OK, Im going to take a different approach to this (much to great surprise of most of you
)
I am largely basing this on 3 of the premises posited in the OP, namely:
1) No Card Counting -
I will incluide the constraint that since this is not allowed, neither is any other action which a Casino would frown upon (break your fingers in old school Vegas), ie using a betting system, even a simple, progressive system as in a later post benny the cunt did say that the house always retains its +EV over us (which I think you will find is a tad bigger the 0.5%??)
-This denies
any possibility of negating some or all of the mathematical +EV the 'house' enjoys over us.
-Having even a vague idea of some sort of count is almost unconcious for me when I play BJ and not doing so would akin to trying to deliberately ignore pot odds in poker, ie: hard and completely messes with your game (if you gather some info but cant use it)
(Also, having a shoe of 8 decks is very possible to beat with counting, and under the right circumstances more shoes == more profits even)
2) You must play for an entire 24 hour period.
3) Its either make a loss of anywhere upto $1M (with no downside)
OR walk away with some winnings...
I will also impose the restriction myself, that we are only allowed to play 1 hand at a time against the house (nothing is stated either way in OP, but it really doesnt affect my conclusions too much) and assume this is live and not online play (for less hands per hour)
Any reference to playing small stakes BJ for the first X hours, then ramping up the wagers will do no good. The only way altering bet size is going to win you money is if you happen to get lucky for those hands OR you are counting and know when to do so (which is explicitly forbiden) OR you are using a betting system (implicitly forbidden), and neither are about increasing the wager because your 24 hours is running out. (After all, making profit at BJ counting is all about increasin the bet when we have a +ve EV rather than the usual -ve)
How often are we likely to get the opportunity to have a risk free $1M to gamble with, and keep any winnnings? (The OP didnt mention anything about us being anyway hurt if we blew our whole BR??? Didnt say it was OUR money).
Even playing a good BJ strategy, it is unlikely we will profit much (in % terms), and why not shoot for the biggest win possible?
With either choice, you are going to need variance on your side to come out ahead... So if we
need variance working for us, and if it does happen to be, then don't we want that varince to be as large as possible..?? ie try to capitalize on it to the maximum?
Also, lose $1 or $1M makes absolutely no difference to us, but WIN $1 or $1M makes a huge difference....
So, I chose HU with Ivey.
But I in no way mean this to imply that I have any illusions that I can mix it with him on most days ending in 'Y'...
And his ability to rebuy could actually be in our favour... (but also reduce our chances of retaining the maximum of any winnings we do get)
There IS a chance that we can either felt Ivey, or cripple him to the point where he needs to rebuy, early and in a single hand. Given the right set of circumstances this could even happen more than once. (regardless of stakes, although extrememly unlikely if he choses something like $50/$100)
If this happens, it becomes almost trivial (but boring) to walk away with a (big) profit.
But even if we double up only the once, it is still possible to keep most of it.
a) You WILL still win some pots off Ivey during the remaining time.
b) If all you do is steal Ivey's BB a little less half of the hands (on average), you break even, so will hang on to your initial $1M allin profit (a little less cos he
will fold his SB to you sometimes...
***). Taking less than half will also significantly reduce the rate at which you hand him back your (his?) chips...
Granted, doing so will make it extremely difficult to get more chips off Ivey when you do get a monster hand, or a very strong one preflop, but who cares? We've doubled up (or more), and are in loss minimization mode...
Even if we doubled up once, then just folded every hand the most we would lose is about 1.2M, leaving us $800K (15K/hand x ~750 hands in 24 hours)... And you are still going to get hands worth playing (high pockets), cheap flops we hit hard, and win pots off him, so this is a worse case scenario
Of course, one major flaw in this I think (and Im sure there are more, which will be duly pointed out rather quickly) is that Ivey needs to chose the higher stakes, which isnt the most likely thing, but hey, neither is playing a hand where you can double up off him reasonably early!
I think it would be difficult to double any amount of money at BlackJack (even up 70%), given we must continue to play for 24 hours. Perhaps if we went on our winning streak near the end of the session?
And you might play 24 hours of BJ, to come up just short or maybe a little up. Ivey might felt you within 1 hour, and its all over- quick and (relatively) painless, compared to 24 hour session of grinding BJ. (Although nothing is mentioned in OP regarding the possibility of you losing it all, on either game, in far less than 24 hours?)
Actually, considering that last part about playing a full 24 hours, it may be interesting to see if offering a bonus just for lasting that long (but then also placing a minimum BJ wager), would make a difference to anyones answers, as going busto before then is a real possibility in either choice... Say a bonus over what u have left (ie, if its less than you are down, you still get nuthin, but if its 100K and you only 50K down u keep 50)
Basically, regardless of the choices, I would choose the option with the most
potential gain, not the one with the highest probability of ANY gain, no matter how small.
And IMHO, the poker offers the chance of the biggest windfall, albeit harder and less probable.
In all likelyhood we will not have more than we started with in either case, so why not aim the highest if we do manage to?
Sure Ivey will felt me the vast majority of times, but I will also be down to the BJ dealer most times to (which amounts to the same thing, ie 0EV).... And if I get lucky against Ivey, its a much bigger pay day...
However (and here is where the gun would enter the picture) if it WAS my money I had to risk... AND I could play an entire 7 seater Blackjack table to myself, preferable also allowed to play atleast some kind of simple progressive betting system, BlackJack would be my choice.
American style BJ, Im not so sure about though...
But thanks for a great post/thought-experiment benny the cunt....
Certainly got the old neurons firing!
*** Clearly you can't do this the entire time as when he hooks onto your strategy he will just raise 100% of his buttons and 3-bet most raises you might make from the SB; and if you play back- fold knowing you have QQ+ (unless he also has a big PP), so then it becomes how slow can you play the game... 
... why waste 24 hours ?
...11.59% of bad beat stories are just misplayed hands ...