• Log InLog In
  • Register
Liquid`
Team Liquid Liquipedia
EST 22:53
CET 04:53
KST 12:53
  • Home
  • Forum
  • Calendar
  • Streams
  • Liquipedia
  • Features
  • Store
  • EPT
  • TL+
  • StarCraft 2
  • Brood War
  • Smash
  • Heroes
  • Counter-Strike
  • Overwatch
  • Liquibet
  • Fantasy StarCraft
  • TLPD
  • StarCraft 2
  • Brood War
  • Blogs
Forum Sidebar
Events/Features
News
Featured News
RSL Revival - 2025 Season Finals Preview8RSL Season 3 - Playoffs Preview0RSL Season 3 - RO16 Groups C & D Preview0RSL Season 3 - RO16 Groups A & B Preview2TL.net Map Contest #21: Winners12
Community News
ComeBackTV's documentary on Byun's Career !6Weekly Cups (Dec 8-14): MaxPax, Clem, Cure win4Weekly Cups (Dec 1-7): Clem doubles, Solar gets over the hump1Weekly Cups (Nov 24-30): MaxPax, Clem, herO win2BGE Stara Zagora 2026 announced15
StarCraft 2
General
ComeBackTV's documentary on Byun's Career ! When will we find out if there are more tournament Weekly Cups (Dec 8-14): MaxPax, Clem, Cure win RSL Revival - 2025 Season Finals Preview Weekly Cups (Dec 1-7): Clem doubles, Solar gets over the hump
Tourneys
RSL Offline Finals Info - Dec 13 and 14! Master Swan Open (Global Bronze-Master 2) Winter Warp Gate Amateur Showdown #1: Sparkling Tuna Cup - Weekly Open Tournament $5,000+ WardiTV 2025 Championship
Strategy
Custom Maps
Map Editor closed ?
External Content
Mutation # 504 Retribution Mutation # 503 Fowl Play Mutation # 502 Negative Reinforcement Mutation # 501 Price of Progress
Brood War
General
FlaSh on: Biggest Problem With SnOw's Playstyle How Rain Became ProGamer in Just 3 Months BGH Auto Balance -> http://bghmmr.eu/ [BSL21] RO8 Bracket & Prediction Contest BW General Discussion
Tourneys
Small VOD Thread 2.0 [Megathread] Daily Proleagues [BSL21] WB SEMIFINALS - Saturday 21:00 CET [BSL21] RO8 - Day 2 - Sunday 21:00 CET
Strategy
Game Theory for Starcraft Current Meta Simple Questions, Simple Answers Fighting Spirit mining rates
Other Games
General Games
Stormgate/Frost Giant Megathread Path of Exile Nintendo Switch Thread General RTS Discussion Thread Dawn of War IV
Dota 2
Official 'what is Dota anymore' discussion
League of Legends
Heroes of the Storm
Simple Questions, Simple Answers Heroes of the Storm 2.0
Hearthstone
Deck construction bug Heroes of StarCraft mini-set
TL Mafia
Mafia Game Mode Feedback/Ideas Survivor II: The Amazon Sengoku Mafia TL Mafia Community Thread
Community
General
US Politics Mega-thread Things Aren’t Peaceful in Palestine The Games Industry And ATVI Russo-Ukrainian War Thread YouTube Thread
Fan Clubs
White-Ra Fan Club
Media & Entertainment
Anime Discussion Thread [Manga] One Piece Movie Discussion!
Sports
2024 - 2026 Football Thread Formula 1 Discussion
World Cup 2022
Tech Support
Computer Build, Upgrade & Buying Resource Thread
TL Community
TL+ Announced Where to ask questions and add stream?
Blogs
The (Hidden) Drug Problem in…
TrAiDoS
I decided to write a webnov…
DjKniteX
James Bond movies ranking - pa…
Topin
Thanks for the RSL
Hildegard
Customize Sidebar...

Website Feedback

Closed Threads



Active: 1371 users

Penney's Game

Blogs > MarlieChurphy
Post a Reply
MarlieChurphy
Profile Blog Joined January 2013
United States2063 Posts
Last Edited: 2013-10-23 07:44:44
October 23 2013 07:38 GMT
#1
The Setup: using a totally fair quarter (or whatever common coin to your native locale) and a pen & paper, you and your friend (victim) will place bets on which sequence of coin tosses are most likely to come first... while it looks totally fair, you'll have up to a 7 to 1 advantage over them!

