• Log InLog In
  • Register
Liquid`
Team Liquid Liquipedia
EST 06:26
CET 12:26
KST 20:26
  • 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
Rongyi Cup S3 - RO16 Preview3herO wins SC2 All-Star Invitational12SC2 All-Star Invitational: Tournament Preview5RSL Revival - 2025 Season Finals Preview8RSL Season 3 - Playoffs Preview0
Community News
Weekly Cups (Jan 12-18): herO, MaxPax, Solar win0BSL Season 2025 - Full Overview and Conclusion8Weekly Cups (Jan 5-11): Clem wins big offline, Trigger upsets4$21,000 Rongyi Cup Season 3 announced (Jan 22-Feb 7)22Weekly Cups (Dec 29-Jan 4): Protoss rolls, 2v2 returns7
StarCraft 2
General
PhD study /w SC2 - help with a survey! herO wins SC2 All-Star Invitational Oliveira Would Have Returned If EWC Continued StarCraft 2 not at the Esports World Cup 2026 [Short Story] The Last GSL
Tourneys
OSC Season 13 World Championship $21,000 Rongyi Cup Season 3 announced (Jan 22-Feb 7) $70 Prize Pool Ladder Legends Academy Weekly Open! SC2 All-Star Invitational: Jan 17-18 Sparkling Tuna Cup - Weekly Open Tournament
Strategy
Simple Questions Simple Answers
Custom Maps
[A] Starcraft Sound Mod
External Content
Mutation # 509 Doomsday Report Mutation # 508 Violent Night Mutation # 507 Well Trained Mutation # 506 Warp Zone
Brood War
General
BGH Auto Balance -> http://bghmmr.eu/ Fantasy's Q&A video [ASL21] Potential Map Candidates BW General Discussion Gypsy to Korea
Tourneys
[Megathread] Daily Proleagues Azhi's Colosseum - Season 2 Small VOD Thread 2.0 [BSL21] Non-Korean Championship - Starts Jan 10
Strategy
Current Meta Simple Questions, Simple Answers Soma's 9 hatch build from ASL Game 2 Game Theory for Starcraft
Other Games
General Games
Nintendo Switch Thread Battle Aces/David Kim RTS Megathread Stormgate/Frost Giant Megathread Beyond All Reason Awesome Games Done Quick 2026!
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 European Politico-economics QA Mega-thread Canadian Politics Mega-thread NASA and the Private Sector
Fan Clubs
The herO Fan Club! The IdrA Fan Club
Media & Entertainment
Anime Discussion Thread [Manga] One Piece
Sports
2024 - 2026 Football Thread
World Cup 2022
Tech Support
Computer Build, Upgrade & Buying Resource Thread
TL Community
The Automated Ban List
Blogs
How Esports Advertising Shap…
TrAiDoS
My 2025 Magic: The Gathering…
DARKING
Life Update and thoughts.
FuDDx
How do archons sleep?
8882
James Bond movies ranking - pa…
Topin
Customize Sidebar...

Website Feedback

Closed Threads



Active: 2450 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
RongYI Cup
11:00
Group D
Maru vs Cyan
Solar vs Krystianer
RotterdaM910
IndyStarCraft 188
Harstem127
Rex110
3DClanTV 81
BRAT_OK 70
Liquipedia
Replay Cast
09:00
Rongyi Cup S3 - Group C
CranKy Ducklings140
LiquipediaDiscussion
[ Submit Event ]
Live Streams
Refresh
StarCraft 2
RotterdaM 910
IndyStarCraft 188
Harstem 127
Rex 110
BRAT_OK 70
uThermal 2
StarCraft: Brood War
Horang2 6702
Sea 4871
Hyuk 1579
Jaedong 671
GuemChi 535
BeSt 467
Stork 338
Larva 334
actioN 315
Mini 278
[ Show more ]
EffOrt 264
firebathero 204
Last 200
Shuttle 166
ggaemo 136
Hyun 120
ZerO 112
Rush 99
Pusan 90
Killer 85
Light 85
hero 66
Mong 61
Sharp 54
Mind 54
Yoon 42
Barracks 31
Backho 31
soO 27
Soulkey 27
Hm[arnc] 26
GoRush 23
Noble 19
Sea.KH 18
Free 9
JulyZerg 9
zelot 7
sorry 6
Dota 2
420jenkins441
Fuzer 168
XcaliburYe86
League of Legends
C9.Mang0381
Counter-Strike
zeus1186
oskar167
edward135
Super Smash Bros
Mew2King81
Heroes of the Storm
Khaldor149
Other Games
gofns14348
singsing1625
XaKoH 170
Sick130
ToD35
ZerO(Twitch)13
Organizations
StarCraft 2
ComeBackTV 785
Blizzard YouTube
StarCraft: Brood War
BSLTrovo
sctven
[ Show 12 non-featured ]
StarCraft 2
• AfreecaTV YouTube
• intothetv
• Kozan
• IndyKCrew
• LaughNgamezSOOP
• Migwel
• sooper7s
StarCraft: Brood War
• Michael_bg 1
• BSLYoutube
• STPLYoutube
• ZZZeroYoutube
League of Legends
• Jankos2039
Upcoming Events
uThermal 2v2 Circuit
34m
BSL 21
3h 34m
Replay Cast
12h 34m
Wardi Open
1d 2h
Monday Night Weeklies
1d 5h
OSC
1d 12h
Replay Cast
1d 21h
WardiTV Invitational
2 days
Replay Cast
2 days
WardiTV Invitational
3 days
[ Show More ]
The PondCast
3 days
HomeStory Cup
5 days
Korean StarCraft League
5 days
HomeStory Cup
6 days
Replay Cast
6 days
Liquipedia Results

Completed

Proleague 2026-01-24
OSC Championship Season 13
Tektek Cup #1

Ongoing

C-Race Season 1
BSL 21 Non-Korean Championship
CSL 2025 WINTER (S19)
KCM Race Survival 2026 Season 1
Acropolis #4 - TS4
Rongyi Cup S3
Underdog Cup #3
BLAST Bounty Winter 2026
BLAST Bounty Winter Qual
eXTREMESLAND 2025
SL Budapest Major 2025
ESL Impact League Season 8
BLAST Rivals Fall 2025

Upcoming

Escore Tournament S1: W6
Escore Tournament S1: W7
Acropolis #4
IPSL Spring 2026
uThermal 2v2 2026 Main Event
Bellum Gens Elite Stara Zagora 2026
HSC XXVIII
Nations Cup 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
IEM Kraków 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.