Strangely, ten reds in a row is not particularly good evidence of an unfair wheel.

For an American wheel, the odds of red in a single spin is 18/38= 0.4737. So ten in a row is 0.4737^10, which is about 0.0005689.

So one should expect five or so such sequences in ten thousand spins. Or one in every two thousand spins.

If a casino spins its roulette wheel 200 times a day, you would expect to see a sequence of ten reds in a row every ten days. If the casino runs ten roulette wheels, it's an every day occurrence.

Low probability events happen regularly with enough samples.

Depends on the situation. At a well-regulated, long-lived casino with lots of tables, it's not good evidence.

But if you see it run by carnies at the county fair where the wheel will be gone tomorrow?

Coming up red 10 times in a row is expected to happen once every 2000 rolls. Given 45 spins an hour that means a table will spin red 10 times in a row once a month. Given a casino with 20-30 tables you can expect to see it once a day. Hardly a reason to shake your faith.

Always happy to see this Motie idiom still in use!

I was familiar with the phrase, but not the origin. Since "motie" is somewhat hard to search for (Ministry of Trade, Industry and Energy?), here's a reference page in case others are interested:

In the science fiction classic The Mote in God’s Eye, we are introduced to the Moties, a species that is trapped near a star without interstellar travel, but that has evolved extraordinary abilities. Anatomically, the Moties have two normal hands … and a third one, which gives them the ability to make and manipulate tools with great dexterity. This leads to the idiom of “on the gripping hand,” following “on the one hand or the other,” and suggesting another way, a better alternative.

https://ellingtonlab.org/blog/2014/12/1/on-the-gripping-hand