Or you could look at it this way...
The chance of success on any one attempt is 20%. The chance of seven consecutive failures is 20.97% (80%^7). So if you manage to get a success within seven tries, consider yourself lucky because you beat the odds. One success in eight tries is even money and anything beyond that...you're unlucky, don't play the lotto
I follow your math, but not your conclusions. How is one success in eight, "even money"? The odds of one or more success in eight trials is 1 - (0.8^8) = 83.22%. Those odds are much more than even money, are they not? i.e. I wouldn't bet money against having at least one success in eight trials. In the long term, you would lose all your money.