Should we bet on a losing cause?

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The obvious answer is “Of course not!”.

Reality though is different. People persist in losing bets all the time. From continued marketing effort into a product that is losing, from persisting in a job that they do not like, by living in a neighborhood they do not want to, not selling a house that has lost money. We can all think of simple situations in everyday life when this happens – we get invested in something and find it hard to make a change. We get into a slow lane in traffic, we stand at the slow lane in a queue but do not want to change, we persist with a way of doing things and become “technology laggards” and on and on.

There is a bet on status quo because we are emotional creatures afraid to recognize a loss in our investment of time and resources already made. Is this rational or irrational? We are poor decision makers when faced with losses. It is a well established fact in economics that “Loss Aversion” is a significant bias and overrides gains. Amos Tversky and Daniel Kahneman coined this term and  studied the phenomenon. In the world of business where the questions – what to change? to what to change? and how to make the change? are a constant, organizations can make errors of changing when they should not and not changing when they should, with real and opportunity costs in both situations. Is it worthwhile to look at this situation a little more carefully?

Consider a simple betting game with the following rules – You and an opponent are going to bet on the outcome of a tossed coin. The coin will be tossed by a referee. The coin may be biased but you do not know in which direction before you start. If the coin shows up heads you win, if it shows up tails you lose. The minimum bet to start the game is $10. After the minimum bet has been entered the rules are:

  • The referee shares with both players the bias in the coin – for example the coin can have a 60% chance of being heads, and 40% tails or any other such combination
  • Both of you get a chance to double the bet. If the other person accepts you raise the stakes to $20 for both parties. If the double is not accepted you lose the $10 minimum stake

The question is: the referee announces that the coin is biased with a 40% chance of heads. Your opponent doubles, should you accept the bet or not?

The immediate answer is that you should not accept the bet. It is a losing cause, why would we accept it. But let us examine this a little more closely – What is the expected value of the game for you?

You have a 40% chance of winning $20 if you accept and a 60% chance of losing $20. The expected value is (40% of $20) – (60% of $20) which means that you are expected to lose $4 if you accept the double. Now let us see what happens if we do not accept the bet – we are guaranteed to lose $10. It does seem that it is better to accept the losing bet!

That is really strange. You are given the chance to get out of a losing situation but hard cold logic suggests that it is a bad idea to get out. You must persist and accept the potentially bigger loss. What if the odds were 70% – 30%. Would we still get the same answer? Well, then the loss is $8 if you accept the bet and $10 if you do not. What is the break even point? The break even point is at 75% odds of losing – in this case you are indifferent because in both situations you expect to lose $10.

Is this a reasonable example to model the variety of situations where we persist in bad choices? Of course there are many nuances that are missing. I may only have $10 to bet and so will not accept the double regardless of the expected value. The threat of bankruptcy is akin to this. If I know that my opponent can double again and again that knowledge can also change my behavior. Now my expected loss climbs dramatically if I accept the bet. These are two of the assumptions that are critical to the analysis.

Strange as the behavior is it does seem to have some justification. It is not as irrational as it seems at first to accept the losing situation. It is a valid intuition in many situations. It is particularly cruel when the rules are not well defined and we have to guess if the bet will be offered again and again or only once. We end up putting on a brave face and doubling down rather than cutting our losses!

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Published by ajaikapoor

Dr. Ajai Kapoor holds a PhD in Operations Research from Carnegie Mellon University. He is the winner of the Fulkerson Prize. He completed his B.Tech from IIT Delhi. He has over 16 years of consulting experience helping companies design innovative logistical solutions based on Theory of Constraints (TOC). His passion is to help companies deploy these solutions as a disruptive force in order to obtain a decisive competitive advantage. His focus is on applying first principles to create simple solutions that can be implemented at scale. He believes in using the power of TOC to resolve deep conflicts within and between organizations, strengthening the integration within companies and with their suppliers and partners. Ajai’s consulting focus has been on Operations Solutions for high uncertainty environments. These include New Product Development, Airline Maintenance, Supply Chain and R&D organizations. He has worked with Boeing, Amdocs, Larsen and Toubro, Alaska Airlines, Delta Airlines, Medtronics and US Air Force. Ajai is an entrepreneur, having started a company that focused on providing TOC based software for project management. Currently he is Partner at Goldratt Consulting. He lives in San Jose with his wife and two sons.

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