The tigers have win-to-lost ratio of 2: 3. the gulls have a win-to-total game ratio of 1: 2. who has the better ratio of wins-to-total games?

Tiger:
Win : Lost : Total
  2   :   3    :    5
(x3)   (x3)
  6   :   9    :    15
  
Gull:
Win : Lost : Total
  1       2    :    3
(x5)   (x5)
  5   :   10    :  15

Tiger →Win : Total →  6:15
Gull  → Win : Total  → 5:15

If both played a total of 15 games, Tiger has a 6 wins chance whereas Gull has 5 wins chance.

Tiger

We need to compare ratios

2/3 and 1/2

make the same denominator

2/3= 4/6
1/2=3/6
4/6>3/6
so 2/3 >1/2
2/3 better ratio (Tigers)