It's too bad Alex normal doesn't drop 1 type of token with varying item costs instead of the mess it is now. Everything you get is over taken by lore gear so fast anyway, it's not like it would be game breaking if you got a chest or legs in the first week because you spent all 4 floor tokens on it. Most people are getting their lore chest and Alex legs on week 2 anyway.
Having only 1 type of token would mean people could just roll and leave. Try again if they lost, or move to the next floor if they won. Most of the waiting on loot is because of coveted tokens.
Seriously, a base raid shouldn't be as convoluted as it is.
