Since I started thinking about "allmighty algorithm" motivate by your video, I started making step by step approach how to construct any given range balanced (off course not perfectly balanced, but the goal is to be decent).

**Assumptions**:

1) current ranges of both opponents are known.

2) hero open raises, villian calls IP all other fold (HU)

3) villian is very good player, who is going to spot all leaks and exploit them

**Goal**:

Construct as much as possible balanced range, try to minimize our leaks using step by step approach for any given input ranges of hero and villian using above assumptions

I will start explaining approach using example, and after example I will formulate step by step approach to make it general.

Example is, preflop hero open raises from CO and BU calls, all other fold.

Hero opens 28% range (352 combos), BU calls with stanard pokerstrategy range from charts.

Flop: 8

4

2

**Phase 1: Splitting into categories**
**step1:**
Find hands that are able to bet 3 streets for value:

99+, 22, 44, 88

(45 combos)
**step2:**
Find hands that are able to value bet 2 streets, or to cbet flop and cc turn, or to cc flop and turn:

8x hands, 55, 66, 77, A2s, A4s

(65 combos)
**step3:**
Find hands that are able to cc flop and give up vs 2nd barrel:

AJ+

(32 combos). (here fd and bdfd combos

are excluded)

**step4:**
Find hands that are good bluffs for cbet (that retain equity) like backdoor draws and draws with >= 4 outs:

(125 combos) here I dont want to listt them because it is longer list and it is unimportant

**step5:**
Find hands that are not having SD value able to call or bet even flop, and not having good playability. It is simply the rest of range, which is (

82 combos).

Now when we splitted all ranges, we can assign them to different ranges

**Phase 2: Assigning combos to ranges**
**step1:**
Determine maximum possible hands that are able to cbet at least flop and to either cbet turn or c/c turn. It is simply range from phase1, step1 and step2. Put them initially all in cbet range

(110 combos)
**step2:**
Determine number of bluffs for the value combos from step1, choosing bluffs that retain equity well. For each 3 street value combo (phase1, step 1 range) use 2 bluff combos, and for each combo from phase1, step2 use 1 bluff combo. These are 125 combos of range in phase1 step4 and 30 strongest hands from phase1 step5.

(155 combos)
**step3:**
Because the hands from phase1 step3 (weak SD hands) and remaining of bluffs cant be in current cbet range (current cbet range is using max value combos and max bluffs in balanced range), they HAVE to be in the check range (if they would be in cbet range we would have to be bluff heavy, or to cbet hands that dont ratain equity well, and to c/f hands that retain equity well which are both bad).

So, put all 32 combos from phase1 step3 in check range and also all remaining of 52 combos from phase1 step5.

(87 combos)
**step4:**
Deterimine c/f range. The combos from phase1 step5 that are not added to cbet range HAVE to be in cf range. (hands bad for bluffing and very low SD value)

(52 combo)
**step5:**
Determine number of combos that are in check/defend range. Since we want to fold 40-50% of time once we check (assuming 3/4 bet size), I will choose 40% fold. It means we need to defend (52/0.4 - 52)

(78 combos)
**step6:**
Determine range from phase2, step5. We need to start moving value hands and draws from cbet range in check/call and check/raise range in order to defend 78 combos on flop after checking. The more drawy the board is, i add more strong combos in check/raise range.

Here I put all sets in check/raise range to reduce villians big positional advantage. 9 combos set, and we can use for each value raise combo 2 bluffs, so in total 27 raise combos.

This means that from 91 combos in check/defend range, we should call 91-27=

64 combos.
As summary, we c/f flop 61 combo, c/r 27 combo, c/c 64 combos.

Since I moved only 9 combo sets from cbet range to check range, and 18 combos bluff (simply buttom bluffs for cbet range, to keep it simple initially) cbet range still remains balanced.

**step7:**
Determine number of combos that c/c flop and c/f turn unimproved. We want to fold turn around 35% vs 3/4 pot size bet, so we fold on turn 64 * 0.35 =

22 combos and we c/c turn with remaining of

42 combos
**step8:**
On river vs 3/4 pot size bet, we want to fold 42% range and to call 58% range.

So we fold 42 * 0.4 =

17 combos and

we call

25 combos
**step9:**
Move value hands from cbet range, into range from step8. On river we usually want to defend at least top pairs, otherwise our range would be too weak and villian could use overbets. We dont want to defend it with too many strong hands because they would loose too much value by playing passive, but we want to put some strong hands. For few strong hands, add hands that dont need much protection and are blocking villians defend range. I would add in this example AsAx, because it needs least protection and it can call down on any runout.

The remaining of 22 combos, I would add 22 weakest top pair combos because hands like A8 can value bet (have more value than 78), same is for any top pair.

Now since we moved 3 combos AsAx from cbet range that can value bet 3 streets, we need to move 6 bluffs to check range so that cbet range remains ballanced. We also need to move 22 combos bluff from cbet range to check range for all 8x combos. In total we will currently remember that we need to move

28 combos bluffs to check range from cbet range.

**step10:**
Now when we have river defend range, we need to determine completely turn defend range. On turn we defend 22 combos 8x and 3 combos AsAx (which we defend also on river), and we need now to determine additional 17 combos that call turn and fold river (unimproved). Since we want to be able to defend on river if flush completes, I would put As9s-AsKs, KsQs, KsJs (8 combos fd) which can also improve to top pair on river and have SD value so they can win even unimproved some % of time.

So we need 9 additional combos, and I would add 6 combos 77 and 3 combos 66.

So since we moved 8 combos fd from cbet range to check range, we need to move 20 bluff combos more so that cbet range remains balanced.

**step11:**
Determine range that c/c flop and c/f turn unimproved (22 combos). For that, imo some of AT-AK combos are the best because they have SD value and can check down on later streets, and also we will have some TPTK hands on turn if T-A cards come. Also I would add to that range some GS (maybe also some bdfd) because we want also some floats that have little SD and can improve to nuts, because when villian checks back turn we have combos to bluff on river unimproved. So I would add 67s 56s, 57s (12 combos) and 10 combos from AT-AK (from each 2 combos).

... to be continued no time now.