# ADVANCED PLO THEORY

## Chapter Summary

Chapter 3: Advanced Combinatorics (71 pages)

This chapter covers the implications of card-removal on the basic combinatorics introduced in Chapter 1. It has two main sections which have been split into three modules.

The first (Module 3A) deals with the core card-removal cases (flop given known hand, hand given known flop, hand given known flop and hand).

The second (Modules 3B and 3C) uses the connectedness categories developed in Chapter 2 alongside basic pairedness and suitedness combinatorics to enable a comprehensive analysis of how hands hit flops in different ways.

## Modules

Module 3A: Card Removal Combinatorics (22 pages)

This module explicitly summarizes flop possibilities given a known hand, hand possibilities given a known flop, and hand possibilities given a known hand and flop. It also covers some specific interesting blocker combinatorics cases.

To view the first page of Module 3A, click here.

Module 3B: Hand-Flop Interaction Analysis - Connectedness (24 pages)

This module covers the frequencies and types of straights and straight draws that starting hands can flop. This module includes comprehensive charts with frequencies of every straight/draw type for every starting hand. It also includes text analysis organized by connectedness-based starting hand groups.

To view the first page of Module 3B, click here.

Module 3C: Hand-Flop Interaction Analysis - Pairedness, Suitedness, Multi-Component (25 pages)

This module covers the frequencies of hand-flop combinations in terms of pairedness (no pair, one pair, two pair, trips, set, etc) and suitedness (backdoor flush draw(s), flush draws, flushes). Like Module 3B this module contains comprehensive charts and text analysis organized by starting hand groups.

The module also includes some example of combining the three component types, which serves as an introduction to the flopped-hand-strength ranking system discussed in Chapter 4 and then used in Volume 2.

To view the first page of Module 3C, click here.