You can see some explanations regarding shares in https://eosbutton.io/about.
It seems that whenever you press the button prior to others, you will get shares of that round.
The actual amount of shares is dynamic according to 3 factors below.
One round never ends as long as the countdown doesn't reach to zero.
So, it's like accumulating all shares of the players until the end of the round and you will get rewarded according to your final shares.
Enjoy your game and receive airdrop every hour distributed.

Quotes:
When you press the button, you will receive shares of that round, which will bring you rewards at the end of that round. The interesting part of this game is that the number of shares you get is dynamic. There are 3 factors that affect the number of shares you get for each press.
The number of tokens attached to the press action: The more tokens you attach, the more shares you will get.
Remaining time of the countdown: This is the most interesting part. The lesser the remaining time, the more shares you will get.
How long the round has lasted for: The longer the round has lasted for, the lesser shares you will get.