• Log InLog In
  • Register
Liquid`
Team Liquid Liquipedia
EDT 00:47
CEST 06:47
KST 13:47
  • 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
[ASL22] Ro8 Preview: In A Tizzy10[ASL22] Ro16 Preview: Holy Diver5[ASL22] Ro16 Preview: Rough Waters10[ASL22] Ro24 Preview: Siren's Call8[ASL22] Ro24 Preview: Summer's End9
Community News
Weekly Cups (Sep 13-20): herO scores triple2BSL Season 2312Weekly Cups (Sep 7-12): SHIN, ByuN, MaxPax double down1StarCraft open world shooter announced at BlizzCon101Weekly Cups (Aug 30-Sep 7): herO thrives amid growing schism10
StarCraft 2
General
How do you feel about the StarCraft shooter announcement at BlizzCon 2026? Blizzard Classic Cup @ BlizzCon 2026 - $100k prize pool Balance hotfix patch 5.0.16b (July 16) Weekly Cups (Sep 13-20): herO scores triple The Death of Cheese: From a Professional Cheeser
Tourneys
2026 GSTL GRAND FINALS Sparkling Tuna Cup - Weekly Open Tournament Master Swan Open (Global Bronze-Master 2) Stellar Fest TWO the Moon (Dec 16-20) 2026 GSTL Announcement
Strategy
[H] ZvP Mid-Late Game: Stalkers Collossi HT
Custom Maps
[M] (2) Frigid Storage
External Content
Mutation # 544 Double Trouble The PondCast: SC2 News & Results Mutation # 543 Enhanced Defenses Mutation # 542 The Ascended
Brood War
General
[ASL22] Ro8 Preview: In A Tizzy Bot on ladder BSL Season 23 PLAYzone Challenge - open offline tour in Prague SC4ALL II: Brood War Player Announcement 4/4
Tourneys
[ASL22] Ro8 Day 2 [IPSL] IPSL is Back With Winter 26-27! PLAYzone Challenge - open offline tour in Prague [ASL22] Ro16 Group D
Strategy
Cliff Jump Revisited (1 in a 1000 strategy) Replay Review Process - What do you do? Simple Questions, Simple Answers Odyssey Mineral Stack Saturation
Other Games
General Games
Stormgate/Frost Giant Megathread EVE Corporation Nintendo Switch Thread Warcraft III: The Frozen Throne Diablo IV
Dota 2
Dota 2 Champions League Season 3 Begins April 25! Official 'what is Dota anymore' discussion
League of Legends
[TL LoL EUW IHs] Teemo shall perish
Heroes of the Storm
Heroes of the Storm 2.0
Hearthstone
Deck construction bug
TL Mafia
TL Mafia Community Thread
Community
General
Russo-Ukrainian War Thread US Politics Mega-thread Things Aren’t Peaceful in Palestine Artificial Intelligence Thread All you football fans (soccer)!
Fan Clubs
MarineLorD Fan Club The Creator Fan Club The ShoWTimE Fan Club
Media & Entertainment
Movie Discussion! [Manga] One Piece Diablo Animated Series on Netflix
Sports
Football (Soccer) Thread
World Cup 2022
Tech Support
Computer Build, Upgrade & Buying Resource Thread
TL Community
Recent Gifted Posts
Blogs
Violent-Cooperative Play and…
TrAiDoS
38 yo Retired SWE loo…
PurE)Rabbit-SF
Can Bots Beat Pros?? Starcr…
namkraft
[meme] I finally understa…
LUCKY_NOOB
Regacy Esports:Our Goa…
regacyesports
Customize Sidebar...

Website Feedback

Closed Threads



Active: 8926 users

Penney's Game

Blogs > MarlieChurphy
Post a Reply
MarlieChurphy
Profile Blog Joined January 2013
United States2065 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 States2065 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 States2065 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 4h 13m
[ Submit Event ]
Live Streams
Refresh
StarCraft 2
FoxeR 42
ProTech2
StarCraft: Brood War
Britney 3669
Larva 400
actioN 270
ggaemo 37
Sea.KH 17
Terrorterran 8
Icarus 7
Dota 2
NeuroSwarm223
Counter-Strike
taco 465
Other Games
summit1g8633
WinterStarcraft392
C9.Mang0291
ViBE144
RuFF_SC2105
Organizations
StarCraft: Brood War
Afreeca ASL 289
Other Games
BasetradeTV43
[ Show 12 non-featured ]
StarCraft 2
• mYiSmile18
• AfreecaTV YouTube
• intothetv
• Kozan
• IndyKCrew
• Migwel
StarCraft: Brood War
• Azhi_Dahaki15
• BSLYoutube
• STPLYoutube
• ZZZeroYoutube
Dota 2
• lizZardDota2121
League of Legends
• Lourlo1212
Upcoming Events
Replay Cast
4h 13m
WardiTV Invitational
6h 13m
Korean StarCraft League
22h 43m
CranKy Ducklings
1d 5h
AI Arena Tournament
1d 12h
GSL
2 days
Yamato Cup
2 days
Replay Cast
2 days
Afreeca Starleague
3 days
Soma vs Jaedong
WardiTV Weekly
3 days
[ Show More ]
Monday Night Weeklies
3 days
Sparkling Tuna Cup
4 days
Afreeca Starleague
4 days
Leta vs Soulkey
PiGosaur Cup
4 days
Kung Fu Cup
5 days
The PondCast
6 days
Replay Cast
6 days
Liquipedia Results

Completed

Super Anchor Qualifying S3
Blizzard Classic Cup 2026
Big Dog Cup 2026 Div 1

Ongoing

ASL Season 22
CSL 2026 AUTUMN (S22)
Acropolis #5
Acropolis #5 - GSA
Calamity Invitational
1win Private Club #1
Logitech G Play Connect 2026
SL StarSeries Fall 2026
FISSURE Playground #3
BLAST Open Fall 2026
Esports World Cup 2026
BLAST Bounty Summer 2026
BLAST Bounty Summer Qual
Stake Ranked Episode 3

Upcoming

Acropolis #5 - GSB
Acropolis #5 - GSC
BSL Season 23
SC4ALL II: Brood War
BSL 23: Non-Korean Championship
HSC XXX
Stellar Fest 2: Lunar Cup
SC4ALL II: StarCraft II
Kung Fu Cup 2026 Grand Finals
RSL Offline Finals
Custodian Cup
Copium Cup
PGL Major Singapore 2026
Stake Ranked Episode 6
BLAST Rivals Fall 2026
IEM Beijing 2026
Stake Ranked Episode 5
PGL Masters Bucharest 2026
1win Private Club #2
Thunderpick World Champ. '26
ESL Pro League Season 24
Stake Ranked Episode 4
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.