The Scam: This is an old math problem called "Penney's Game". In this game, each player chooses a 3-digit sequence of coin flips... a coin is flipped over and over again, and whom ever's sequence of heads and tails comes first, wins.

in other words, player 1 may choose HTH (heads, tails, heads) as his sequence, while player 2 would choose HHT. when the coin is flipped, the results may be: TTHTTHHT, in which case, player 2 would win.

The Trick: you can always get an advantage over your opponent by going second, and choosing your pattern based on what they pick. The algorithm is simple: just take the first two digits of their pick, and move them to the last 2 spots in your pick. For your first digit, choose the OPPOSITE of whatever your last digit is.

For example: if they choose, HHT, you'll take their first two digits (HH) and move them to the back for your pick: _HH. to choose your first digit, pick the opposite of your last digit... so you'd pick THH.

check out the full wikipedia article for your exact odds, but if you follow these steps, you'll win MUCH more often than lose!


http://en.wikipedia.org/wiki/Penney's_game




Thoughts:
You could make a lot of money or get a lot of free drinks if you memorize the pattern and odds of each scenario and make bets according to the odds. For example. On the 2:1 you can bet someone 2 dollars to their 1, or 10 dollars to their 5.Which is essentially an even money bet, but they don't know this and think they are in an easy win game. And for the 7:1 , you can still bet like 4 dollars to their 2, or 30 to their 10 and be coming out ahead. Alternatively you can always be betting 2 drinks to their one and come home a winner almost every night out at the bar.


odds:

[image loading]

Assuming you memorize the patterns and the odds, you can also still place bets if you let them pick second (hoping to gain better odds) and bet according to your odds.


RIP SPOR 11/24/11 NEVAR FORGET
Nisyax
Profile Blog Joined January 2012
Netherlands756 Posts
Last Edited: 2013-10-23 09:12:36
October 23 2013 09:12 GMT
#2
Nice, going to use this Friday night at the bar to get some money from my mates.
GeckoXp
Profile Blog Joined June 2013
Germany2016 Posts
October 23 2013 09:36 GMT
#3
Your write up is kinda nice, but it'd be way easier to "learn" how to throw the coin so it always comes up with the side you pick. It has a bit to do with how you lay it on the backside of your thumb and how you create the illusion of the coin rotating in air. I'm sure there are guides on youtube or such. More semi drunk people will play with you, because they don't have to bother with patterns, plus it doesn't need a pen. If you want to scam people, go for the easiest way.
ruiyang
Profile Blog Joined April 2010
252 Posts
October 23 2013 09:58 GMT
#4
This is totally awesome. I can totally see myself using this as a drinking game. Thnx OP
Osmoses
Profile Blog Joined October 2008
Sweden5302 Posts
October 23 2013 13:58 GMT
#5
I think the fact that you always go second would be a huge red flag for anyone with even a slightly suspicious nature :p
Excuse me hun, but what is your name? Vivian? I woke up next to you naked and, uh, did we, um?
Trozz
Profile Blog Joined November 2008
Canada3456 Posts
October 23 2013 16:49 GMT
#6
wow what a mind fuck
sick application of math
ill have to try it
A build is not a guess, an estimation or a hunch, a feeling, or a foolish intuition. A build is a dependable, unwavering, unarguably accurate, portrayer of your ambition.
MarlieChurphy
Profile Blog Joined January 2013
United States2063 Posts
Last Edited: 2013-10-24 09:51:02
October 24 2013 09:49 GMT
#7
On October 23 2013 18:36 GeckoXp wrote:
Your write up is kinda nice, but it'd be way easier to "learn" how to throw the coin so it always comes up with the side you pick. It has a bit to do with how you lay it on the backside of your thumb and how you create the illusion of the coin rotating in air. I'm sure there are guides on youtube or such. More semi drunk people will play with you, because they don't have to bother with patterns, plus it doesn't need a pen. If you want to scam people, go for the easiest way.



I recently was informed that a coin is not actually 50%, it's 51%. The reason being is that your thumb rotates the coin on multiple axis from your thumb. So it's always important to cover the coin and let the non tosser guess the flip (so no one cane be aware of the 1% edge)

Related: If you want another 4:1, bet spin a penny on the table and always bet tails. It lands that way 80% of the time of course.







