When you apply with a group enrty, you have the same odds as a group as everyone else that put in as an individual.
When you put in on a party tag, everyone is entered together on one application. It does not increase the odds in the sense that if any one person on the app gets drawn then everybody else on the group application gets a tag because everyone is on one entry. That is why if there are only two tags left and a party application with 3 people is drawn then none of them get the tag, their entry is thrown out.
The advantage is that when a party entry is drawn and enough tags remain for everyone on the application then everyone gets a tag. This is good for people who want to hunt together, because either everyone will get a tag or nobody will. If everyone put in separately some might draw and others wouldn't and a family group would have to split their hunting time together.