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This is a long post. Readers beware!
1). If either villan has A-x(diamond), they are probably going to at least call the flop bet, if not raise. If they don't have a diamond, they will probably fold.
2). If either villan has SC's (flush on flop), they are probably going to raise or push on the flop.
3). If either villan has a PP (diamond), they might call a medium sized bet on the flop (10-10+). However, even if they do hit their flush it would be tough to imagine that they would play for stacks.
4). If either villan has a set, they are probably going to raise or push on the flop.
5). If either villan has anything else, they will probably fold to any bet on the flop.
- I don't think either villan has A-K.
How are we doing against villans ranges?
Against A-xo(diamond), you are a 30/70 underdog.
Against A-x(no diamond), you are essentially 50/50.
Against SC's (flush on flop), you are a 25/75 underdog.
Against smaller PP's (with a diamond), you are a 90/10 favorite
Against sets on the flop, you are a 35/65 underdog.
You are significantly favored over all other hands that either villan might be holding. None of those hands will play past the flop if you bet, unless they decide to bluff (10% chance of a bluff, HOH).
How likely is it that either villan is holding these combinations of hands?
A-x (with a diamond): 10%
A-x (no diamond): 10%.
SC's (flush): <1%, considering that you are also holding a diamond, and the odds of flopping a flush are less than 1:100.
A pocket pair(with a diamond): 15%
A flopped set: <1%
Anything else: ~60%
What line maximizes value against this range?
Well, you are an underdog against A-x(diamond). However, with a bet/3bet line, i would imagine that most of their A-x range would be folding, except Ax-Qd, and sometimes Ax-10d.
Against A-x(no diamond), you will usually only get called if they don't fold. A turn bet would probably be enough to get them to fold their hand, as long as it is around 1/2PSB (also a good price for you to see the river for if you don't make your flush on the turn).
Againt SC's, you will not be able to get them to fold on the flop.
Against a pocket pair(diamond), your bet might get called. If you do get called, i would lead 1/2PSB on the turn, whether the turn was a diamond or not. If the turn isn't a diamond, those PP's with a diamond might call considering that they are getting okay odds to see if they can river a flush. If the turn is a diamond, you might get raised (which then pot commits them), or at least a call and you can go ahead and value bet river (1/4-1/3PSB).
Against a flopped set, you will rarely get them to fold on the flop.
Against any other hand, it is very likely that your opponent will be folding to any bet.
-I am not sure how A-x(diamond) will play the flop. So, i am assuming that they will raise 25%, call 50%, fold 25%.
-I am not sure how A-x(no diamond) will play the flop. So, i am assuming that they will fold 80%, call 20%
Summary:
If you get raised on the flop, you are probably against flopped flushes, sets, or A-xd. Assuming that all hands have an equal probability of being held (after the flop raise, obviously if put against a whole range of hands the probabilities are different), you only get villan to fold out probably 25% of his range to a 3bet (the weaker A-xd hands, sometimes sets). ~75% of his range here will still play for stacks, and against that range you are probably ~35/65. Considering the pot odds i think a shove is probably best. Since bet/call is a weak line, and you most likely won't get to see the river card and try to make your flush.
If you get called on the flop, you are probably against A-xd, A-x(no diamond), or smaller PP's (1 diamond). You are favored against this range of hands (assuming all hands have an equal probability of being held), so making a 1/2PSB lead would probably be best. This way, most the A-x(no diamond) hands will probably now give up if they called you on the flop, and smaller PP's (1 diamond) might call the turn getting okay odds to see if they can catch a 4th diamond on the river. Plus, you lose the least against A-x(1 diamond) hands, and get to see the river for a reasonable price.
And if they fold, you avoid playing a big pot OOP with a hand that is basically just a big draw.
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