Well, that’s really simple. No need to do the modular thing as that won’t help to make it any fairer. Just record the number of total valid entries upon the end time and do a dice roll with that number.
For example, the giveaway ends at this post. And the participants so far are (correct me if I’m wrong XD):
So, just do a roll with 3. @discobot roll 1d3
3
Thanks discobot.
And the winner is Scribesake.
Hi! To find out what I can do, say @discobot display help.
Ha ha. Premature but might out to be true, lol
Well, either all my good luck is being used or the randomization on here likes to keep it to the third person…
One can only hope. 
Lol, I personally don’t know how to tell them without my taste XD
probaly that i hit my toes on the staires every week for 7 years 
Dude, I’m with you. I can walk into a door, that’s standing open and I mean wide open at that.
There’s a chair I walk pass everyday, but every now and then: there goes the toe. Owwie!
Also, if you’re entering, don’t forget ze dice roll.
I found out yesterday that Driftland was in the coin shop and I missed it. I had enough coins too. I guess it was sold out quickly.
And discobot already predicts I will lose. Let’s try again.
1 = I win
2 = I lose
3 = I lose
4 = I lose
@discobot roll 1d4
edit: hmm? I guess I messed it up?
discobot is so picky!
I currently know how to do the following things:
@discobot start new user
Starts one of the following interactive narratives: new user, advanced user.
@discobot roll 2d6
@discobot quote
Carry out a random act of kindness, with no expectation of reward, safe in the knowledge that one day someone might do the same for you — Princess Diana
@discobot fortune
You may rely on it
Thanks for the giveaway @Danacscott!
Clumsiest thing I’ve ever done, honestly I can’t think of too much right now, but I remember when I used to rollerblade a lot, I was skating with someone and we were trying to see how fast we could go and I ended up pretty much tripping myself up by going so fast that I ended up sliding on my back. It was a pretty good distance too. It honestly didn’t hurt that bad though. As far as I can remember. Pretty funny looking back at it now. Good times. 
@discobot roll 1d100