When odds are in your favour

Asset allocation, risk, diversification and rebalancing. Pros/cons of hiring a financial advisor. Seeking advice on your portfolio?

How much money have you ended up with, after 30 minutes

$250 (the maximum allowed)
14
61%
$100 to $249.99
2
9%
$25 to $99.99
2
9%
$10 to $24.99
0
No votes
$0.01 to $9.99
0
No votes
Went bust
5
22%
 
Total votes: 23

User avatar
adrian2
Diamond Ring
Diamond Ring
Posts: 11555
Joined: 19 Feb 2005 08:42
Location: Greater Toronto Area

When odds are in your favour

Post by adrian2 » 03 Dec 2016 11:49

The reason for posting it here, instead of the Watercooler, is given at the end of the post.
You are being given $25 to give 30 minutes of your time to playing a coin flipping game.

The coin you can flip is programmed to have a 60% chance of coming up heads and a 40% chance of coming up tails.

You can bet any amount of money in your balance, but not more, on heads or tails on each flip.

If your balance goes to 0, you cannot play anymore, but we kindly request you stay in the room until the 30 minutes has elapsed.
http://coinflipbet.herokuapp.com/

Of course there is some science on how much you should bet. You may (or may not) do it "scientifically".

BTW, I did follow the theory and ended up with the maximum allowed in about 20 minutes.

I've heard of this from a note on TDW. Quoting the author:
Ian McGugan wrote:Nothing sounds simpler than winning at such an outrageously rigged game. Yet, when it was played with real money in a controlled experiment, a surprising number of professional investors and finance students somehow managed to go bust. Full confession: I didn’t do so well myself.
...
Given the odds in the coin flip game, all of us can see it makes sense to favour heads. The problem is deciding how much of our bankroll we should risk on each flip of the coin. Choosing the right amount to wager is similar to deciding how much of your actual portfolio to devote to a promising stock or fund.

Then there are the inevitable ups and downs of the game. Throughout half an hour of coin flipping, you probably hit at least one sorry patch when you found your bankroll melting away despite your best efforts. When that happens, the temptation to do something – anything – to break the losing streak becomes nearly unbearable.

How unbearable? By the 15-minute mark, I was swearing at the screen. I had begun by betting $5 a flip on heads, but my first three tosses came up tails and quickly dragged me down to $10. I then sliced my bet in half, then in half again, but I couldn’t get any traction. I wound up with the distinctly unimpressive total of $3.85.

At least I wasn’t alone. The two creators of this experiment, Victor Haghani of Elm Partners and Richard Dewey of Pimco, found 28 per cent of their test subjects went bust when playing the game with real money. A full third of their test subjects wound up with less money than their starting amount.

The results are startling because all 61 subjects in the initial experiment were either young money managers or university students in economics. They all had the training to play the game intelligently, but most of them flopped.

Bettors sabotaged themselves in many ways – by overbetting, by underbetting, by shifting bets erratically (the latter was probably my own undoing). Amazingly, two thirds of the test subjects bet on tails at some point despite the miserable odds against that outcome. And nearly a third of them gambled everything on a single coin flip at least once.
...
To my mind, the single most valuable insight is that it’s discipline that counts in investing, not brilliant investing ideas. The subjects in the coin-flipping contest knew that betting on heads was a great proposition, but most failed to reap a reasonable reward because they didn’t stick to a simple, consistent strategy that realistically balanced risk and reward.
Imagefiniki, the Canadian financial wiki
“It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.” [Richard P. Feynman, Nobel prize winner]

User avatar
Shakespeare
Diamond Ring
Diamond Ring
Posts: 20761
Joined: 15 Feb 2005 23:25
Location: Lethbridge, AB
Contact:

Re: When odds are in your favour

Post by Shakespeare » 03 Dec 2016 12:08

ISTM that this game can be won *most of the time* by a simple strategy: always bet 50% of your stash, *whatever it is*, on heads.

If you analyze that in advance and keep to it, it takes the emotion out of it.


Added: it's similar to running a 50-50 portfolio and rebalancing. But it ignores the Iron Rule, since you don't need the $25.

The Iron Rule - Financial Wisdom Forum
“A wise man should be prepared to abandon his baggage at any time.” -- R.A. Heinlein, The Door Into Summer.

User avatar
adrian2
Diamond Ring
Diamond Ring
Posts: 11555
Joined: 19 Feb 2005 08:42
Location: Greater Toronto Area

Re: When odds are in your favour

Post by adrian2 » 03 Dec 2016 12:17

Shakespeare wrote:ISTM that this game can be won *most of the time* by a simple strategy: always bet 50% of your stash, *whatever it is*, on heads.
Quite far from the optimal strategy.

