Battle Royal 🏆

The Battle Royal format transforms your wheel into an exciting tournament where participants face off against each other in head-to-head battles. Think of it as a knockout tournament where only the strongest survive!

How It Works

When you select Battle Royal format, the application automatically creates a tournament bracket for all your participants. Here's what happens:

Tournament Structure

• Bracket Generation: All participants are organized into a tournament bracket
• Head-to-Head Battles: Each spin features only 2 participants with similar point amounts
• Winner Takes All: The victor claims all points from their opponent
• Advancement: Winners move to the next round, losers are eliminated
• Final Showdown: The last two standing face off with roughly equal points

Point Distribution

The tournament is designed so that the final round features two participants who each hold approximately half of the total auction points. This creates an intense, balanced finale where both finalists have equal chances of victory.

Fair Play Guarantee

Despite the tournament format, Battle Royal maintains the same mathematical fairness as the normal wheel.

Mathematical Proof

Theorem: In Battle Royal format, each participant's probability of winning the tournament equals their points divided by total points.

Given:

• Participants have points p₁, p₂, ..., pₙ
• Total points P = p₁ + p₂ + ... + pₙ
• In each battle between participants i and j, P(i wins) = pᵢ/(pᵢ + pⱼ)

To Prove: P(participant i wins tournament) = pᵢ/P

Proof by Mathematical Induction:

Base Case (n = 2): With 2 participants having points p₁ and p₂:

P(participant 1 wins) = p₁/(p₁ + p₂) = p₁/P ✓

Inductive Step: Assume theorem holds for k participants. Consider k+1 participants.

For participant i with points pᵢ who battles participant j with points pⱼ:

1. Survival Probability: P(i survives battle) = pᵢ/(pᵢ + pⱼ)

2. Points After Victory: i gains j's points → total points = pᵢ + pⱼ

3. Remaining Tournament: By inductive hypothesis, P(i wins remaining) = (pᵢ + pⱼ)/P

4. Total Probability:

P(i wins tournament) = P(i survives) × P(i wins remaining)
                    = [pᵢ/(pᵢ + pⱼ)] × [(pᵢ + pⱼ)/P]
                    = pᵢ/P ✓

Key Insight: Point conservation and proportional battle outcomes ensure that initial point ratios determine final winning probabilities, regardless of tournament bracket structure.

Example:

• Alice: 300 points (30%)
• Bob: 500 points (50%)
• Charlie: 200 points (20%)
• Total: 1000 points

No matter how the tournament unfolds, Alice always has exactly 30% chance of winning, Bob has 50%, and Charlie has 20%.

Why Choose Battle Royal?

✅ Dramatic Tension: Creates exciting knockout-style entertainment
✅ Engaging Storylines: Viewers can follow their favorite participants through rounds
✅ Balanced Finals: Ensures competitive final matches

Settings

Grouping

The Battle Royal format includes a special Grouping setting that lets you control the pace of your tournament:

Default: Duels (1v1)

• Each round features exactly 2 participants
• Best for smaller participant pools

Multi-Participant Groups

• Adjust the grouping slider to include more participants per round
• Speeds up tournaments with many participants
• Still maintains competitive balance

💡 Tip: If you have 100+ participants, consider increasing the grouping to 3-4 participants to keep your stream moving at a good pace.

When to Use Battle Royal

Perfect for:

• Gaming streams with competitive themes
• Longer streams where you can build tension over time
• Underdog Stories: Watch smaller participants defeat larger ones