I'd describe it as being a mashup of voting machine development with game design. Gambling is a form of entertainment for most people who do it. When they go to a casino they vote with their dollars on which games they find entertaining. But we can't send our games directly to players, we sell to casinos. And every single one gets tested and approved by and independent regulatory board whose rules create a lot of boundaries/limits on how creative our designs can be.
And the mathematician part is exactly like being a "fun accountant" for the game. We set your fun budget and make sure the player (randomly, on average) never exceeds it.
I did gaming math in Vegas for what I believe to be the biggest gaming math consultancy in Nevada (at least at the time). The games were divided between Table, Slot, and Video Poker. I did table games, because I find slot and video poker math to be boring.
Each assignment to me I was provided the rules of the game and the payout table. It was my job to determine the optimal way to play the game and calculate the house edge if you played with the optimal strategy. When I turned in my assignment I only provided the exact house edge. The owner of the business worked independently to determine the house edge as well, and if our numbers matched then he was confident that it was correct. If we had different numbers then we had to dig in to see who made a mistake.
I found table games fun to work on because of the variety of games people came up with, and it was mostly fun to determine the optimal strategy.
The owner of the company was very ethical. He attempted to convince clients to not spend money on introducing new table games. He would tell them that there was about a 1 in 1,000 chance that they would be able to convince a casino to let them do a 3-month trial run, and another 1 in 1,000 chance that the game would outperform blackjack in terms of dollars earned per square foot per month (not necessarily because it isn't a good game, but just because people love blackjack and are more wary of a game they aren't familiar with (it is intimidating to walk up to a game you don't know how to play, especially if you can't practice online first, and you don't want to feel dumb in front of strangers)).
Slots do fine in terms of making the casino money and plenty of room for variety. They have a high house edge. Video poker has a lower house edge, but a new variant of video poker is just adding the game to the menu of a video poker machine already in the casino. There is also less risk for someone that hasn't played a slot or video poker game because it is just them and the machine and no one to feel embarrassed watching you figure out how to play. So he didn't need to warn people that came to him with those types of games.
For new table games the gaming commission requires a trial period to verify that the drop (the profit the casino made) was statistically consistent with the calculated house edge.
I wouldn't have wanted to do it full time, I did about one game a month on a contract basis. I was going to work on a game a month no matter what to satisfy my curiosity and need to do math (finding a new game in a casino). I found a new game with a mistake that gave the player and edge, shared it with the guy that ran the company and he hired me when he confirmed I was correct.
The exception to his warning about table games was adding side bets to existing table games. That doesn't take up any additional square feet, and the house edge is much higher on all of the side bets, and very easy for the player to understand how to participate in the side bet.
As far as I can recall the only new table game introduced in the last few decades that succeeded was Three Card Poker, and the other poker-variants that spawned from it.
If you want to get into this, you are probably better off working for a company like IGT or Arsitocrat that makes their own games and is constantly trying to come up with new ideas and testing them.
What value are you adding here by shitting on another poster's job? Just because it isn't something that interests you personally, is it necessary to announce that?
And the mathematician part is exactly like being a "fun accountant" for the game. We set your fun budget and make sure the player (randomly, on average) never exceeds it.