Please try it and report back to the poll.
If you analyze that in advance and keep to it, it takes the emotion out of it.
For me, there was still plenty of emotion during play.
Imagefiniki, the Canadian financial wiki
“It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.” [Richard P. Feynman, Nobel prize winner]

User avatar
NormR
Gold Ring
Gold Ring
Posts: 4005
Joined: 18 Feb 2005 11:19
Contact:

Re: When odds are in your favour

Post by NormR » 03 Dec 2016 12:51

See https://en.wikipedia.org/wiki/Kelly_criterion

Depending on the setup, one also has to factor in the probability that the game is rigged in some way. But I'm off to read the article before commenting further. :)
[url=http://www.ndir.com]www.ndir.com[/url]

User avatar
NormR
Gold Ring
Gold Ring
Posts: 4005
Joined: 18 Feb 2005 11:19
Contact:

Re: When odds are in your favour

Post by NormR » 03 Dec 2016 12:54

A link to Ian's article, which is behind the G&M paywall: http://www.theglobeandmail.com/globe-in ... e33183678/
[url=http://www.ndir.com]www.ndir.com[/url]

User avatar
always_learning
Silver Ring
Silver Ring
Posts: 253
Joined: 01 Mar 2005 21:44
Location: Halifax

Re: When odds are in your favour

Post by always_learning » 03 Dec 2016 13:02

I've posted my result ($250). I encourage people to try it. I won't say any more now, so as to not spoil the enjoyment of playing the game.
a_l
p.s. I didn't read about the scientifically proper approach beforehand. Instead, in my head, I took a guess at what the most efficient way to play would be. It turns out I played reasonably close to the optimal strategy. :shock: Feeling quite pleased.
Last edited by always_learning on 03 Dec 2016 13:08, edited 1 time in total.

User avatar
NormR
Gold Ring
Gold Ring
Posts: 4005
Joined: 18 Feb 2005 11:19
Contact:

Re: When odds are in your favour

Post by NormR » 03 Dec 2016 13:03

It's hard to apply the Kelly approach to the market because (apart from a few specialized cases) it's hard to calculate the odds correctly. As a result, one should generally under bet. IIRC, "half Kelly" is rather common rule of thumb.
[url=http://www.ndir.com]www.ndir.com[/url]

longinvest
Gold Ring
Gold Ring
Posts: 1410
Joined: 10 Sep 2012 17:26
Location: QC

Re: When odds are in your favour

Post by longinvest » 03 Dec 2016 13:06

Is there a way to play without giving away my personal information?
Bogleheads investment philosophy | Simple index portfolios | Lifelong Portfolio: 25% each of (domestic/international)stocks/(nominal/inflation-indexed)bonds | VCN/VXC/VAB/ZRR

User avatar
adrian2
Diamond Ring
Diamond Ring
Posts: 11555
Joined: 19 Feb 2005 08:42
Location: Greater Toronto Area

Re: When odds are in your favour

Post by adrian2 » 03 Dec 2016 13:21

longinvest wrote:Is there a way to play without giving away my personal information?
I did not get any emails from them after giving the real details; you may enter as John Doe, John.Doe@example.com
Imagefiniki, the Canadian financial wiki
“It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.” [Richard P. Feynman, Nobel prize winner]

User avatar
kcowan
Diamond Ring
Diamond Ring
Posts: 13035
Joined: 18 Apr 2006 20:33
Location: Pacific latitude 20/49

Re: When odds are in your favour

Post by kcowan » 03 Dec 2016 15:07

The site says it is closed to new players.
For the fun of it...Keith

longinvest
Gold Ring
Gold Ring
Posts: 1410
Joined: 10 Sep 2012 17:26
Location: QC

Re: When odds are in your favour

Post by longinvest » 03 Dec 2016 15:10

kcowan wrote:The site says it is closed to new players.
Just click "Accept" and enter dummy personal info.
Bogleheads investment philosophy | Simple index portfolios | Lifelong Portfolio: 25% each of (domestic/international)stocks/(nominal/inflation-indexed)bonds | VCN/VXC/VAB/ZRR

User avatar
adrian2
Diamond Ring
Diamond Ring
Posts: 11555
Joined: 19 Feb 2005 08:42
Location: Greater Toronto Area

Re: When odds are in your favour

Post by adrian2 » 03 Dec 2016 16:05

kcowan wrote:The site says it is closed to new players.
What it means is that they are not going to pay you real dollars, like they did in the first place.
Imagefiniki, the Canadian financial wiki
“It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.” [Richard P. Feynman, Nobel prize winner]

ig17
Gold Ring
Gold Ring
Posts: 2382
Joined: 21 Feb 2005 20:54

Re: When odds are in your favour

Post by ig17 » 03 Dec 2016 16:51

I got to $180 on the first try and voted accordingly. Then I realized that I had followed the right strategy but couldn't get to $250 due to under-betting. Tried again and got to $250 with 10 minutes to spare.

