>It’s not obvious to me that, with only fifty rounds, you have enough time to identify exploitable agents and exploit them
That was the first line of thinking I had too.
If so, you might want to check-open and call down with your 2′s early in the game to see if you’re going to only be paying 3′s, or what frequency they bluff 1′s.
Also very important to observe whether they call-down with 2′s or toss them in either position, and with what frequency.
On a quick think, the inability to raise means that bluffing (1′s) and semi-bluffing (2′s) is probably more viable… if the opponent wasn’t running any based-on-opposition-adjustment, I wonder to what extent “bet every hand from opening position” might play out. It’s certainly not optimal but might do better than expected. Presumably second-position always folds 1′s and calls 3′s, so you’d wind up with —
ALWAYS BET OPENING HANDS
If each hand mix is around 1/9th of the distribution of hands (it doesn’t say how large the deck is)...
1v1: You steal a little more than a half chip than expected, instead of push or fold to bluff. Opponent never calls.
1v2: You steal one chip… 50% of the time? 70%? And lose an extra chip the remainder of the time.
1v3: You lose two chips 100% of the time, instead of losing one chip as expected.
2v1: You get one chip with minimal gained equity (small value in you don’t have to face a bluff).
2v2: You steal one chip… 50% of the time? 70%? And you push the remainder of the time.
2v3: You lose two chips 100% of the time, instead of losing one chip as expected.
3v1: They fold, gain one chip as expected.
3v2: They fold… 50% of the time? 70%? You get a second chip the remainder of the time.
3v3: They call, it’s a push.
So you’d wind up with...
1v1: +0.5 expected over equity.
1v2: +equity if they fold at 67% or higher, -equity if they fold 66% or less.
1v3: −1 expected over equity.
2v1: Minimally small +equity for not having to make decision against bluff, but not much gained.
2v2: Guaranteed +equity if they ever fold, with their fold rate of 2′s being the equity gained rate.
2v3: Slightly less than −1 expected over equity (since you’d check-call sometimes to protect).
3v1: They fold, as expected. Breakeven.
3v2: +equity on whatever their calling rate is.
3v3: Push, as expected. Breakeven
Assuming the deck is large enough that these are all similarly weighted matchups (EX 1v1 or 2v2 isn’t much less likely), then you’d get +0.5, ???, −1, +tiny, +medium, −1, 0, +medium, 0 [as compared to expected normal equity].
I think that comes out ahead — I’d speculate that among people who don’t sit and run analysis, that they fold 2′s to open bets slightly too often. Or, hmm, maybe not. You could do better than this of course… but the fact that I’m even running the analysis to see if “literally bet everything from opening position” is good shows just how much the inability to raise changes the game.
>It’s not obvious to me that, with only fifty rounds, you have enough time to identify exploitable agents and exploit them
That was the first line of thinking I had too.
If so, you might want to check-open and call down with your 2′s early in the game to see if you’re going to only be paying 3′s, or what frequency they bluff 1′s.
Also very important to observe whether they call-down with 2′s or toss them in either position, and with what frequency.
On a quick think, the inability to raise means that bluffing (1′s) and semi-bluffing (2′s) is probably more viable… if the opponent wasn’t running any based-on-opposition-adjustment, I wonder to what extent “bet every hand from opening position” might play out. It’s certainly not optimal but might do better than expected. Presumably second-position always folds 1′s and calls 3′s, so you’d wind up with —
ALWAYS BET OPENING HANDS
If each hand mix is around 1/9th of the distribution of hands (it doesn’t say how large the deck is)...
1v1: You steal a little more than a half chip than expected, instead of push or fold to bluff. Opponent never calls.
1v2: You steal one chip… 50% of the time? 70%? And lose an extra chip the remainder of the time.
1v3: You lose two chips 100% of the time, instead of losing one chip as expected.
2v1: You get one chip with minimal gained equity (small value in you don’t have to face a bluff).
2v2: You steal one chip… 50% of the time? 70%? And you push the remainder of the time.
2v3: You lose two chips 100% of the time, instead of losing one chip as expected.
3v1: They fold, gain one chip as expected.
3v2: They fold… 50% of the time? 70%? You get a second chip the remainder of the time.
3v3: They call, it’s a push.
So you’d wind up with...
1v1: +0.5 expected over equity.
1v2: +equity if they fold at 67% or higher, -equity if they fold 66% or less.
1v3: −1 expected over equity.
2v1: Minimally small +equity for not having to make decision against bluff, but not much gained.
2v2: Guaranteed +equity if they ever fold, with their fold rate of 2′s being the equity gained rate.
2v3: Slightly less than −1 expected over equity (since you’d check-call sometimes to protect).
3v1: They fold, as expected. Breakeven.
3v2: +equity on whatever their calling rate is.
3v3: Push, as expected. Breakeven
Assuming the deck is large enough that these are all similarly weighted matchups (EX 1v1 or 2v2 isn’t much less likely), then you’d get +0.5, ???, −1, +tiny, +medium, −1, 0, +medium, 0 [as compared to expected normal equity].
I think that comes out ahead — I’d speculate that among people who don’t sit and run analysis, that they fold 2′s to open bets slightly too often. Or, hmm, maybe not. You could do better than this of course… but the fact that I’m even running the analysis to see if “literally bet everything from opening position” is good shows just how much the inability to raise changes the game.
I assumed that it was a three-card deck, and thus there are only six possible hands.
Confirmed.