The Coin Flip: A Fundamentally Unfair Proposition? (2009) (opens in new tab)

(econ.ucsb.edu)

41 pointsgluxon10y ago30 comments

30 comments

"1% may not sound like a lot, but it's more than the typical casino edge in a game of blackjack or slots."

The house edge for slots games is anywhere from 2% to 15%+ and is one of the worst bets you can make in the casino.

Blackjack, video poker and some bets on craps are the only times in a casino where the house edge shrinks to below 1%.

  Blackjack, video poker and some bets on craps are the only
  times in a casino where the house edge shrinks to below 1%.

Care to cite your source for this or are you a gaming industry insider?

PhantomGremlin10y ago

There's no need for a source. It's common knowledge. Many books, websites, and research papers have extensively studied those games.

Edward Thorp is a mathematician who did a lot of analysis about blackjack over 50 years ago.[1] He's a seminal figure in this field.

Here's one site I recall mostly because it has a memorable name: http://wizardofodds.com/

[1] https://en.wikipedia.org/wiki/Beat_the_Dealer#History

1 more reply

albedoa10y ago

> Care to cite your source for this or are you a gaming industry insider?

Strange dichotomy to those of us who have been to a casino. They tell you right at the games — you don't need to be an industry insider.

1 more reply

windowsworkstoo10y ago

It says it right on the card on the table that explains the min/max bets (in Aus at least). Also, it's basic stats which can be applied depending the house rules.

plonh10y ago

A commenter explains that the most interesting claim (51% bias) is not explained correctly in the article. Humans flipping a coin add a bit of precession (spin) that biasses the toss. The "odd/even time in the air" analysis is incorrect -- that only matters if it is possible to stop the coin before the first flip.

letstryagain10y ago

Yep. To see this, consider a coin flipped into the air so that it's tilted 45 degrees with the floor and spinning only around the vertical axis. To a casual observer it will appear as if the coin is tumbling but in fact one side faces up 100% of the time.

thret10y ago

This is a trick that can be learnt with practice. If you spend a lot of time around gamblers, don't ever accept a coin toss proposition.

1 more reply

shuriu10y ago

This video from Numberphile goes in depth about this: https://www.youtube.com/watch?v=Obg7JPd6cmw . The guy talking, is Persi Diaconis, is the main author of the paper this article is based upon.

He also has done research on the randomness of shuffling cards: https://www.youtube.com/watch?v=AxJubaijQbI . Pretty cool stuff!

jmount10y ago

My small take: http://www.win-vector.com/blog/2015/04/i-still-think-you-can...

plonh10y ago

If the coin has a substantial thickness, is it still accepted as a coin? I think not. How much density differential do you need to generate a 1% bias in a coin no thicker than any existing UN member currency?

jmount10y ago

Persi Diaconis did a lot of experiments- the biases are very low.

qznc10y ago

The paper ends with "The caveats and analysis also point to the following conclusion: For tossed coins, the classical assumptions of independence with probability 1/2 are pretty solid."

RogerL10y ago

I think this link botches the explanation for 51%. 51% is because of precession, as explained in the paper[1]. With enough precession the coin will always come up heads if it starts out heads. That's how magicians control coin tosses.

He tries to describe it in terms of HTHTHT. Coins do not have memory. They don't know if they've previously flipped 3 times, 4 times, or 1e308 times. If you draw from [HTHTHT..HT] randomly, you'll get 50% heads and 50% tails. Change that to [THTHTH..TH] and the answer is the same.

With precession the answer changes because it stays in the initial state longer. As the paper points our "Keller showed that in the limit of large initial velocity and largerate of spin, a vigorous flip, caught in the hand without bouncing, lands heads half the time." Keller assumed no precession.

[1] http://statweb.stanford.edu/~susan/papers/headswithJ.pdf

edit: I just saw that in the comments they point this flaw out. It gets hand waved away by the author as a "oversimplification" that he made. My opinion is that it is okay to simplify, but not to the point of being wrong. The explanation is not how probability works, at all.

zw12345610y ago

The most interesting part to me was this "A coin will land on its edge around 1 in 6000 throws, creating a flipistic singularity." (https://en.wikipedia.org/wiki/Flipism)

I assume that was as the result of using the tossing machine, but I really thought it would not have been that frequent.

danieltillett10y ago

I have this happen a lot when tossing on wooden floors with a gap between the boards - basically the coin gets stuck in the gap. My brother and I got quite good at deliberately doing this.

I have never had it happen on a flat surface and I must have tossed 10,000 of coins in my youth.