longinvest
Gold Ring
Gold Ring
Posts: 1410
Joined: 10 Sep 2012 17:26
Location: QC

Re: When odds are in your favour

Post by longinvest » 03 Dec 2016 16:54

Once you know the trick, it's pretty simple to beat the system.
Bogleheads investment philosophy | Simple index portfolios | Lifelong Portfolio: 25% each of (domestic/international)stocks/(nominal/inflation-indexed)bonds | VCN/VXC/VAB/ZRR

User avatar
IdOp
Gold Ring
Gold Ring
Posts: 2857
Joined: 16 Feb 2006 11:27
Location: On the Pacific sea bed, 100 mi off the CA coast.
Contact:

Re: When odds are in your favour

Post by IdOp » 03 Dec 2016 17:23

I was curious to see how the results of Shakespeare's strategy, which was to bet 50% of the stash on each flip, would vary if you changed the 50%. So I wrote a quick program to check it in steps of 5%, from 5% to 100%. For each bet level, the average of the final total over a large number of pseudo-random trials is taken. One change from the game is that I didn't stop it at $250 max, just kept going up to 60 flips (representing 30 seconds per flip). Here's a sample result for 1 million iterations per bet level:

Code: Select all

% bet: 0.05,  ave total: 45.37
% bet: 0.10,  ave total: 81.68
% bet: 0.15,  ave total: 145.79
% bet: 0.20,  ave total: 254.08
% bet: 0.25,  ave total: 438.39
% bet: 0.30,  ave total: 732.24
% bet: 0.35,  ave total: 1194.13
% bet: 0.40,  ave total: 1970.06
% bet: 0.45,  ave total: 2967.81
% bet: 0.50,  ave total: 5385.84
% bet: 0.55,  ave total: 6468.49
% bet: 0.60,  ave total: 6690.02
% bet: 0.65,  ave total: 7300.19
% bet: 0.70,  ave total: 6784.96
% bet: 0.75,  ave total: 5598.87
% bet: 0.80,  ave total: 4073.21
% bet: 0.85,  ave total: 77107.93
% bet: 0.90,  ave total: 252.96
% bet: 0.95,  ave total: 46.25
% bet: 1.00,  ave total: 0.00
There still seems to be quite a bit of randomness at the upper levels.

User avatar
Shakespeare
Diamond Ring
Diamond Ring
Posts: 20761
Joined: 15 Feb 2005 23:25
Location: Lethbridge, AB
Contact:

Re: When odds are in your favour

Post by Shakespeare » 03 Dec 2016 17:26

What are the chances of going broke per bet percentage?
“A wise man should be prepared to abandon his baggage at any time.” -- R.A. Heinlein, The Door Into Summer.

User avatar
IdOp
Gold Ring
Gold Ring
Posts: 2857
Joined: 16 Feb 2006 11:27
Location: On the Pacific sea bed, 100 mi off the CA coast.
Contact:

Re: When odds are in your favour

Post by IdOp » 03 Dec 2016 18:24

You can't go broke unless you bet 100%; in that case the probability is very very high to go broke, i.e., 1 - (0.6)^60. [ That ignores discretising things to a penny. ;) ]

User avatar
Shakespeare
Diamond Ring
Diamond Ring
Posts: 20761
Joined: 15 Feb 2005 23:25
Location: Lethbridge, AB
Contact:

Re: When odds are in your favour

Post by Shakespeare » 03 Dec 2016 18:34

All right, what are the chances of reaching the quantization limit (one cent)?
“A wise man should be prepared to abandon his baggage at any time.” -- R.A. Heinlein, The Door Into Summer.

longinvest
Gold Ring
Gold Ring
Posts: 1410
Joined: 10 Sep 2012 17:26
Location: QC

Re: When odds are in your favour

Post by longinvest » 03 Dec 2016 18:47

Shakespeare wrote:All right, what are the chances of reaching the quantization limit (one cent)?
Pretty good. I reached 1 cent with a constant 50% of portfolio bet (rounded up). Then I bet it and I went bankrupt. :oops:
Bogleheads investment philosophy | Simple index portfolios | Lifelong Portfolio: 25% each of (domestic/international)stocks/(nominal/inflation-indexed)bonds | VCN/VXC/VAB/ZRR

longinvest
Gold Ring
Gold Ring
Posts: 1410
Joined: 10 Sep 2012 17:26
Location: QC

Re: When odds are in your favour

Post by longinvest » 03 Dec 2016 18:51

The thing is that losing 50% of portfolio really hurts. It only takes 12 losses to reduce $25 to $0.01.
Bogleheads investment philosophy | Simple index portfolios | Lifelong Portfolio: 25% each of (domestic/international)stocks/(nominal/inflation-indexed)bonds | VCN/VXC/VAB/ZRR

