FoundationsTerminologyMatricesRangesThe Four CategoriesConcepts Ranges Foundations-+Range NotationWhen describing hands or a board, we use a specific notation. All the hands in a range being discussed are written inside square brackets [ and ], with hand types, ranges and/or individual hands separated with commas.For instance, if we are talking about a range of AA, KK, QQ, and AKo, it would be written as [QQ+,AKo]. [QQ+] represents [QQ] as well as all better pocket pairs possible in a given range.Sometimes our range will be "capped" for a particular situation. For example, if we expect our opponent is 3-betting [QQ+] and only calling with JJ and TT, that calling range is written as [JJ-TT]. We write the range from A5s to A2s as [A5s-A2s].If the only possible pocket pairs in your range at a given time were TT and JJ, then [TT+] would represent these two hands and not represent QQ, KK, and AA as they are not possibly contained in your range.If, for instance, we use [8+] on a board that has an eight, it means that we include all hands in our range that are a pair of eights as well as all stronger hands.We will also use range notation to convey the board we are using as an example. The first three cards, the flop, are written in the first brackets, the turn in the next set of brackets, and the river in the final set of brackets.For instance, if the flop is Jack of hearts, Ten of clubs, Nine of spades, the turn is the Eight of hearts, and the river is the Two of diamonds, it would be written as [Jh-Tc-9s][8h][2d].In general there are three types of ranges: Polarized, Merged, or Capped.Polarized RangePolarized Range – These hands are strong or weak, without medium-strength hands. Examples:If you were to 3-bet a range preflop of ……you would also be polarized. Your strong hands would be [TT+, 66, 44, QJs, QJo, 87s] and your weak ones would be [AKs, KQs, 97s+, AKo, KQo].When you bet the river, you are polarized; either you have a strong hand and are looking to be called or a weak hand and are looking to get them to fold.If you were to bet the river on a board of:with a range of …… you would also be polarized. Your strong hands would be [TT+, 66, 44, QJs, QJo, 87s] and your weak ones would be [AKs, KQs, 97s+, AKo, KQo]. When you bet the river, you are polarized, either you have a strong hand and are looking to be called, or a weak hand and are looking to get them to fold.Merged RangeMerged Range – These hands are strong, medium strength, and weak. All of the RFI ranges are merged. Any situation where your entire range makes the same action is said to be merged. Since every hand preflop to open the pot is raised, the range is said to be merged.MP RFI range.Let’s use the same range and suppose a flop ofIf the entire range decides to bet this flop, it would also be merged.As a general rule, preflop ranges will be merged and postflop ranges will become more polarized.Capped RangeCapped Range – These hands are medium strength or weak. This range lacks any super-strong hands. Below is an example calling range for MP versus an UTG open:This range is capped as it does not have any very strong hands (such as AA or KK), only medium strength and weak hands (on a relative basis, many of these hands are very strong).Let’s say our range is … On a board of… our range in this situation is capped, as the best hand we could possibly have is Q9, which means if our opponent has A9, then he has the effective nuts against our range.Equity RealizationLet’s refer to the situation we described earlier where Equilab ranked the top 14% of hands as……but we ranked the top 14% of hands to RFI as …Why the discrepancy? The reason is that Raw All-In Equity and Postflop Realization Equity are two different things. If you are All-In preflop, there is no postflop consideration or skill involved-- there is no postflop play.When you introduce postflop play, you add layers of complexity to the game. There is now a slew of strategic decisions that players will have to make, introducing more elements of skill to the game. [KJo] is favored by the Raw All-in Preflop equity, but not by the our Postflop Realization Equity. Why is that?The value of [KJo] is that it will make very strong pairs. When All-In preflop or playing at shorter stack depths, this is a valuable trait.As stack sizes increase, so does the complexity of the game, and thus the role of skill.At deeper stack depths, the value of making a single pair stays the same while the value of making a set, straight, or a flush increases.Sets, straights, and flushes are hands we will rarely make – but when we do, we expect to win very large pots at deep stacks. This is why we rank hands such as [87s, 55] higher than [KJo]. Hands such as [87s, 55] may have less All-In equity than some hands; however, we expect them to realize more postflop equity. 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