Vsauce: The Probability of Russian Roulette

Introduction

• Presenter: Kevin from Vsauce
• Topic: Analyzing the probability in Russian Roulette using Balloon Kevin as a proxy.

Russian Roulette Basics

• Traditional Rules: Revolver with six cartridges, one loaded round, spin the cylinder, pull the trigger.
• Odds:
  • 5/6 chance of survival
  • 1/6 chance of fatality
• Balloon Kevin's Version: Using needles in darts to burst Balloon Kevin

Analyzing Survival Odds

• Standard Game:
  • 1 in 6 odds of fatality
  • 83% chance of survival
  • 17% fatality risk

Complex Scenario

• Setup: 6 chambers with two missile positions placed adjacent
• Initial Survival Odds:
  • 2/3 chance of survival
  • 1/3 chance of burst

Round 2 Choice: Spin or Not?

• Option 1: Spin
  • Odds remain the same as Round 1: 2/3 chance of survival
• Option 2: Don't Spin
  • Toy fired once already, knowledge of an empty chamber
  • 75% chance of survival
  • 25% chance of fatality

Insight with Adjacent Darts

• Probability Improvement:
  • Not spinning offers 8% higher survival probability (75% vs. 67%)
• Math Explanation:
  • 4 possible empty chambers
  • Only one chamber is directly before two filled chambers

Random Placement of Darts

• Combination Counts:
  • 6 ways darts are adjacent
  • 6 ways with one space in between
  • 3 opposite positions
• Survival Probabilities:
  • 75% for adjacent
  • 50% for one space apart
  • 50% for opposite

Overall Calculation

• Weighted Probability: Combining all scenarios
  • (6/15 x 3/4) + (6/15 x 2/4) + (3/15 x 2/4)
  • Total: 3/5 (60% survival)

Conclusion

• Survival Rates:
  • Adjacent darts knowledge: Gain 8% (75% vs. 67%)
  • Random knowledge: 60% if not spin
• Implications of Percentages:
  • 8% is significant in various contexts (DNA differences, Election margins, Road safety, Investment gains)
• Final Thoughts:
  • Every advantage matters in a deadly game

Closing

• Sign Off: Thanks for watching.