On October 23 2013 22:58 Osmoses wrote:
I think the fact that you always go second would be a huge red flag for anyone with even a slightly suspicious nature :p


That's why I wrote the last line in the OP.
RIP SPOR 11/24/11 NEVAR FORGET
MarlieChurphy
Profile Blog Joined January 2013
United States2063 Posts
October 24 2013 10:01 GMT
#8
I'm not sure if this was addressed anywhere, or the odds of it are astronomically low, but what happens if you do the 10 flips and neither person makes their 3? Like what if you flip it 10 times and get heads every time?
RIP SPOR 11/24/11 NEVAR FORGET
Please log in or register to reply.
Live Events Refresh
Next event in 7h 7m
[ Submit Event ]
Live Streams
Refresh
StarCraft 2
RuFF_SC2 170
ProTech135
Nathanias 78
Ketroc 53
StarCraft: Brood War
Sharp 497
Bale 193
Mong 45
scan(afreeca) 34
Noble 28
Hm[arnc] 13
Icarus 7
Dota 2
monkeys_forever376
League of Legends
C9.Mang0405
JimRising 367
Super Smash Bros
hungrybox347
Other Games
summit1g10230
XaKoH 451
PiGStarcraft250
ViBE201
Mew2King60
Trikslyr42
Livibee39
Organizations
StarCraft 2
Blizzard YouTube
StarCraft: Brood War
BSLTrovo
sctven
[ Show 16 non-featured ]
StarCraft 2
• practicex 10
• AfreecaTV YouTube
• intothetv
• Kozan
• IndyKCrew
• LaughNgamezSOOP
• Migwel
• sooper7s
StarCraft: Brood War
• Azhi_Dahaki16
• BSLYoutube
• STPLYoutube
• ZZZeroYoutube
Dota 2
• masondota22501
League of Legends
• Doublelift3491
• Rush414
Other Games
• Scarra807
Upcoming Events
WardiTV 2025
7h 7m
ByuN vs Creator
Clem vs Rogue
Scarlett vs Spirit
ShoWTimE vs Cure
OSC
10h 7m
Big Brain Bouts
13h 7m
YoungYakov vs Jumy
TriGGeR vs Spirit
CranKy Ducklings
1d 6h
WardiTV 2025
1d 7h
Reynor vs MaxPax
SHIN vs TBD
Solar vs herO
Classic vs TBD
SC Evo League
1d 8h
Ladder Legends
1d 15h
BSL 21
1d 16h
Sziky vs Dewalt
eOnzErG vs Cross
Sparkling Tuna Cup
2 days
Ladder Legends
2 days
[ Show More ]
BSL 21
2 days
StRyKeR vs TBD
Bonyth vs TBD
Replay Cast
3 days
Wardi Open
3 days
Monday Night Weeklies
3 days
WardiTV Invitational
5 days
Replay Cast
6 days
WardiTV Invitational
6 days
ByuN vs Solar
Clem vs Classic
Cure vs herO
Reynor vs MaxPax
Liquipedia Results

Completed

Acropolis #4 - TS3
RSL Offline Finals
Kuram Kup

Ongoing

C-Race Season 1
IPSL Winter 2025-26
KCM Race Survival 2025 Season 4
YSL S2
BSL Season 21
Slon Tour Season 2
CSL Season 19: Qualifier 1
WardiTV 2025
META Madness #9
eXTREMESLAND 2025
SL Budapest Major 2025
ESL Impact League Season 8
BLAST Rivals Fall 2025
IEM Chengdu 2025
PGL Masters Bucharest 2025
Thunderpick World Champ.
CS Asia Championships 2025
ESL Pro League S22

Upcoming

CSL Season 19: Qualifier 2
CSL 2025 WINTER (S19)
BSL 21 Non-Korean Championship
Acropolis #4
IPSL Spring 2026
Bellum Gens Elite Stara Zagora 2026
HSC XXVIII
Big Gabe Cup #3
OSC Championship Season 13
ESL Pro League Season 23
PGL Cluj-Napoca 2026
IEM Kraków 2026
BLAST Bounty Winter 2026
BLAST Bounty Winter Qual
TLPD

1. ByuN
2. TY
3. Dark
4. Solar
5. Stats
6. Nerchio
7. sOs
8. soO
9. INnoVation
10. Elazer
1. Rain
2. Flash
3. EffOrt
4. Last
5. Bisu
6. Soulkey
7. Mini
8. Sharp
Sidebar Settings...

Advertising | Privacy Policy | Terms Of Use | Contact Us

Original banner artwork: Jim Warren
The contents of this webpage are copyright © 2025 TLnet. All Rights Reserved.