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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
Canada3457 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
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