If you Chaos Warp the Rathi Fiend, you can make them lose 3, which puts them in range of Bogardan Hellkite + Chain of Plasma. Problem is, you lose 3 too, so I can't figure out how to get to the 13 mana that line of play requires without using your Fetchland and City of Brass.
I think your best shot is to put Conspiracy on top of their deck with Noxious Revival, Chaos Warp Alexi's Cloak (50/50 odds ftw), and then cast Hellkite to kill Labman and Blood Artist (plus 2 to the dome), block their attackers, then pass the turn back to them so they can deck out.
If anyone has a better than 50/50 plan for this game, good on them.
Edit: Nope. Fails because they can Burial up Labman, recast, Mulldrifter.
For posterity's sake, here's the solution that existed for this puzzle back when it still had one.
It's great that you got to draw Bogardan Hellkite off the top. But knowing it was there, you would have been better off not drawing it at all!
Tap four basic lands and the Birds of Paradise to unearth Hell's Thunder. This leaves 6 basic lands up (the City and Foothills aren't going to be used).
Go to combat, and attack with Hell's Thunder alone. It has flying, so Chris has no blockers and will take 4 damage, going to 7.
Play Chain of Plasma, leaving 4 lands up. You can target either Hell's Thunder, or your own face. 3 damage will not be lethal to either one, and because you're targeting your own stuff, you get presented with the ricochet option. Discard Bogardan Hellkite to make a copy.
With the copy, choose to target Chris. He takes 3 damage, going to 4, and this time he gets the option. He could have the same kind of trick in mind--discard once, target his own creature to kill it off for a Blood Artist trigger, discard again, and finish you off--but it doesn't matter what he chooses to target (if anything), since everything else can be done in response to his copy.
Play Noxious Revival, going down to 3 lands, or if you targeted the Hell's Thunder with the first Chain, you can pay life for this. Put Bogardan Hellkite back on top of the library.
Play Chaos Warp, targeting Hell's Thunder.
Under the rules of the time, 701.16d read:
If an effect would cause a player to shuffle one or more specific objects into a library, and a replacement or prevention effect causes all such objects to be moved to another zone instead, that library isn't shuffled.
Because Hell's Thunder was brought back using Unearth, it has an effect over its head that'll send it to exile rather than any other zone change it might partake in. Chaos Warp is just such a zone change, so Hell's Thunder goes to exile, and the library order under this rule was not disturbed. Bogardan Hellkite was still guaranteed to be on top for Chaos Warp to reveal. Its ETB ability could hit Chris for 5 damage, winning.
Nowadays, the old 701.16c and 701.16d have been merged into one rule, which has undergone a complete reversal of course--all "shuffle into" wordings now guarantee that a shuffle takes place, and the Chaos Warp procedure fails unless you're fortunate enough to shuffle the Hellkite or some other card with equivalent effect back on top again.
You're playing a brewsy brew in modern, agianst a run-of-the-mill jund deck, it's going pretty well, but then a goyf comes down and they turn around the game. Last turn they cast Kolaghan's Command, destroying your Meteorite and forcing you to discard your last card, a Ezuri's Brigade and it looks like they're going to kill you on their next turn.
Are the opponent's creatures tapped? If they have you at 1 life, no cards in hand, and no blockers, there's no reason why they wouldn't just finish you off last turn if they had the opportunity. Therefore, they either attacked to reduce you to 1 with the intent of finishing you off with the Bolt next turn even if you draw removal, or the opponent is sandbagging and this position cannot rightfully be considered a win.
Inquistor Exarch is the closest to what I had, and totally counts. I had Razor Hippogriff. I imagine with some thinking, most of the other options can be removed. Maybe the game went differently and both Courser and Goyf were cast last turn. I was also thinking there could be a notion theif in play, I had thought of manamorphose, but that doesn't really go with the jund theme.
Razor Hippogriff only puts the card in hand, rather than the battlefield. If the opponent's next card after Lightning Bolt is a land, it doesn't even win (although, between the lifegain and the Tarmogoyf-shrinking, it does just enough to let you survive the first attack).
So, I came up with a variation of the previous Conjurer's Ban puzzle. Here's the set up:
Your opponent went infinite, capsized your board, time twistered, tormod's crypted your graveyard, played elish norn, pacifism on elish norn, cast Sphere of Safety, cast Uba Mask, cast Nevermore naming Dark Ritual, cast Liquimetal Coating, made Nevermore an artifact, cast Karn, Silver Golem, made nevermore a creature, cast Soulfire Grand Master, cast Mirror Gallery, cast Mangara of Corondor, cast rite of replication kicked targeting Mangara and bought back with Soulfire Grand Master. Then they copy Nevermore for every non-land card in the game, ending with rite of replication. Then they use Mangara to exile liquimetal coating, Karn and Soulfire Grand Master. They then pass turn, and dare you to kill them. For simplicity, assume they have 15,000 Nevermores. How quickly can you kill them? They're at 20 life, 0 poison counters, 49 cards in their deck, 7 cards in hand. You have 7 cards in hand, you can stack your deck, and have up to 4 copies of non-basic cards.
Proof that you can win: If your deck is 30,000 Forests, your hand contains 6 forests and a Treetop Village, you can play the Treetop Village, play all the forests, then activate treetop each turn, pay for the sphere, and swing 20 turns in a row. 30,024 turns.
1: "Draw" and play Tolaria
2: "Draw" and play Karakas, tap Tolaria targeting Elesh Norn and triggering Kira (oh no, we don't get to make it lose bands with other!), then tap Karakas to bounce Elesh Norn
3: "Draw" and play City of Traitors, tap it for 2, exile a spirit guide, and play Daru Sanctifier face down (which survives, now that there's no Elesh Norn). 5 cards in hand.
Exile a second spirit guide and tap Karakas to turn Daru Sanctifier face up. Choose to destroy the Nevermore that's naming Echoing Truth. 4 cards in hand.
Exile a third spirit guide and tap Tolaria to play Echoing Truth on a copy of Nevermore; all of them will be bounced. 2 cards left in hand.
Play Black Lotus followed by Timetwister, and the rest is easy. The card draws will be replaced by Uba Mask, but you still have access to them for the turn, and nothing's stopping you from playing them.
This relies on perfect luck for more than just the stacked deck, but it otherwise fits the bill perfectly.
1: "Draw" and play Karakas, exile Simian Spirit Guide and Shinen of Life's Roar to waste the Kira protection on Elesh Norn, then tap Karakas to bounce it. 5 cards in hand.
2: "Draw" and play City of Traitors, tap it, and exile another Spirit Guide to play Daru Sanctifier face down. 3 cards left.
Pitch a spirit guide and tap Karakas to turn Sanctifier face up. Choose to destroy the Nevermore that's naming Mana Clash. 2 cards left.
Pitch a fourth spirit guide to play Mana Clash. Flip 21 straight heads, against 20 tails and a heads.
Given the privilege of just one face up spell, Aura Barbs wins easily against this opponent without needing to manipulate 42 coin flips, but it also needs more mana.