# Multipliers

### 🎰 Base Multipliers (Per Round)

The base multiplier for each choice is determined by the **RTP (Return to Player)** and **probability** of that choice.

⚠️ **Important**: 10% of letters have **special properties** that can instantly win or lose, bypassing normal multiplier calculations!

**Formula:** `BaseMultiplier = RTP / Probability`

#### Choice Probabilities

* Stay with original choice: Monty Hall probability (lower)
* Switch to alternative choice: Monty Hall probability (higher)

#### RTP Values

* **MAX RTP**: 96% (95% if XP selected as bonus reward)
* **MIN RTP**: 75-80%

#### Example Base Multiplier Calculations:

Each round randomly assigns **High RTP (96%)** or **Low RTP (75-80%)** to either Stay or Switch choice:

**High RTP Choice:**

* `BaseMultiplier = 96% ÷ 33.33% = 2.88x` (Stay)
* `BaseMultiplier = 96% ÷ 66.67% = 1.44x` (Switch)

**Low RTP Choice:**

* `BaseMultiplier = 75% ÷ 33.33% = 2.25x` (Stay)
* `BaseMultiplier = 75% ÷ 66.67% = 1.125x` (Switch)

***

### 🚀 Cumulative Multiplier System

For each step climbed, we multiply the base multiplier of that step with **ALL** previous step multipliers.

**Formula:** \
`CumulativeMultiplier = Step1Multiplier × Step2Multiplier × ... × CurrentStepMultiplier`

#### Example — Cumulative multiplier after 3 successful steps:

`CumMultStep3 = StayMultiplier₁ × SwitchMultiplier₂ × StayMultiplier₃`

If player:

* Step 1: Stayed (2.88x)
* Step 2: Switched (1.44x)
* Step 3: Stayed (2.88x)

`CumMultStep3 = 2.88 × 1.44 × 2.88 = 11.94x`

***

### 🪜 Corporate Ladder (7 Rounds)

*(Display values for UI - actual multipliers are dynamically calculated)*

| Step | Max Multiplier |
| ---- | -------------- |
| 1    | 2.88x          |
| 2    | 8.29x          |
| 3    | 23.88x         |
| 4    | 69x (nice)     |
| 5    | 198x           |
| 6    | 570x           |
| 7    | 1,643x         |

Actual multipliers are calculated at the start of the game based on [provably fair](/general/provably-fair.md) random assignment of RTP values to each choice at each step.


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