• Log InLog In
  • Register
Liquid`
Team Liquid Liquipedia
EST 05:55
CET 11:55
KST 19:55
  • 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
Behind the Blue - Team Liquid History Book8Clem wins HomeStory Cup 289HomeStory Cup 28 - Info & Preview13Rongyi Cup S3 - Preview & Info6herO wins SC2 All-Star Invitational14
Community News
PIG STY FESTIVAL 7.0! (19 Feb - 1 Mar)9Weekly Cups (Jan 26-Feb 1): herO, Clem, ByuN, Classic win2RSL Season 4 announced for March-April7Weekly Cups (Jan 19-25): Bunny, Trigger, MaxPax win3Weekly Cups (Jan 12-18): herO, MaxPax, Solar win0
StarCraft 2
General
How do you think the 5.0.15 balance patch (Oct 2025) for StarCraft II has affected the game? Rongyi Cup S3 - Preview & Info Behind the Blue - Team Liquid History Book Clem wins HomeStory Cup 28 HomeStory Cup 28 - Info & Preview
Tourneys
PIG STY FESTIVAL 7.0! (19 Feb - 1 Mar) WardiTV Mondays $21,000 Rongyi Cup Season 3 announced (Jan 22-Feb 7) Sparkling Tuna Cup - Weekly Open Tournament $5,000 WardiTV Winter Championship 2026
Strategy
Custom Maps
Map Editor closed ? [A] Starcraft Sound Mod
External Content
Mutation # 512 Overclocked The PondCast: SC2 News & Results Mutation # 511 Temple of Rebirth Mutation # 510 Safety Violation
Brood War
General
Liquipedia.net NEEDS editors for Brood War BGH Auto Balance -> http://bghmmr.eu/ BW General Discussion Can someone share very abbreviated BW cliffnotes? StarCraft player reflex TE scores
Tourneys
[Megathread] Daily Proleagues Escore Tournament StarCraft Season 1 Small VOD Thread 2.0 KCM Race Survival 2026 Season 1
Strategy
Zealot bombing is no longer popular? Simple Questions, Simple Answers Current Meta Soma's 9 hatch build from ASL Game 2
Other Games
General Games
ZeroSpace Megathread Diablo 2 thread Battle Aces/David Kim RTS Megathread EVE Corporation Nintendo Switch Thread
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
Vanilla Mini Mafia Mafia Game Mode Feedback/Ideas
Community
General
US Politics Mega-thread Russo-Ukrainian War Thread YouTube Thread The Games Industry And ATVI Things Aren’t Peaceful in Palestine
Fan Clubs
The herO Fan Club! The IdrA Fan Club
Media & Entertainment
[Manga] One Piece Anime Discussion Thread
Sports
2024 - 2026 Football Thread
World Cup 2022
Tech Support
TL Community
The Automated Ban List
Blogs
Play, Watch, Drink: Esports …
TrAiDoS
My 2025 Magic: The Gathering…
DARKING
Life Update and thoughts.
FuDDx
How do archons sleep?
8882
StarCraft improvement
iopq
Customize Sidebar...

Website Feedback

Closed Threads



Active: 1322 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 1h 5m
[ Submit Event ]
Live Streams
Refresh
StarCraft 2
Livibee 93
herO (Afreeca) 30
StarCraft: Brood War
Sea 13788
Calm 5790
Hyuk 1722
Bisu 1461
Flash 791
Horang2 670
BeSt 569
Larva 478
Soma 360
JulyZerg 246
[ Show more ]
JYJ 237
Zeus 202
actioN 201
Sharp 180
EffOrt 151
Mini 119
PianO 99
Pusan 72
hero 60
Soulkey 60
ggaemo 57
Rush 53
Backho 52
Sea.KH 48
ZerO 45
Mind 39
ToSsGirL 37
Shinee 34
Free 29
910 25
GoRush 23
sorry 22
soO 21
Shuttle 21
Noble 19
Bale 17
Movie 16
SilentControl 11
HiyA 11
Dota 2
NeuroSwarm105
ODPixel101
XcaliburYe61
febbydoto23
Counter-Strike
olofmeister1454
shoxiejesuss1376
allub245
kRYSTAL_58
Super Smash Bros
Mew2King121
Other Games
singsing1468
ceh9539
crisheroes197
Sick155
Pyrionflax78
B2W.Neo55
ZerO(Twitch)16
Organizations
Other Games
BasetradeTV75
StarCraft 2
Blizzard YouTube
StarCraft: Brood War
BSLTrovo
sctven
[ Show 11 non-featured ]
StarCraft 2
• AfreecaTV YouTube
• intothetv
• Kozan
• IndyKCrew
• LaughNgamezSOOP
• Migwel
• sooper7s
StarCraft: Brood War
• iopq 4
• BSLYoutube
• STPLYoutube
• ZZZeroYoutube
Upcoming Events
Wardi Open
1h 5m
Monday Night Weeklies
6h 5m
Replay Cast
13h 5m
Sparkling Tuna Cup
23h 5m
LiuLi Cup
1d
Reynor vs Creator
Maru vs Lambo
PiGosaur Monday
1d 14h
Replay Cast
1d 22h
LiuLi Cup
2 days
Clem vs Rogue
SHIN vs Cyan
The PondCast
2 days
KCM Race Survival
2 days
[ Show More ]
LiuLi Cup
3 days
Scarlett vs TriGGeR
ByuN vs herO
Replay Cast
3 days
Online Event
3 days
LiuLi Cup
4 days
Serral vs Zoun
Cure vs Classic
RSL Revival
4 days
RSL Revival
4 days
LiuLi Cup
5 days
uThermal 2v2 Circuit
5 days
RSL Revival
5 days
Replay Cast
5 days
Sparkling Tuna Cup
5 days
LiuLi Cup
6 days
Replay Cast
6 days
Replay Cast
6 days
Liquipedia Results

Completed

CSL 2025 WINTER (S19)
Rongyi Cup S3
Underdog Cup #3

Ongoing

KCM Race Survival 2026 Season 1
Nations Cup 2026
IEM Kraków 2026
BLAST Bounty Winter 2026
BLAST Bounty Winter Qual
eXTREMESLAND 2025
SL Budapest Major 2025
ESL Impact League Season 8

Upcoming

Escore Tournament S1: W8
Acropolis #4
IPSL Spring 2026
HSC XXIX
uThermal 2v2 2026 Main Event
Bellum Gens Elite Stara Zagora 2026
RSL Revival: Season 4
WardiTV Winter 2026
LiuLi Cup: 2025 Grand Finals
CCT Season 3 Global Finals
FISSURE Playground #3
IEM Rio 2026
PGL Bucharest 2026
Stake Ranked Episode 1
BLAST Open Spring 2026
ESL Pro League Season 23
ESL Pro League Season 23
PGL Cluj-Napoca 2026
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 © 2026 TLnet. All Rights Reserved.