The chances are dependent on how many TH/s you are getting. For example if you used 1 R909 at 2 TH/s your chances are 1 in 295,479,206. If you buy 1 S19 XP which is around 140 TH/s then the odds drop to 1 in 4,221,132.
I don't think it's a good idea to mine solo with s19 xp it is currently earning $20 a day minus power cost daily.
USB ASIC sticks would be the best option for solo mining for lottery purposes than solo mining with s19 unit. There are many here still mining solo with Compac F and you will just be wasting the money and power if you mine solo with s19 XP.