While I don't really like this card, I've decided that the ability is not deleterious to a properly constructed deck. It's just so weak that I don't think it's worth a card and 3 mana.
He ain't that bad...
You're familiar with the Monty Hall problem, right? If not, go look it up; it's an example of how asking someone with knowledge of hidden information to make a choice can make a seemingly random choice not so random anymore. The thing is, here, you don't really keep the information the opponent gained; the opponent makes a choice that immediately removes the option that the revealed card is behind the closed door.
It's true that your opponent is replacing one random draw with another. But, they also get to see every other card you're drawing and get a chance to deny you that specific card. It's kind of like a Fateseal, except that you draw past the card whether it is good or bad - the only choice is whether you get it in your hand. So, it's a bit more like showing your opponent a random card in your deck and allowing them to mill it.
If your deck relies on silver bullets to function, this might actually be a really dangerous thing to do. Sure, it's only one card a turn, but if you're going to late game, the opponent is seeing 3, 5, maybe even more cards and milling them. If one of those was your only Hurkyl's Recall, you might be in trouble. If it was one of your twelve copies of Lightning Bolt / Chain Lightning / Rift Bolt, then no sweat.
So yeah, as long as your deck is constructed such that it doesn't mind getting randomly milled, the ability itself is probably okay.
..but he's also not very good.
HOWEVER, this Demon still costs you a card and 3 mana. Is it worth that expense? Well, you wouldn't pay that for a vanilla 3/2 Menace; not in a world full of tokens, anyway. So, if the ability isn't really BAD for you, is it actually any GOOD?
Put another way, how often will this card actually DO anything?
Well, first off, you will never draw a card you really need with this Demon. The opponent won't let you have it. So, the only thing that can happen is you get a useless card OR the opponent gets burned.
Assume an aggro deck has 16-18 lands and Vintage acceleration, so we're talking 23 or so cards costing 0 mana. Then maybe another 10 costing 1, and the rest ranging from 2 to 5 (Force?) or something like that.
About 33.3%, the Demon will do nothing (they'll mill cards with zero CC and no one wins).
Another third of the time, the Demon will give the opponent a choice between taking 1 damage or giving you an irrelevant card. Let's say 4 of your 1 drops are Mental Misstep, which might be basically pointless in the midgame depending on the matchup. Probably a Sol Ring when you're already at 4 - 5 mana is also boring. So, let's say that half of your 1 drops are useless in a given situation, so another 8% of the time or so, showing a 1 drop does nothing.
If you're running Demon, you're probably running 2 drops and you need to be running at least 1 Demon as a 3 drop. Let's say you have 10 2cc cards, 10 3cc+ cards. These guys are probably usually gas, often removal or creatures, so let's assume none are ever useless. That is, assume that your opponent will always burn themselves here.
That means something like 41% of the time, I'd expect Sin Prodder to do absolutely jack-all. The other 59% of the time, he will randomly deal somewhere between 1 - 3 damage, very rarely more in a typical Vintage deck.
With all that in mind, would you play Sin Prodder if he said this?
During your upkeep, flip a coin. If you win the flip, flip the coin three more times and deal 1 damage to your opponent for each flip you win after the first.
Because that's what you're getting here.