Interesting idea. I think the gambling aspect works well, because you can re-roll the dice at the cost of money, so even though it is random, it feels like I can control it.
The main issue for me (which is easily fixable) was the speed of the dice rolling. In the last half of the game, I had so much money, and all I did was click to place a tower, then waited 15 seconds for the dice to roll, chose some dice to keep, waited another 10 seconds for the re-roll, and so on. Probably 90% of the game was just waiting.
Also, I never once rolled a cheese. Could be a bug? Or am I really unlucky? :D
Anyway, besides the waiting issue, overall a solid tower defense game.