Hey everybody! It's my first post on this site and am pretty excited about the stuff on here.

For this thread I analysed a situation where we are the pf 3b caller and are ip on a very dynamic board that hits our range very well.
For the sake of this, let's go with the assumption that BB is reg 3bing 10%+ BB vs BU.

Here is the situation:

Bu open 2bb, BB 3bs to 6bb we call.

Opening range: 22+, A2s+, K2s+, Q5s+, J6s+, T6s+, 96s+, 85s+, 74s+, 63s+, 53s+, 43s, 32s, A2o+, K7o+, Q8o+, J8o+, T8o+, 97o+, 86o+, 76o, 65o (694 combos for 52.35%)

Here’s a screenshot of my opening range to make it easier.

PFR calling range on bu vs BB 3b :
TT-22, AQs-A9s, K9s+, Q9s+, J9s+, T8s+, 98s, 87s, 76s, Ad5d, As5s, Ad4d, As4s, Ad3d, As3s, Ad2d, As2s, AQo-ATo, KJo+ ( 194 combos) I put half the combos of A2-A5s because I will be 4bing some of them.

Screenshot:

So we get to the flop with 194 combos out of 694 so we call the 3b around 28% of the time. Is that reasonable?

Same sizing as in OP hand
Board 6c7d9d. (12.5bb)
BB bets 7bb,

I will try to use math for the flop situation. Please tell me if it makes no sense.

First
With villain sizing our minimum defense frequency is:
Risk 7bb to win 12.5bb= 7/19.5= 36%
1-0.36= 64%.

So out of 194 combos we need to continue with 124 combos (194*0.64).

Let’s build our raising range on the flop.

Our value range that we would like to raise and get it in is sets, 2 pairs and straights.
66 = 3 combos
77 = 3 combos
99 = 3 combos
8Ts= 4 combos
67s = 2 combos IN total we have 15 value combos we want to raise gii on this flop.

Now let’s assume that situation

Board 6c7d9d. (12.5bb)
BB bets 7bb, Hero raises to 20bb.

In order to know the amount of bluffs we would like to have we have to determine our optimal bluffing frequency.

This is the formula I have for figuring this out.

Z = X / (2X+Y) (this is the simplified version)
Where Z = the optimal bluffing frequency. HERO bets X$ into the pot of Y$.

Z = 20 / (2*20 + 19.5) X = 20bb (hero’s raise) Y = 19.5bb ( 12.5bb plus 7bb cbet)
Z = 0.336 so let’s say 34%

Now we have found our optimal bluffing frequency. We have to determine the amount of bluff combos.

The formula I have:
Bluff combos / (Nut combos + bluff combos) = 0.34 (0.34 is our optimal bluffing frequency)

B / (15 + B) = 0.34 (15 is from our value gii combos (nuts)
B = 5.1 + 0.34B
0.66B = 5.1
B = 7.7 so let’s say 8 bluff combos.

After thinking about this, to find the bluff raise combos I was trying to find the best hands I was going to fold with possibly the worst sdv we have so I came up with these combos.

3 combos of KdQx, 3 combos of KdJx because if we can make him fold his AK,AQ that are ahead and we block the AKdd and KQdd that he could just ship over so that’s 6 combos. For the last 2 combos I decided to bluff raise 2 combos of 55 which have a bad gs and can apply pressure by raise/folding.

This is our raising range
9h9s, 9h9c, 9s9c, 7h7s, 7h7c, 7s7c, 6d6h, 6d6s, 6h6s, 5d5h, 5d5s, T8s, 7h6h, 7s6s, KdQh, KdQs, KdQc, KdJh, KdJs, KdJc (23 combos)

Screenshot:

We are raising 23 combos out of 194 combos. So around 11.8% of the time. Is that too big? And should I be bluff raising some fd also? Because I like to call them ip because we have good equity and being ip we get to realize our equity more often.

For our calling range. Like I calculated before we need to defend 124 combos from our preflop calling range in order to not get exploited.
We are raising 23 combos so we need to call on the flop (124-23) = 101 combos

Let’s go ahead and create our calling range.

TT, 88, 5d5s, 5d5c, 5h5c, 5s5c, AQs, ATs, KTs, QTs, JTs, KdQd, KcQc, AdJd, AcJc, KdJd, KcJc, QdJd, QcJc, Ah9h, As9s, Ac9c, Kh9h, Ks9s, Kc9c, Qh9h, Qs9s, Qc9c, Jh9h, Js9s, Jc9c, Th9h, Ts9s, Tc9c, 9h8h, 9s8s, 9c8c, 8h7h, 8s7s, 8c7c, Ad5d, Ad4d, Ad3d, Ad2d, ATo, AdQh, AdQs, AdQc, AhQd, AsQd, AcQd, AdJh, AdJs, AdJc, AhJd, AsJd, AcJd, KhQd, KsQd, KcQd, KhJd, KsJd, KcJd

I have 99 combos which is relatively close. Decided to float KxJd, KxQd w bdfd. All combos of AQ. 2 combos of AJ w fd and bdfd. Float all my Tx combos with GS. Combos w a diamond for AQ and AJ. All my fd . All pair plus straight draw. Is there something wrong with this?

Screenshot of cbet calling range:

After all this end up raising 23 combos and calling 99 combos for a total of 122 combos.

The others combos we fold which are 194 combos – 122 combos = 72 combos so we end up folding 72/194 = 37% of the time and defend 63% and is close to the number of 64% we found we need to defend.

Wanted to do this for a while hope it makes somewhat sense. Looking forward to replies.