You also need to factor in the type of game being played. So for example Poker and Sports betting are the gambling games with the best chance of being profitable in the long run, with casino games having the lowest chance of long run profitability.
But it still requires you playing perfectly (poker) or taking advantage of mis-pricing (sports betting).
All games could be profitable, even if you have a house edge of 99%.
It is only a matter of right probability distribution.
Please read up on it:
https://en.wikipedia.org/wiki/Probability_distributionGambling firms do a lot of things to try and remove the player edge, be it as simple as table limits/max bets or cross selling you more profitable games all the way up to refusing any further business for consistent winners. So while mathematically I think you are correct, in reality it can be very difficult to be in the long tail of profitable winners due to random chance.