Believing that playing on a different casino will increase your chances of winning is nothing but another gambler's fallacy. This would be true only if games on the first casino are rigged. If the games are fair (would be better if they are provably fair) and the results are randomly generated then changing the platform will not change the odds of winning (unless they have different house edges/rtp in which case you have to opt for the one with the lower HE)
Each casino has its unique bankrolls and other things so casinos are not the same and gamblers can not apply their one strategy without modifications for all casinos for similar games.
It's like trading, each exchange has different trading volume and gap between buy and sell walls so that with same capital, a trader will have different impacts on price as well as their entries and exits. Generally, people like exchanges with high trading volume because they want to get as less effects on their entries and exits as possible.
Similar for casinos, they will more prefer to choose big casinos with good reputation and good budgets to pay users even big wins. They don't have to worry that when they win big, a casino will run away or pull KYC card or something against user just to avoid paying out.