Does masters/advanced lottery round has a higher chance

[unita]

Hi, I'm currently in my first year of undergrad debating whether or not to do a joint degree of BS and MS (which means that I graduate with a MS in four years) or double majoring. The main reason I'm considering doing BS/MS is that I can go through the masters/advanced degree lottery round when I graduate (which supposedly has a greater chance)? Can I confirm if this is true? Thanks!