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4

I know what you're supposed to do. You start by tightening your range to about 35% openings. You stop checking back your Ax hands and c-bet call down because that means he's check raising with a polarized range. At the same time, checking back gives away your hand. So, assuming he will not try to bluff you off of top pair you start checking back a portion ...

4

The proper balance is going to depend on your opponent's tendencies. Unless both opponents play Game Theory Optimal, there isn't a single correct answer (and even if they both are, we don't know that answer yet!) If you continuation bet the range that you stated, and your opponent starts check/raising a lot, you can adjust by calling those check/raises ...

3

In my opinion, though this is not an easy task, it can be greatly simplified by remembering that balancing ranges usually means choosing between two basic strategies: Playing different types of hands the same way. Playing the same type of hand different ways. An overall strategy which incorporates a combination of both will ensure we do not become too ...

2

I don't think anything is proven, not even that ev_sb >= 0, so the only bounds we have are trivial: -0.5 <= ev_sb <= 1. An easier question is "What ev_sb do people find solving abstracted versions of HUNLHE". It would be be interesting to know the sorts of values people are getting, i.e. 1) The value of the (abstract) game from the SB's point-of-...

1

I have analyzed limping versus raising over enormous samples (in the millions of hands) in poker tracking programs like HM and PT and found that from a profit standpoint there is no comparison. Raising is simply far more profitable than limping.

1

You never have aces on the button, but you always have a range on the button. If you limp with aces only, how can your opponent ever make a mistake? He will only put more money in the pot when he has you crushed. We make money on the mistakes our opponents make. You should try to construct a range to play OTB that gives you the highest EV. A percentage (...

1

Two points might be helpful here: You can strengthen your betting range while achieving another good thing. If you move some of your weak hands into your checking-back range, then you both strengthen your continuation-betting range and you keep your opponent from reliably reading your hand for one pair when you check back. It's not such a bad thing to ...

1

You can get some tighter bounds by calculating the expected value of some specific strategy (call it S1), knowing that the GTO strategy will be >= S1. For instance let S1 be the strategy where the small blind goes all-in with AA, and folds all other hands. It is a pretty simple probability problem to calculate the expected values in that situation. There is ...

1

I think there is a problem with your definition of ev_sb; you've included a recursive definition that doesn't make sense to me. Also, your definition of r_ev has possibly complicated the problem definition. Instead of r_ev is the part of the initial pot of 1.5BB the sb wins when r I redefine r_ev to be the EV to the SB when SB open-limps or open-...

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