When I wrote ISF Theorem a half year ago, I was at a very frustrating point in my game. I was a very marginal winner at 200nl and was going on two straight losing months, which was absolutely devastating to my bankroll. Then one day, I stumbled upon one of the most fundamental concepts of poker, and my game completely changed. That fundamental concept I named ISF theorem. After that moment, my game had completely changed, and the following month I made 20k. Finishing January with another 20k month made me look back onto my old post ISF Theorem and saw that there were a lot of issues in clarity and simplification. Many were reading it and still could not apply it correctly. So today I’m going to revise it.

The process of learning poker is a funny and disappointing process for beginners. Overwhelmed subconsciously by the massive amounts of information that needs to be processed, beginners hold on to the most outwards expressions of poker and begin to memorize them, i.e. should I cbet when I raise AA preflop on a K62 board? They answer these questions through self referral and advice of better players. They rinse and repeat this process until they have memorized nearly all they can and bam, they’ve peaked out at whatever amount of information their brain can hold, whether that be beating 50, 100 or 200 NL.

I will tell you right now, this process of learning is the worst way to learn poker, yet 99.9999% of poker players have done this at one point in their career. Why is this process of learning so bad? It’s like learning math by someone telling you the answer to every addition, multiplication, division, and subtraction problem without you actually bitcoin roulette knowing how to come to those answers. But there are infinite problems and answers in math, so this seems silly doesn’t it? You’d want to be taught how to add, subtract, divide and multiply and then you could know every answer when presented a problem. This is how I want to teach you poker: Rather than simply testing how well you can memorize decisions, tell you what concepts go behind actions so you can know millions of answers to problems rather thank just one. On another note, people tend not to look at poker this way. They think complicated is simple, and simple is complicated. The highest concepts of poker are not “higher thinking” at all, but rather simplified forms of poker knowledge. The specific decisions, the “simple,” is by far the most complicated, as you have to know all the more fundamental concepts to that decision to make a 100% correct one.

So then it would make the most sense to learn the most fundamental concepts first. At an extremely basic level poker is simply this: You have a range and your opponent has a range. Right below this, branching off is how ranges relate to each other. One of those relationships is this: Your range has strength and your opponents range has strength. Strength is defined by a term called equity, which itself is dependent on range gerth (amount of hands), board textures, type of hand (made hand or draw), as well as a few others.

Right below this level is ISF theorem. When your range is strong your inclined to play your range more aggressively, and when it’s weak you are inclined to play your range more passively. In the same way, when your opponents range is weak, you’re inclined to play your range more aggressively, and when your opponents range is strong, you’re more inclined to play your range passively.

Now when I wrote about this months ago, the idea of strength of range still eluded me. I felt like the best definition involved the amount of nut hands you had. For example, in my original post I made the assertion that our range was stronger than our tagg opponents when we raise in the CO and get called in the BB on an 852 rainbow flop. But is it really? Well in some ways it is and in some ways it isn’t. Focusing only on the flop, it surely isn’t. Although we have more nut hands on this board (22,55,88+, 85s, A8s, compared to 88,55,22 only), our range surely isn’t stronger. Almost all good players will raise 20%+ of hands in the CO. But people don’t tend to be that loose from the blinds. Calling ranges from the blinds are mostly pocket pairs, with some suited connectors as well as QJ/KJ type hands. On this type of board we can only expect a very small amount of hands to fold to one bet. Equity wise, on the flop our opponent has better equity than we do.

This was my biggest problem with ISF theorem. Strength of range clearly isn’t exclusive to hands you will stack off with, as when someone decides whether or not to call a flop bet his stack isn’t in mind yet. Explaining how to fix the hole in this logic however is no simple task, but I’ll try my best.

When examining the strength of your opponents range on the flop, you have to group different hands in regard to how they will respond to certain lines. For example in this situation, to a bet flop, check turn, and check river line, our opponents range is strong. To a bet flop, bet turn, check river line, it’s significantly weaker, and to a bet flop, turn, and river line (stack off range). So in general, strength of range applies to many different possible lines that could be taken and how our opponent will respond to those lines. And that’s about as far as I can explain it. In my original post, it seems that people are still confused on how exactly to use ISF theorem in strong range versus weak opponent range situations, hopefully this clarified that a bit.However, one application of ISF Thorem I see almost no one post on is using it to shore up weak ranges. If the roles are reversed, and we are the BB facing a CO raise and the flop comes 852, we are in quite a predicament. Our range is so weak to turn and river bets we risk being exploited by large aggression from our opponents. He could go as far as playing all flopped overcards, draws, and nut hands with a bet, bet, bet line on good turn and rivers, which is a gigantic amount of bluffing, and still make calling on a turn or river bet –EV for us. Because of this, we may want to manipulate our range strength on later streets. We can do this in a few ways.

1. Cold Call nut hands preflop a small percentage of the time (AA-TT in this situation)
2. Folding weak hands on the flop that still have a good shot at being best (44,33 and A2s in this case)
3. Cold calling nut hands on flop and possibly turn some % of the time (sets here).

Number 3 is probably the best way, and 2 and 1 are pretty close to even as far as strengthening your range on versus different lines, in this case involving late street aggression.

I know, I know low stakes players who are reading this. “WTF Danny this doesn’t apply to me at all.” Well the issue with adjustments to shore up strength of range versus certain lines is we sacrifice maximum vacuum EV. For example it may be better for our range facing a turn bet if we cold call 88 to a cbet on an 852 board, but the most +EV decision is almost surely raising the flop. So, what we have to weigh out is whether or not our opponent is going to correctly act against a weak stack off range (which is playing very aggressive). If he isn’t, which is likely, then sacrificing EV to strengthen your range versus different lines is stupid. So even though it may not be best to manipulate your own ranges for this ranges, it’s important to realize that you are making this trade-off.

In fact, when you’re facing a player oblivious to the strength of his range or your range, you should purposely manipulate your range to be super exploitable. For example, for someone who in the scenario previously mentioned is betting one street with air and then giving up. You can call preflop with a ton of hands, float the flop with air, call with super weak draws, severely weakening your range. In spots where they refuse to fold, you can play a super strong range. You could check behind weak to medium strength hands on the flop, but never strong hands, which weakens your flop cbet range as well, knowing your opponent isn’t going to exploit it by aggressively raising your cbets or playing aggressively on the turn and river when you check behind the flop. You probably already do a lot of these things! The concept behind this could be called its own theorem itself, which I will coin as Low Stakes ISF Theorem: Versus passive lines, you should be inclined to play weaker ranges, and versus aggressive lines you should be inclined to play stronger ranges. Although this is still an application of ISF Theorem, differentiating may help you understand the concepts better.

That’s it for this week. I know this is a plethora of information but hopefully you can understand it.