Why would you make a straight (“5 sequential cards”) worth more than 4 of a kind? Poker values hands in the order of rareness. Quads are quite rare, which is why they’re worth more than a common straight.

If you’re ignoring “signs” (suits) then does that mean you don’t play flushes?

I really don’t like the idea of forcing players to reveal their cards. Showing your cards strategically is a skill in poker, so removing that lowers the skill ceiling and strongly changes what strategy you use for bluffing. Poker is not just about playing one hand at a time, but is also just as much about learning how another player plays and trying to read and exploit that; and inveseley it’s also about manipulating how other players view your playstyle and how they’re likely to try to exploit you. That whole depth is simply removed if you always see what they had.

Is there a reason you don’t want to just play normal poker rules? Giving everyone their own set of 5 cards completely removes the community cards in the centre, so this is now a completely different game and is much simpler. Sharing the community cards is the point of poker. And, have you considered that if you have 10 players at a table, which is common in poker, and each player has 5 cards, then you’ve very nearly used the whole deck (50/52)? That means on a full table you can work out what cards haven’t been revealed yet, while a half-full table would not have the same strategy.

Why are bets limited to doubling? Again, sizing your bet appropriately is a very deep and skillful component of poker, which is now just removed.

Could you explain why you came up with these rules the way they are? They seem quite arbitrary and I wouldn’t play with these rules. I’d gladly play a standard game such as texas holdem or omaha though.

I wouldn’t try to reinvent the wheel. Unless you have a specific goal that you’re aiming for, I wouldn’t change the rules too much - poker is a pretty battle-tested game and the rules are there for a reason. If you want to make changes then that could be interesting, but you’d have to understand how the game is played and what affect the changes would have.

edit: ok, so that I’m not just being negative here, I will add that I don’t think I’ve seen a tournament style which periodically removes the player with the smallest stack (or in your terms, number of points). That could be an interesting new style of tournament, where the objective isn’t necessarily to accrue the most points but just to survive to the next round. In itself it wouldn’t change much, but if you had some other synergetic rule about maybe redistributing/resetting stacks after each round or something, I’d actually be interested in exploring that idea. Maybe if instead of resetting to zero, everyone’s points are halved every 3-5 hands, so negative points are less negative and positive points are less positive. That would reward wins in the short term, but the effect of both blunders and big wins would decay away quite quickly, assuming you aren’t knocked out. So the focus would be much shorter term of just surviving the next cull. Without playing it through I couldn’t say for sure, but sounds like it could potentially foster interesting strategies.