How to describe the dynamics of this gamble? Suppose you have a $100 and you are offered a chance to play a game involving a fair coin toss:


*

*If you throw heads your wealth increases by 50%. 

*If you throw tails your wealth decreases by 40%. 
Assume that there is no upper bound to your wealth, i.e., you play the game until you are bankrupt. Let's assume that bankruptcy is an absorbing state and it is reached when your wealth is less than a dollar. 
How one might describe the dynamics of your wealth when you go from coin toss $n$ to $n+1$. Moreover, what is the probability that you have increased your wealth after $N$ tosses?  
 A: Unless otherwise specified, if we are asked if something is a good bet we answer in terms of expected value.  If the expected value of the payoff is greater than the bet, we say it is good.  That is fine when you will play the game lots of times, so the law of large numbers kicks in and you confidently expect that much profit.  It is also fine for a small number of plays where the stake is not enough to change your life.  Being one dollar richer than you are now is probably about as nice as being one dollar poorer is bad.  When the stake becomes meaningful, at the extreme when it involves bankruptcy, the linear approximation is not a good one.  Losing all your money is a lot worse than doubling your money is good.  When people propose a bet where bankruptcy is one of the possible outcomes and say it is unconscionable, they are asking the wrong question.  They should define a utility function to be maximized, then we can take the expected value of that function and see if it is a good bet or not.  
One utility function I have seen is the log of your money.  That has the nice properties of making bankruptcy infinitely bad and being convex upward so that increases in your fortune become progressively less interesting than losses, both of which are in accord with many people's perception.  Of course many other functions satisfy these two conditions, but logs are nice because they are easy to compute with.  In the case of this problem, a head adds $\log 1.5 \approx 0.405$ while tails adds $\log 0.6 \approx -.511$.  If this is your utility function, this is a bad bet each time. 
