Game theory, Parrondo’s paradox and how combining two losing strategies can result in winning strategy.

Juan Parrondo is Spanish physicist how introduced a new concept in game theory– Parrondo’s Paradox. It is an interesting concept- what it states is if two losing strategies are combined i.e. played alternatively, they can result in a winning strategy.

Can two losers come together and use their complementary skills to device a winning strategy? Sounds ridiculous, but Juan Parrondo thinks it is possible.

Take two games- game A and game B, if played exclusively each will result in loss, but when played in combination can result in win.

Let game A be you lose Rs.1 every time you play game, and game B is you count money you have, if it is an even number you win Rs. 3, else lose Rs.5.

Now if you start with Rs. 100, and play game A exclusively, you will lose all your money in 100 rounds (lose Rs. 1 every time you play, so in 100 rounds you lost Rs. 100)

If you play game B exclusively, then also you will lose all your money in 100 rounds. You can use excel sheet to make calculations. Ex. you start with 100, since it is even number you get Rs. 3, so you have Rs. 103, since 103 is odd number you lost Rs.5, so now you are left with Rs. 98, which is even number so win Rs. 3, total now is Rs. 101, which is odd, so lose Rs.5 and so on…

Now use combination of games i.e. first plays B, then A, then again B, then A i.e. BABABA…, you will start winning.

Here you start with Rs. 100, under game B you win Rs. 3 as 100 is even number, so you are left with Rs. 103, now play game A i.e. lose Rs. 1, so you are left with Rs. 102, now play game B, win Rs. 3 as 102 is even, back to game A and lose Rs.1 and so on. With every BA game combination you gain Rs.2.

If you have losers in your team, don’t give up on them, study their competencies and see if combination can deliver a win.


What is your mindset- Fixed or Growth?

“Did I win? Did I lose? Those are the wrong questions. The correct question is: Did I make my best effort?”

       – Carol .S. Dweck

Alfred Binet designed a test to measure intelligence. It gave what is known as IQ level. It was number that told you how intelligent you are. Higher the IQ score, more intelligent you are.

Later cognitive psychologists felt that IQ as measure of intelligence was over rated ex. a person can have average IQ score but he can be genius in areas like music , art , sports etc.

Carol Dweck, professor of psychology at Stanford University did research in area of intelligence. She came with entity and incremental theory of talent.

Entity theory states that intelligence is a relatively unchangeable fact about who you are and about your potential to succeed i.e. you are born with fixed intelligence and creativity and you cannot do anything about it. So intelligence will act as limiting factor for some and supercharge fuel for others.

Incremental theory states that intelligence can be changed, esp. through efforts/hard work. Genetics is only starting point i.e. you are born with certain IQ, but with efforts and hard work you can master the art. Incremental theory holders have what is called as growth mindset.

Entity theory holders choose task that they already know will lead to success and avoid those that have chance of failure, as they ascribe failure to their limitations.

Incremental theory holders feel motivated by failure and see failure as opportunity to do better.


Bad bosses are firm believers in fixed intelligence, for them employees are either born competent or incompetent. They never believe in spending time with employees to enhance his talent through efforts ex. Coaching.

Good bosses always consider setback as temporary and will encourage subordinate to learn from failure and help him to live up to his potential.






Teresa Amabile, Progress Principle and Creativity at your workplace.

“The desire to do something because you find it deeply satisfying and personally challenging inspires the highest levels of creativity, whether it’s in the arts, sciences, or business.”

― Teresa Amabile, Professor of Business Administration at HBS.

I was not aware of Teresa Amabile’s work till I started doing projects on innovation and studying cognitive psychology. Teresa has done lot of work in area of creativity and even designed an inventory to measure creativity in organisations- KEYS. Impressed with her work, I obtained licence to administer KEYS.

Her latest book on creativity- Progress Principle- gives some simple tips on how to make improve creativity in organisation.

Everything starts with great inner work life– which is cluster of work that you do, your inner motivation, your positive emotions and perception of your colleagues.

If you have great inner work life, then you find your work meaningful, besides you also improve your creativity and productivity.

Few things you can do improve inner work life are…

  1. Progress Principle– While doing your work; always celebrate the progress that you and your team makes every day esp. small wins. We tend to ignore incremental progress.
  2. Dealing with setbacks– Organisation should treat setback as learning opportunity and address setback quickly.
  3. Catalysts & Inhibitors– Catalysts like clear goals and sufficient resources speed up progress, while inhibitors like lack of clarity and purpose block progress.
  4. Nourishers and Toxins– Nourishers like encouragement and recognition improve inner work life, while toxins like office politics poisons inner work life.


