Poker against other players is not a game of chance, so breaks the premise in the OP.
Not trying to fight the hypo, but I need more info. If my objective is to maximise my enjoyment, and time is not a factor, I’ll play Blackjack, probably for $25 a hand. With a good dealer/table, that could be a fun way to while away a couple of hours, and I would expect to leave with around $500.
If the goal is to maximise the expected value of the money in my left pocket by the end, I think some sort of Martingale strategy might be appropriate, either on even money roulette bets or (my preference, especially if a 00 wheel) Blackjack. I’d probably go with an initial bet size of 1/31 of my remaining bankroll (i.e. the contents of my right pocket, including the current stake). That’s a starting stake of $32, which would allow for 5 losses in a row (assuming doubling the bet on every loss) before going bust. If the first bet wins, I move the winnings to my left pocket, reduce the stake slightly, and go again. If the first bet of any of these sequences loses, I double it. I’m not sure what the EV would be on this strategy but since the worst-possible outcome is losing $1,000, and the second-worst (four losses followed by a win) leaves $512 in my left pocket and $512 still on the table (plus $8 still in the right pocket), I expect the overall EV to be slightly more than $500.
And, having worked all that out, I see it probably wouldn’t maximise my EV at all - that can be achieved by a single bet of $1,000 on an even money chance, which has EV of just under $1,000, exact amount depending on which game you play. You’re about 48% to end up with $2,000 in your left pocket, and 52% to have nothing.