Since this is limit holdem, the maximum pot for this scenario is $355, of which you can invest a maximum of $69 (after a forced blind post). Hence you will never win less than $200 - $69 = $131 if you always bet/raise and are shown a better hand. However, it is still possible to play this hand suboptimally even if it's impossible to lose at showdown. Here's the optimal line:
- If you are a pot-odds dog vs. your opponent's range, always check/call.
- If you are a pot-odds favorite vs. your opponent's range, always bet/raise.
As you are favored on every street in the hand history you posted, your line up to the river is definitely optimal.
On the river, your expectation for calling is (1 - x) * $70 + x($200 - $6) = $124x + $70, where x is how often you lose. Your expectation for raising is (1 - y) * $70 + y[(1 - z) * $76 + z($200 - $12)] = y($112z + $6) + $70, where y is how often your opponent calls and z is how often you lose when he calls (we've assumed he never reraises for simplicity). Hence your line is correct if $124x + $70 > y($112z + $6) + $70. If your opponent always calls and wins, the inequality becomes $124x > $118, making calling the best play if you lose the hand more than about 95% of the time when you do call.
This is as simple as it gets without analyzing bluffing ranges etc. and is quite a bit more complicated and probably not worth doing for no limit games and limit games for which the pot frequently exceeds the bonus. (And for significantly larger jackpots, utility considerations come into play.)
To summarize, if your opponent can fold a better hand to your reraise, which seems impossible here, reraising would be a clear mistake. As played out the dollar difference either way doesn't warrant being berated, and in general the optimal line for this game with the given bonus is given by the two rules above.
EDIT: Fixed some calculations, and additional comments...
Interestingly, the better the Aces Cracked bonus is, the more that skilled players draw from it; and the worse it is, the less that skilled players draw from it. In this case, then, the value of the promotional drop is worse than breakeven for the worst player at the table. (Think seven-deuce side bet in no limit.)
The justification for #2 has an analog in no limit through fold equity on a draw, though it presents itself in the reverse manner of putting in money. That is to say, it's only correct to raise all-in on a draw as a pot-equity underdog if you have enough fold equity to cover the loss. In your case, you always have enough "backup equity" to cover the case when you are behind your opponent's range, but when you are behind with a greater frequency than your pot odds, you lose money on every additional dollar that goes in the pot even though it's deducted from a net gain.
This is essentially a pot odds argument. You're obviously ahead on the turn since your opponent has more draws in his range than made hands better than yours. Without dissecting entirely, let's say you're a 2:1 favorite. You win roughly that portion of the pot and are compensated $200 when you lose. It's always going to be good to bet since your bet lays you almost 8:1. The key addition is that when you bet/raise as the favorite, you never bet out a hand which beats you - the strategy changes if this were not the case.
Do whatever it takes to get to showdown, but do so passively as the pot underdog. There may be special cases where aggression as the favorite folds out a better hand, but this is mostly against overly cautious players or particularly scary boards.
EDIT: Correction for multiway pots...
My apologies, the above analysis is only good when the hand goes heads-up. The multiway case depends on the stakes relative to the bonus, which here I think "trying to lose" is a good basic strategy.
Your preflop play is correct as you are unlikely to fold out players who stand to release your bonus, at the same time value raising if you happen to win the hand anyway. If you were not last to act, raising may be suboptimal.
From the flop forward, I like playing the hand passively until the hand goes heads-up, after which you adopt the strategy I outline above (playing normal, good poker). I think Villain is correct about your mistake on the turn.
I like a check on the river, planning on check-calling. Your reasoning is sound, and there is an off-chance you can gain a bet from a bluff.
The "trying to lose" strategy has an analog in tournament poker bubble situations in which you can maximize your money equity by cooperatively checking down. To be a bit more thorough, on the turn your hand is 70% to win against Villains with assumed ranges of {any two clubs}, {pair plus straight draw}, {any nine}, and {a random hand}, of which the draws are about 26% chance to catch up. If we fold out straight draws half the time and all non-flush-draw hands, our bet wins us $6 * 70% + $200 * 23% = $50, whereas checking would win us $200 * 30% = $60.
