The PeakGTO Poker ELO rating system was designed to help players to track their progress and get motivated to improve their gameplay, ultimately aiming to master the perfect GTO (Game Theory Optimal) strategy. This unique ELO-based system was adapted for poker, where every hand is an opportunity for the player to earn or lose points based on their decision quality, helping them identify areas where they need to improve. Similar to the chess ELO system, the PeakGTO poker ELO score is not an absolute measure of skill but reflects relative performance based on expected outcomes. Let’s dive into how this system evaluates your gameplay and how your rating is adjusted after each hand.

PeakGTO uses an adapted ELO system to evaluate the player’s performance and results when playing against the Trainer. This system uses a rather complex but effective formula that fits the unique nature of poker decision-making and gameplay.

Just like ELO in chess, the adapted poker ELO rating is not a measure of the player’s absolute strength. It is designed in a way where player’s rating is adjusted every hand, comparing their performance with expected outcomes.

The Poker ELO formula used by PeakGTO is: **E’ = E + B + EMC,** where:

**E:**Current ELO rating of player A before the hand.**E’:**New ELO rating of player A after the hand.**B:**Best answer factor**EMC:**Expected mistake calculation

The first two items are self-explanatory. **E **is the rating that you have at the start of every new hand, while **E’ **is the resulting rating, which is calculated based on the formula. The other two are key ingredients, and we’ll now explain them in more detail.

## Expected Mistake Calculation

Of the two elements in the rating formula, the EMC carries the most weight, as it determines how costly a mistake is for the player’s ELO rating. To accomplish this, it uses the following formula:

**EMC = [-K x (Mev – Aev), **where:

**K:**Scaling factor, possibly dynamic based on current ranking**Mev:**Max EV of the best answer**Aev:**Actual EV of the chosen answer

‘**K**’ is a scaling factor that depends on the player’s rating to start the hand. This means that a higher-rated player can receive a bigger penalty for an error than a lower-rated one. This is a foundation of ELO-based systems, which take into consideration the player’s expected skill level when determining the impact of a particular outcome, be it a result of the game (in chess) or the expected result of a decision (in poker).

**‘Mev’ **stands for the maximum EV of the best answer, i.e., the highest expected value of the best GTO play, while ‘**Aev’** is the expected value of the decision selected by the player.

For example, if you have three options to choose from, where:

- Raising has the expected value of 2bb
- Folding has the expected value of -1b
- Calling has the expected value of 0

Raising is the best option, as it yields the best value. If you choose to call instead, your EMC for the hand would be:

- EMC = -Kx(2-0)

As explained previously, ‘K’ is a scaling factor so it will change as your rating increases or declines.

### EMC Max Impact

The Expected Mistake Calculation Max Impact is a number introduced to the system to prevent one mistake from tanking a player’s ELO rating.

The formula to calculate the Max Impact is:

**If EMC > WAF, Then EMCmax, else EMC**, where

- WAF – Worst Answer Factor, determined by the current rating
- EMCmax – The maximum value of the expected mistake calculation

This system takes into account the player’s current rating, ensuring that one single mistake doesn’t have a huge impact on their overall score. The table for the Worst Answer Factor by different ELO scores is shown below.

Score | Worst Answer Factor | ||

Points Added | |||

Super Pro | 2800 | infinity | -100 |

Endboss | 2500 | 2799 | -75 |

Master | 2200 | 2499 | -50 |

Expert | 2000 | 2199 | -50 |

Pro | 1800 | 1999 | -30 |

Shark | 1400 | 1799 | -25 |

Student | 1000 | 1399 | -20 |

Recreational | 700 | 999 | -20 |

Novice | 400 | 699 | -20 |

Noob | 0 | 399 | -20 |

**The Best Answer Factor**

The second key element in the Poker ELO formula is the Best Answer Factor, marked by the letter ‘B.’ It plays a smaller role in the overall calculation, but it exists to reward the player for making the best (the most +EV) decision in the given situation.

Like the EMC Max Impact, the Best Answer Factor is also affected by the player’s rating at the start of the hand, with lower-rated players getting more points for picking the best option. This makes sense within the system, as a low-rated player isn’t expected to offer as many best picks as a high-rated one, and as they move up, the Best Answer Factor declines.

Score | Best Answer Factor | ||

Points Added | |||

Super Pro | 2800 | infinity | 2 |

Endboss | 2500 | 2799 | 2 |

Master | 2200 | 2499 | 2 |

Expert | 2000 | 2199 | 3 |

Pro | 1800 | 1999 | 4 |

Shark | 1400 | 1799 | 6 |

Student | 1000 | 1399 | 8 |

Recreational | 700 | 999 | 8 |

Novice | 400 | 699 | 8 |

Noob | 0 | 399 | 10 |

PeakGTO’s Poker ELO rating system provides a dynamic way to evaluate players’ skills by comparing their decisions to the optimal Game Theory Optimal (GTO) play. The system leverages the Expected Mistake Calculation (EMC) and the Best Answer Factor (B) to adjust ratings after every hand, ensuring fair progression based on the quality of decisions made. With safeguards like EMC Max Impact, it prevents drastic drops due to single errors, encouraging steady improvement. Overall, this ELO-based approach offers players a clear and motivating path to track their development and refine their poker strategies.