OP, you can definitely think of this as a separate strategy because it is impossible for a gambler to stop in time and only those who can make this impossible possible can succeed in gambling. After three consecutive wins, a gambler should definitely stop gambling for a while. But instead of stopping, many gamblers start betting again, and thus a gambler forgets that he should have stopped in time. This strategy is certainly difficult for a gambler to master and can certainly be called a strategic quality.
You can't be sure that you will win three games in a row. Gambling is full of uncertainty. You may not be able to predict when you will win, most of the time you will lose. In gambling, your strategy may not be effective if you cannot control yourself. What I mean is that you have to practice self control and keep within the allotted limits. When you stop depends on your budget and your own plan. In my opinion, if you can win at least one game, you should stop playing for that period because you may lose the next game.
Following you with your statement, allowing yourself to perform your created strategy always depends on how you control yourself, executing things in a discipline ways and not to allow emotions to dominates, stopping on the right time is a self defined thing in each gambler, if you believe that you can execute your strategy what best to combine is the timing of execution, like you said if you already win why bother to push forward better to quit and enjoy your earnings, there are always lots of time for your gambling activities. Enjoy the opportunity that's being given it's not always be the same outcome.