User avatar
IdOp
Gold Ring
Gold Ring
Posts: 2857
Joined: 16 Feb 2006 11:27
Location: On the Pacific sea bed, 100 mi off the CA coast.
Contact:

Re: When odds are in your favour

Post by IdOp » 03 Dec 2016 18:54

I put in a simple cut-off of $0.01 and quit if the stash went below that. Here is a sample run with 100,000 iterations per level:

Code: Select all

% bet: 0.05,  ave total: 45.38,  P(stash<0.01): 0 %
% bet: 0.10,  ave total: 81.78,  P(stash<0.01): 0 %
% bet: 0.15,  ave total: 145.27,  P(stash<0.01): 0 %
% bet: 0.20,  ave total: 251.43,  P(stash<0.01): 0 %
% bet: 0.25,  ave total: 435.12,  P(stash<0.01): 0 %
% bet: 0.30,  ave total: 707.91,  P(stash<0.01): 0.022 %
% bet: 0.35,  ave total: 1184.03,  P(stash<0.01): 0.326 %
% bet: 0.40,  ave total: 2104.78,  P(stash<0.01): 1.631 %
% bet: 0.45,  ave total: 3163.12,  P(stash<0.01): 5.346 %
% bet: 0.50,  ave total: 4263.62,  P(stash<0.01): 13.072 %
% bet: 0.55,  ave total: 6184.05,  P(stash<0.01): 24.501 %
% bet: 0.60,  ave total: 14764.56,  P(stash<0.01): 41.543 %
% bet: 0.65,  ave total: 7467.63,  P(stash<0.01): 55.459 %
% bet: 0.70,  ave total: 4489.66,  P(stash<0.01): 72.162 %
% bet: 0.75,  ave total: 4849.49,  P(stash<0.01): 84.305 %
% bet: 0.80,  ave total: 5173.44,  P(stash<0.01): 92.501 %
% bet: 0.85,  ave total: 942.48,  P(stash<0.01): 97.43 %
% bet: 0.90,  ave total: 9.99,  P(stash<0.01): 99.466 %
% bet: 0.95,  ave total: 0.62,  P(stash<0.01): 99.955 %
% bet: 1.00,  ave total: 0.00,  P(stash<0.01): 100 %
It doesn't pay (usually) to bet the farm. ;)

longinvest
Gold Ring
Gold Ring
Posts: 1410
Joined: 10 Sep 2012 17:26
Location: QC

Re: When odds are in your favour

Post by longinvest » 03 Dec 2016 18:57

IdOp, your random number generator seems biased. According to math, the optimal ratio should not be 60%.
Bogleheads investment philosophy | Simple index portfolios | Lifelong Portfolio: 25% each of (domestic/international)stocks/(nominal/inflation-indexed)bonds | VCN/VXC/VAB/ZRR

User avatar
Insomniac
Gold Ring
Gold Ring
Posts: 1835
Joined: 29 Oct 2011 19:01
Location: Vancouver Island

Re: When odds are in your favour

Post by Insomniac » 03 Dec 2016 18:57

Started playing and did OK. Got up to $175 and looked at the clock. Crap! Only 3 minutes gone! This is boring! I am not doing this for 30 minutes. So, I bet the lot and lost it all. :lol:

Why do they allow you to bet "tails" when the odds are stacked in favour of "heads"? :?

I don't understand gambling.

longinvest
Gold Ring
Gold Ring
Posts: 1410
Joined: 10 Sep 2012 17:26
Location: QC

Re: When odds are in your favour

Post by longinvest » 03 Dec 2016 18:59

longinvest wrote:IdOp, your random number generator seems biased. According to math, the optimal ratio should not be 60%.
Hmmm.... Maybe it's not biased. You're calculating the "average". So, a lucky streak can get you extremely rich. I see. But, the probability of going broke is high; 40% of the time!
Bogleheads investment philosophy | Simple index portfolios | Lifelong Portfolio: 25% each of (domestic/international)stocks/(nominal/inflation-indexed)bonds | VCN/VXC/VAB/ZRR

User avatar
adrian2
Diamond Ring
Diamond Ring
Posts: 11555
Joined: 19 Feb 2005 08:42
Location: Greater Toronto Area

Re: When odds are in your favour

Post by adrian2 » 03 Dec 2016 19:01

Insomniac wrote:Why do they allow you to bet "tails" when the odds are stacked in favour of "heads"? :?
You obviously have not considered reading the (ticker) tape.
Heads, heads, heads... I feel like tails is coming!
Amazingly, two thirds of the test subjects bet on tails at some point despite the miserable odds against that outcome.
Imagefiniki, the Canadian financial wiki
“It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.” [Richard P. Feynman, Nobel prize winner]

Post Reply