There is difference between inhibitors and toxins- Inhibitors directly hinder the project work, while toxins affect interpersonal relations that undermine people doing work. Negative events are more powerful than positive ones -impact of toxins and inhibitors on work life is more than impact of catalysts and nourishers, so always try to minimize toxins and inhibitors.

  1. Reduce time pressure– If your team is working under high time pressure due to unrealistic deadlines and burdened with too many unrelated tasks, then creativity of individual/team will go down. Try to keep high time pressure period as low as possible. A team will be creative if it works under low or moderate time pressure.



Polio eradication, India and Our two neighbours

“There is no patent. Could you patent the sun?”

–          Jonas Salk

Today is 100th birthday of Jonas Salk, man who discovered polio vaccine. Polio vaccine was result of tireless efforts of Dr. Jonas Salk & his team, credit also goes to thousands of Americans who raised fund for vaccine research esp. March of Dimes Foundation and risked their life by becoming volunteers for testing vaccine.

Dr. Salk did not patent his discovery and used it for welfare of mankind. Not just American children, but children all over world benefited from this vaccine. Before vaccine was discovered polio was most feared disease in America. Painter Andrew Wyeth painted his neighbour, Christina Olson, a polio victim, which shows helplessness of a polio child. Vaccine helped in total eradication of polio in US.


Thousands of children in third world countries were affected by polio. The respective countries started polio vaccination programs of their own for eradication of polio.

It is interesting to see how political system impacts vaccination program esp. our country and our two neighbours.

Communist China carried out vaccination program in 1993, in two days 80 million children were vaccinated, next year only 5 cases of polio were reported.

Democratic India intensified its polio eradication program in 1999, thousands of volunteers visited homes which had children below the age of 5 to give oral polio vaccine drops. Amitabh Bacchan became brand ambassador for polio eradication program. This year India was declared polio free.


Politically unstable Pakistan still has not been able to eradicate polio; in fact it is only nation in world which has reported increase in incidents of polio!

Problem Solving, Expert and Novice

Domain experts are in demand when it comes to trouble shooting. Domain experts gain knowledge through experience gained from working on projects over a period of time. Can there be a case when while solving a problem a domain expert is as effective as novice?

Psychologists conducted experiments to verify this. In one experiment psychologists created two groups – one of chess experts and other of those who were beginners in chess. In first case they were shown chess pieces in positions they were familiar with and then were asked to recreate positions, as expected experts did better than beginners. In second case, the chess pieces were put in position which made no sense, now when it came to recreation of positions experts were as good as and in some cases worse than beginners.


Further research showed that domain expert do well when it comes to resolving problems in area they are familiar with, but in situations that are ambiguous, unfamiliar or entirely new then domain experts are as effective as novice.


So when your organisation faces problems which are new, not just domain experts, but even those who are new to that field can offer innovative solutions. There is a possibility that they may offer solutions which domain experts may not even thought of.


Justice, Inferential Statistics and Lucia de Berk

Students of inferential statistics are very fond of “p value”. A null hypothesis is either rejected or not rejected based on p value. If p value is lower than accepted level of significance then null hypothesis gets rejected.

But this small number can create lot of havoc- in case of Lucia de Berk it turned her life upside down.

Lucia de Berk was a paediatric nurse who worked at hospital in Hague. It was her third job, prior to this she had worked in two other hospitals. One day when she was on duty a child called Amber died. This led to investigation and it was found that there were 8 more such cases when she was on duty, so 9 cases of death in 3 hospitals.

lucia de berk

During prosecution, Henk Elffers was used by courts as statistics expert. Based on data collected from hospitals he calculated p value for each hospital, and then did meta-analysis by multiplying p values, to arrive at grand p value. This method of calculating composite value by simply multiplying p values is not correct; there is method for  that- Fisher method.

Henk Elffers method of calculation was not just incorrect, but also hilarious. P values are very small values, generally p value less than .05 is considered to be statically significant.. Now let us assume that p value for each case is .06 i.e not statistically significant, now if Lucia worked for 3 hospitals then p value as per Henk’s method is .06x.06x.06= .0002 i.e. highly significant. Now if Lucia has worked in 10 hospitals, we would end up with ridiculously low p value- .06^10.

Based on his wrong calculations, Henk concluded that chance of a nurse working at the three hospitals being present at the scene of so many unexplained deaths is one in 342 million, which was equated with chances of her being innocent.

Based on these calculations Lucia was declared guilty and sentenced with life imprisonment.


Later case went to higher court and all statistical evidence against Lucia was dismissed and Lucia was set free. A film was made on her called Lucia de B.

So next time when you accept or reject null hypothesis based on p value, think of impact this small number can create.