It looks like the current base rate is a very competitive yield, and I'd expect the odds to be lowered soon, since their lottery gives the equivalent of about 3.6% in interest in addition to the 0.20 base interest. Another startup (Level Bank) using the same banking partner (Evolve Bank and Trust), launched with 2.1% APY in February, but soon had to lower it to 0.5%. This comment (
https://news.ycombinator.com/user?id=adammoelis) by the CEO suggests they are subsidizing the lottery temporarily.
The variance should be relatively low for deposits in the 5 figures and above. See the results of my calculations below, based in part on the spreadsheet linked from https://news.ycombinator.com/item?id=23781247
If one holds $10K in the account, one should get 400 entries a week, and the expected number of times to hit each prize under $1 is between 1 and 9 times every week. I calculate the equivalent interest rate from the <$1 prizes alone is about 2.02%.
The $10 and $15 prizes should be hit about once every 2-3 months, and add about another 1.16% to the expected winnings.
Since the $300 and up prizes are split amongst all winners, it's hard to calculate the expected value, but assuming 10 million entries a week, the EV of the larger prizes is adds about 0.42% extra per year, with the vast majority coming from the expected value of the $5.8 million prize.
I believe that would be very unlikely for one to get below the equivalent of 2% interest over a few months if they held tens of thousands of dollars in an account, with the median outcome being around 3.4%. One could run a simulation to confirm this.