The easiest fair games depend on equal, binary outcomes like flipping a coin or drawing a playing card that can only be either red or black. If a game depends on both players choosing an equally-probable outcome, how can one player have a massive advantage over the other?
Welcome to the Humble-Nishiyama Randomness Game, a variant of Walter Penney’s classic demonstration of the power of non-transitivity in simple games. In a straightforward transitive situation, A beats B and B beats C -- which means A beats C, too. But if A beats B, B beats C, and C beats A… we’ve gone non-transitive just like Rock, Paper, Scissors. By jumping into the non-transitive game loop at the most advantageous point, Player 2 can become an overwhelming favorite every time. It looks like dumb luck, but it’s really just smart math.
*** SOURCES ***
“Penney Ante: Counterintuitive Probabilities in Coin Tossing,” by RS Nickerson: ~sdunbar1/ProbabilityTheory/BackgroundPapers/Penney ante/
“Humble-Nishiyama Randomness Game - A New Variation on Penney’s Coin Game,” by Steve Humble and Yutaka Nishiyama:
“Probability of a tossed coin landing on edge,” by Daniel B. Murray and Scott W. Teare:
“Antibiotic-mediated antagonism leads to a bacterial game of rock–paper–scissors in vivo,” by Benjamin C. Kirkup & Margaret A. Riley:
*** LINKS ***
Vsauce2 Links
Twitter:
Facebook:
Hosted and Produced by Kevin Lieber
Instagram:
Twitter:
Podcast:
Research And Writing by Matthew Tabor
Editing by AspectScience
Huge Thanks To Paula Lieber
Get Vsauce’s favorite science and math toys delivered to your door!
Select Music By Jake Chudnow:
#education #vsauce2
18 views
837
313
2 weeks ago 00:02:56 1
Oh Wonder - Technicolour Beat - 10 Years On (Official Audio)
3 weeks ago 00:00:46 1
Настойчивый медведь нашел себе дом 🐻 🏡 #новости #милыеживотные
3 weeks ago 00:03:48 74
LISA - FUTW (Vixi Solo Version) (Official Music Video)
3 weeks ago 00:02:19 1
How to DO Block Blast Glitch - GET HIGH SCORE with Block Blast Hack/MOD APK iOS & Android
3 weeks ago 00:14:37 1
🔴 As US Cozies Up To Russia’s Economy, Putin’s Call With China Just Changed Everything
3 weeks ago 00:11:17 1
Potato Tour of Russia 2025: From Storage to Processing at the WEFRY Plant
3 weeks ago 00:04:19 13
Al Bano & Romina Power - Liberta
3 weeks ago 00:05:19 1
How to Grow Elephant Garlic in Containers – The Organic Way! 🧄#garlic #gardening #containergardening
3 weeks ago 00:00:00 2
GET THE SHOT - Pit of Misery (OFFICIAL VIDEO)
3 weeks ago 00:03:00 18
Architects - “Brain Dead (feat. House of Protection)“
3 weeks ago 02:34:09 1
[Longplay] VNC - The Virtual Nightclub (1997) - Complete Playthrough
3 weeks ago 00:00:00 1
EZ3002D
3 weeks ago 00:03:49 1
Céline Dion - Mama (EXCLU 2025)
3 weeks ago 00:25:49 1
Look at This Plastic Bottle Garden – You’ll Regret Not Knowing Sooner!
3 weeks ago 00:00:00 1
RUNNING POINT Netflix Series Review (2025)
3 weeks ago 00:10:04 1
EDM Club Mix Electric Dream [Future Pulse Remix] |Booster Upbeat Bass 2025|
3 weeks ago 00:12:01 159
RTX 5070 Ti vs RTX 4070 Ti Benchmark 💪 Max Settings Gameplay In 10 Games at 4K!
3 weeks ago 00:03:23 3
Killswitch Engage - Collusion
3 weeks ago 00:12:16 1
This $2K Motor Turns Any MTB Into an Ebike In Seconds
3 weeks ago 00:03:31 1
Celtic woman- music for any soul #folkmusic #epicmusic
3 weeks ago 00:02:02 1
Imagine Peace Tower - a beacon to world peace
3 weeks ago 00:01:00 1
THIS GIRL IS ON FIREEE 🔥 #housedj #remix #djmix #mashup #dj #djgirl
3 weeks ago 00:06:29 1
SATYRICON - Phoenix (Piano cover by Katarina Gubanova and Voice cover by Andrei Formalin )
3 weeks ago 00:00:55 1
Брали котёнка, теперь боимся за соседей 🐾🐯🐈 #животные