I see what you mean. Most people are not technical enough to see that the smart contract is not rigged. Maybe if it got audited by some reputable company, they would trust?
If it's a smart contract it should be audited I have participated in a project that did a rugpull and it has become a big lesson for me and for many of us here not to trust smart contract-based platform that is not fully audited.
But anyway another concern that I have, let's say in the 10 minute round, there was 5 participant, but a user deposited 4 times from different addresses, so he will have higher chance to win the deposit of that 1 user? Or maybe actually he takes more risk because if that 1 user is in the winner list, he could be screwed. But since the distribution is not equal, it's fine. I am thinking about this logic.
If you're serious about creating a game like that you should do a lot of testing for possible loopholes, and you need to spend money for marketing and its quite costly.