In the deal or no deal worksheet, you calculated the probability of winning more than the bank's offer simply by using the number of cases that contained more than that offer. As we will see, this is an overly simplified approach. 

Consider the following scenario: 

A player has four cases left in play... $100 $1,000 $5,000 $500,000 Say the bank offered you a measly $8,000. According to our simplified probability calculations, you would only have a 25% chance of earning more than the banker's offer - so, you may be wise to take the deal. BUT, you have a 25% chance of winning $500,000 - that should be worth a lot more, right? (0.25 * 500,000 = $125,000) 

What if the bank offered you $130,000 in this same scenario. It would probably be best to take the deal then, right? 

BUT you could argue that you have a 75% chance of removing a case that is lower than the bank's offer - so it is likely that your next offer will be even larger, hence No Deal. So, what method would you use to determine if the bank's offer is a fair one? 

Is it good enough if the bank's offer simply beats the average of the available cases? 

What calculations would you use to objectively decided whether an offer should result in a deal or no deal? 

If you were the banker, in what circumstances would you offer more than the mean and when would you offer less?