These rules of marbles go back, for me, a long way and can have more or less significant variations.
In my case (say from 1966 to 1972), we had three types of games; the hole, the tick and the eye.

For the hole, a more or less flat corner of land with (of course yes) a hole. We agree between participant the number of marbles to play (3, 5, 100, what we want) and if we play “for real” or “for fake”. Only for real the marbles change owners.
Then everyone puts their marbles on a starting line and, using a flick made with the thumb and forefinger, you must be the first to put all your marbles in the hole. If we win, we postpone all the marbles in play.

For the tick, it is a kind of shooting from far enough (to be agreed between participants) or one wishes to reach a marble placed on the ground using another marble. The first to hit the goal wins the opponent’s goal and marble.

Finally, the eye consists in trying to touch a ball placed on the ground using another marble that is placed near his eye and released to hit the goal. If we hit the marble on the ground, the goal, we win that goal. The game is easy but small gain.

As for “la dégonfle”, it is indeed a way of saying that I heard like “jouer à la dégonfle”, “…à la dégonflette”, etc.

I hope that my answer will suit you and that it will be useful to you.