Hmm, random distribution huh.. shouldn't there be a minimum and a maximum instead? The allure of a lottery is that they pay for a ticket that is a hundred or thousand times lower than the maximum prize that they can get, so there's actually something to look forward to, regardless of the chances that you'd get. If the prizes were random, it may come across to them that the price isn't anything big at all, especially since the prize is split instead of a single (or two, three) winners.

There's the issue of trust and stuff like that, but you should probably fix the idea first imo. Adding twists is fine, but leave the thing that most lottery users want alone. You'd probably lose more than gain more.