 2'10,2'11 bat and it works fine. The other night I even used an over 3' bat (haven't weighed, but 50mm edges) and it worked fine for me, depends on your game and your approach during your batting innings.
Also we use softer yellow balls with a seam, not hockey balls never heard of that before, sounds scary to be fielding.
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