C++

int howManyGames(int p, int d, int m, int s) {
    int cnt = 0;
    while (s >= p) {
        s -= p;
        p = max(p - d, m);
        cnt++;
    }

    return cnt;
}

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Node.js solution:

function howManyGames(p, d, m, s) { let gamesBought = 0; while(s >= p){ s -= p; p = Math.max(p - d, m); gamesBought++; } return gamesBought; }

Why so many test cases?

int games = 0;
    
    while(p>m && s>0){
        
        s-=p;
        
        if(s>0){
            games++;
            p-=d;
        }
    }
    
    if((s-m)>=0){
        return games + (s/m);
    }
    
    return games;