Who Wants To Be Millionaire Strategy

A phenomenally popular quiz show that was shown around the world. In the UK nearly 600 programmes were broadcast. At the height of its popularity 15 million viewers were tuned in. There was even an Oscar winning film that used the show as its theme!

In this popular TV gameshow contestants face up to twelve multiple choice questions. A correct answer increases the amount won, and an incorrect one ends the game. The image below illustrates the amounts of money to be won.

millionaire-prizes

“It took Smith two years to get a network to buy the show. Television companies were terrified that it could bankrupt them if too many people won. In the end Smith persuaded ITV it would work by taking four envelopes containing £250, £500, £1,000 and £2,000 to their offices and actually playing the game with the executives. When Millionaire finally aired in 1998, it was an instant success, capturing 44 per cent of the audience share on its first night.”

At first glance it looks like the contestant’s general knowledge is being tested and no other skills need to be used. There are, however, some lifelines that the contestant can use:

  • Fifty-fifty
  • Ask the audience
  • Phone a friend

A contestant needs to know how useful it will be to use these lifelines.

FIFTY-FIFTY REDUCES THE FOUR POSSIBLE ANSWERS TO TWO

If a contestant knows that the correct answer is definitely one of two possibilities then opting for fifty-fifty gives him a good chance of winning.

millionaire-50-50

Suppose, for example, that of the four options A, B, C and D the contestant knows that the answer is definitely A or B. If the correct answer is A then fifty-fifty will eliminate either B&C, B&D or C&D. In two out of the three cases the contestant will be able to deduce the correct answer.

Similarly if the correct answer is B then fifty-fifty will eliminate A&C, A&D or C&D. Again in two out of the three cases the contestant will be able to deduce the correct answer.

There is an 2/3 chance that the contestant will know the correct answer after taking fifty-fifty.

If the contestant knows that the correct answer is definitely one of three possibilities then opting for fifty-fifty will do him some good.

Suppose, for example, that he knows the answer is A, B or C. If the correct answer is A then fifty-fifty will eliminate B&C, B&D or C&D. In the case where B&D are eliminated he will know the correct answer. Similar arguments hold if the correct answer is B or C. The chance that the contestant knows the correct answer after taking the fifty-fifty lifeline is 1/3.

If the contestant has no idea which is the correct answer there is little point in going fifty-fifty. There is no chance he will know for sure what the correct answer is when two of the options have been eliminated.

In the first 25 series, 1,178 people have sat in the hot seat, winning a total of £50,762,000 - an average of £43,091 each. There have also been 270 celebrities competing, winning a total of £6,431,000 for charity.

ASK THE AUDIENCE

This shows the contestant the percentages of the 200 strong audience who favour the four possible answers.

Interestingly the highest percentage does show the correct answer in over 90% of cases.

This might seem hard to believe. How can it be that a random group of people, who are not chosen for being very good at general knowledge, usually choose the correct answer?

The phenomenon is known as the ‘wisdom of crowds’. The expression came into use in 1906. At a 1906 county fair in Plymouth 800 people participated in a contest to estimate the weight of a slaughtered ox. The median guess of 1,207 pounds was within 1% of the true weight of 1,198 pounds.

Although many of the crowd’s estimates were way out, on average their guessing was accurate.

It is worth bearing in mind, however, that the audience can be spectacularly wrong. When asked which celestial body orbits the Earth: the Sun, the Moon, Mars or Venus, 80% of the audience said ‘The Sun’.

PHONE A FRIEND

This option allows the contestant to speak to a friend for 30 seconds on the phone and ask them which of the four options their friend thinks is the correct answer. (In fact if the contestant has already used his fifty-fifty option there may be only two options for his friend to choose from.)

Interestingly this lifeline is the least successful. If a contestant has opted to phone a friend it is usually because he has no idea what the correct answer is. In which case the question is probably trickier than usual.

Evidence shows that in this case his friend will know the answer less than 50% of the time.

“This lifeline was discontinued early in 2010 because of an increasing trend in contestants’ friends using Internet search engines to look up the right answer.”

TAKING A GUESS

Sometimes a contestant does not know for sure which is the correct answer. Are there any circumstances where it is worthwhile guessing the answer?

Apart from these two sums of money are there any other instances where answering a question when you are not certain of the answer can be justified?

millionaire-gamble

Suppose a contestant has won £20,000 and has just two options to choose from. In this case there is an argument for gambling.

There is a 50% chance he will win the £50,000 and a 50% chance he will leave with just £1,000.

Since £50,000 is a safe haven there is the added attraction that he can try for £75,000 without fear. In this instance mathematicians would say that his ‘expected’ winnings, if he gambles, is 50% of £50,000 plus 50% of £1,000 i.e. £25,050. This is more than the £20,000 he already has and gambling could be justified.

A similar argument holds if the contestant has won £2,000 and knows the correct answer is one of two options. There is a chance of ½ that he wins £5,000 and a chance of ½ that he falls back to £1,000. His expected winnings are ½ of £5,000 + ½ of £1,000 = £3,500. Most contestants would view this as a sound gamble.

Similarly if the contestant has won £75,000 and knows the correct answer is one of two options. There is a ½ chance of winning £150,000 and a half chance he falls back to £50,000. His expected winnings are ½ of £150,000 + ½ of £50,000 = £125,000. Most contestants would take this risk.

This is not to say that it is the ‘right’ option. It may well be that the contestant just happens to need £75,000 to clear his mortgage. In which case £75,000 is very useful to him and he would be wise not to gamble.

SUMMARY FOR SUCCESS

Take the right choices in this TV game show and you could win big. Understand your lifelines and when best to use them to your advantage.

Sure your answer could be one of two possibilities? Go fifty-fifty. Remember the ‘wisdom of crowds’ will give you a 90% chance of the correct answer and phone a friend is least successful. Not forgetting picking your moment to take a guess.

DID YOU KNOW:

In April 2003 British Army major Charles Ingram, his wife Diana and lecturer Tecwen Whitlock were convicted of using fraudulent means to win £1 million when Ingram was a contestant on the show in September 2001.

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