I would like to get some feedback about how people partition their ranges on boards where no one has anything.

(obviously not literally, but the spots where generally both players have weak ranges)

Say for example we are on the BB facing a min raise @ 25BB in a hyper turbo HUSNG.

The opponent model we will assume for this discussion will be:

villain min raising range @ 25BB = 70%

hero flatting range = Ax7x-Ax2x,Ax7y-Ax2y,KxTx-Kx2x,KxJy-Kx2y,QxJx-Qx2x,QxJy-Qx4y,JxTx-Jx2x,JxTy-Jx4y,Tx9x-Tx2x,Tx9y-Tx7y,9x8x-9x5x,9x8y,9x7y,8x7x-8x5x,8x7y,7x6x,7x5x,7x5y,6x5x,5x4x

board = [KK3]

villain cbets 100% of his preflop min raising range 0.5P (where P=pot size before bet) when checked to

'air' will be somewhat arbitrarily defined as

- flopped < pair

- no

'something' will be likewise be defined as (1-air)

Given the above assumptions, if my calculations are correct:

villain has air = 70.56%

hero has air = 79.97%

Which means about 56% of the time both player's ranges are air.

When villain cbets he risks 0.5P to win (P+0.5P) = 1.5P

Which means if we check fold > (0.5 / 1.5) = 33%

Villain auto profits by cbetting 100% of his range.

Note that we will only have 'something' about 20% of the time.

So if we simply check fold all our 'air' and let villain cbet 100% of the time he will exploiting our imbalanced defending range.

I would like to hear player's philosophies/strategies on constructing a range in this spot to find an edge:

Option 1:Bet size differential edge.

If we assume that if roles were reversed that villain would also be giving up too much in this spot then we might be able to find an edge by betting smaller that he would. If we say for example 40% pot and villain folds the same static air range, we profit the differential

40% cbet when BB defends 20%  [ 1 -(0.4 / 1.4) - (0.2 ] P = 0.51 P

50% cbet when BB defends 20%  [1 - (0.5 / 1.5) - (0.2) ] P = 0.47 P

edge = 0.51 P - 0.47 P = 0.04 P

So on average if both players defend here 20% and are not price sensitive, a smaller bet size will on average yield an edge of about 4% of a single raised pot.

Option 2: Defend by calling with more marginal SDV hands or turning more of our hands into bluffs

a) c/r range

b) donking range

c) float and bluff later street range

Considerations: Typically bluffs are most profitable where they are made in spots where:

i) we can rep a lot of strong hands (it is believable we would take the same line for value) => we have a strong perceived range

ii) our opponent's range is weak

So how do we play our value range in this spot?

Or more importantly, how does our opponent typically expect us to play our value range here?

Personally I think 2a and 2b are more heavily correlated to bluffing ranges and a c/c tends to be more correlated to a value range.

That said, psychologically if that is what is perceived, then maybe I do better by donking or c/r my value here and allocating my bluffs into a floating + bluff later range.

Then we also need to think about which hands in our range are best for bluffing?

Option 3: Other options?

eg. Don't care because the spot is so infrequent it doesn't materially contribute to our edge?

Would really appreciate feedback on how to best allocate your ranges in these spots?

+ Any other considerations which I have not factored into my framework? (eg. insight into how players tend to react to lines 2a,2b,2c)