Fatal downside and Wealth effect

Although the overall expected value of dice game version A is positive, there is one situation in which you should not play it - when the potential downside would be fatal or disastrous for you.

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If you had just $1 in your pocket, played the game once, and failed to throw a six, you would be bankrupt.  The positive expected value of the game would be no help to you, since you would be unable to play any more - a fatal downside would have occurred.  In other  words, it is not enough just o look at the expected value of a decision.  The probability of a fatal or disastrous worst-case scenario has to be considered too. 

The presence of a fatal downside might temper your enthusiasm for a decision with a positive expected value, perhaps encouraging some kind of trade-off between expected value and the potential for exposure to a fatal downside.  You might be better finding another dice game perhaps a version that cost 10 cents to play, with a prize of 50 cents.  This would have the advantage of allowing you to stop playing before you went bankrupt, should you hit a bad losing streak.

By doing this, you would be spreading the risk around rather than going for an 'all or nothing' risk- trading off a better risk profile for a lower expected value.  (This approach to managing risk is known as 'diversifying'.)

In business terms, this translates into considering whether the downside of a risk, if it occurred, would result in bankruptcy or any situation from which the business could not recover.  The possibility of this, however remote, would have to be taken into account when contemplating a risk with positive expected value.

The fact that fatal downsides in investment loom much larger for smaller companies results in the 'wealth effect' - the relative ease with which larger companies can accumulate wealth.  They can take investment risk with positive expected values but serious potential downsides, because the fear of bankruptcy is more distant for them.  And the more positive-value decisions they take, the more money they accumulate and the more risks they can tolerate in their investments.  They can also afford to take more risks when considering and trying out new directions.  Individuals can also exhibit the wealth effect:  people with more cash saved up can afford to take bigger risks with their careers, perhaps allowing them to achieve greater successes.

It is the nature of know risk probabilities that the longer the run of risk taking, the closer one gets to the delivery of expected values.  This is how gambling becomes a science - with deep enough pockets (the wealth effect) and enough time, pay-offs come to reflect odds.  It is in the short run that 'luck' brings fortune or disaster.