Mark777:
Starts with 40 life. Goes to 42 on first upkeep. Plays Chasm on turn x, with 38 + 2x life. On turn y, he must pay 2(y-x) life, so his life total change on turn y is 2(y-x-1). On turn z, his life change from turns x+1 to turn z add to Sum(y=x+1->z)[2(y-x-1)] = 2Sum(n=0->z-x-1)[n] = (z-x-1)(z-x). His life total on turn z is, then 38 + 2x - (z-x-1)(z-x) = 38 + (z+x) - (z-x)^2.
And this is without counting the Choker! And without counting any damage I can do to him before he plays the Chasm.
It is of course best for him to play Choker on turn one, since he can play Chasm on two and never lose any life to the Choker. Wow, so at least that's easy. Wait, no, he loses two life on his second upkeep, before he can play the Chasm. So, he can either start hitting me on my turn one, or on my turn two. If he chooses the first option, the above formula is two life points too high.
Every player controls the Choker on his turns. Since I can't deal damage to him, my best strategy is to remove a token from the choker on my upkeep, before the damage-dealing resolves. I can start doing that on my turn four. If he played it on turn one and he started the game, it has eight counters, and it dealt 9 damage to me already. So it deals another seven, then 8, 9, and finally 10, killing me my turn seven. Which is right after his turn seven, and he can easily life that long. In fact, for x=2 and z=7, his life total on his seventh main phase is 20.
So I think it's safe to say I lose, without going into complete details of his best tactic, and the variation for me going first.
I haven't done this much math, and enjoyed it, for a few years now