Look at it this way: if you have four individuals, you can put four individual names in the hat, or one group name in the hat. The odds of drawing the group name are smaller than the odds of drawing at least one of the individuals. In that sense, the odds of at least one individual drawing are greater.
With a group application, everyone draws or no one draws.
Also, group applications will get rejected if there are not enough permits left to fill the entire group. Take a case where there are 10 permits for a hunt. Nine permits have already been drawn when a group application with four names is drawn. There are not enough permits left to give everyone in the group a permit, so the application is rejected.
If you have to all hunt together, then go for the group application. If the group members can accept that not everyone can hunt, but everyone can go and have a good time, then apply separately. The odds of at least one member drawing are definitely greater when applying individually.
One other consideration is bonus points. If you apply as a group the points of all the applicants are averaged. Assume a party of two, and one applicant has 12 bonus points and the other has 2 bonus points: the group application will have 7 points (average of 12 and 2). That helps the odds of the individual with 2, but hurts the odds of the individual with 12.