PhantomGremlin10y ago

I once attempted to hand a quarter to a convenience store clerk. Somehow we dropped it during the exchange. The coin rolled about 8 feet and went thru a tiny gap between two large cardboard boxes on the floor.

I'm sure I could have stood there for an hour attempting to drop a coin onto the floor and have it roll into that gap, and I would have failed.

2 more replies

aetherson10y ago

If the odds of landing on an edge are 1 in 6000, it's not particularly unbelievable that you wouldn't have seen it in 10,000 tries. The odds of not seeing it are about 18%.

I saw a coin land on edge once.

soup1010y ago

Good to know! Relevant clip of some very entertaining gambling by two poker pros:

https://www.youtube.com/watch?v=ZQSIx3CU9rA

raymondh10y ago

coldpie10y ago

Mostly off topic, but boy do I enjoy articles that use the word "tosser" innocuously.

j / k navigate · click thread line to collapse

30 comments

heyitsnick10y ago

"1% may not sound like a lot, but it's more than the typical casino edge in a game of blackjack or slots."

The house edge for slots games is anywhere from 2% to 15%+ and is one of the worst bets you can make in the casino.

Blackjack, video poker and some bets on craps are the only times in a casino where the house edge shrinks to below 1%.

wozniacki10y ago

  Blackjack, video poker and some bets on craps are the only
  times in a casino where the house edge shrinks to below 1%.

Care to cite your source for this or are you a gaming industry insider?

PhantomGremlin10y ago

There's no need for a source. It's common knowledge. Many books, websites, and research papers have extensively studied those games.

Edward Thorp is a mathematician who did a lot of analysis about blackjack over 50 years ago.[1] He's a seminal figure in this field.

Here's one site I recall mostly because it has a memorable name: http://wizardofodds.com/

[1] https://en.wikipedia.org/wiki/Beat_the_Dealer#History

1 more reply

albedoa10y ago

> Care to cite your source for this or are you a gaming industry insider?

Strange dichotomy to those of us who have been to a casino. They tell you right at the games — you don't need to be an industry insider.

1 more reply

windowsworkstoo10y ago

It says it right on the card on the table that explains the min/max bets (in Aus at least). Also, it's basic stats which can be applied depending the house rules.

plonh10y ago

letstryagain10y ago

thret10y ago

This is a trick that can be learnt with practice. If you spend a lot of time around gamblers, don't ever accept a coin toss proposition.

1 more reply

shuriu10y ago

This video from Numberphile goes in depth about this: https://www.youtube.com/watch?v=Obg7JPd6cmw . The guy talking, is Persi Diaconis, is the main author of the paper this article is based upon.

He also has done research on the randomness of shuffling cards: https://www.youtube.com/watch?v=AxJubaijQbI . Pretty cool stuff!

jmount10y ago

My small take: http://www.win-vector.com/blog/2015/04/i-still-think-you-can...

plonh10y ago

jmount10y ago

Persi Diaconis did a lot of experiments- the biases are very low.

qznc10y ago

The paper ends with "The caveats and analysis also point to the following conclusion: For tossed coins, the classical assumptions of independence with probability 1/2 are pretty solid."

RogerL10y ago

[1] http://statweb.stanford.edu/~susan/papers/headswithJ.pdf

zw12345610y ago

The most interesting part to me was this "A coin will land on its edge around 1 in 6000 throws, creating a flipistic singularity." (https://en.wikipedia.org/wiki/Flipism)

I assume that was as the result of using the tossing machine, but I really thought it would not have been that frequent.

danieltillett10y ago

I have this happen a lot when tossing on wooden floors with a gap between the boards - basically the coin gets stuck in the gap. My brother and I got quite good at deliberately doing this.

I have never had it happen on a flat surface and I must have tossed 10,000 of coins in my youth.

PhantomGremlin10y ago

I'm sure I could have stood there for an hour attempting to drop a coin onto the floor and have it roll into that gap, and I would have failed.

2 more replies

aetherson10y ago

If the odds of landing on an edge are 1 in 6000, it's not particularly unbelievable that you wouldn't have seen it in 10,000 tries. The odds of not seeing it are about 18%.

I saw a coin land on edge once.

soup1010y ago

Good to know! Relevant clip of some very entertaining gambling by two poker pros:

https://www.youtube.com/watch?v=ZQSIx3CU9rA

raymondh10y ago

coldpie10y ago

Mostly off topic, but boy do I enjoy articles that use the word "tosser" innocuously.

j / k navigate · click thread line to collapse