If everyone has the same amount of starting capital it is a fair game assuming both can opt out at any time.
That said, the house appears to not be able to opt out (they definitely can, you just don’t think about that part), and the house has more capital. For them each time someone plays a round there are only 3 possible outcomes. Half are the player loses, then a quarter are the player wins and plays another round, and lastly a quarter are the player wins and ends the game. The only case where the player wins is option 3, in all other cases, so 75%, the house wins because the next round has another chance to make the player lose directly at a 50/50 chance or play another round.
The question is not about what is possible, it is about what is common. Also, I am not saying the SAD is good or even better than vegan. Anyone trying to eat well is likely to make some of the same good choices, such as reducing refined sugars, dropping a portion of their ultra processed foods, and monitoring and meeting their protein needs. Being unable to hit your protein needs on a vegan diet is something an incautious person may experience, but supplementing protein or increasing protein components in your meals is manageable.
That all said, it takes extra work. Most people don’t have the spare effort to cook at home for every meal, people are time and money poor and stressed beyond all reasonable limits, so we need to try to make some sort of plan that can actually be followed, not just some ideal. Is vegan possible? With effort and education it seems that some people can manage it, so at least some portion of people could do that. On the flip side if someone eats fish and chicken as their meat rather than beef have they not made progress from a bunch of ways? Definitely fewer carbon emissions. I don’t claim to know the answer for what we should do but saying “do this perfect thing” seems counterproductive.