Estimated Value, Bankroll Management and Who Wants to be a Millionaire

[dondarias]

Imagine the situation… You are on who wants to be a millionaire. You are on the £16 000 question with only a 50 : 50 life line remaining.

The question comes and unfortunately you haven’t a Scooby what the right answer is. You decide to use your one remaining lifeline. Two answers disappear and you still have no idea which of the remaining two answers are correct what do you do next.

(The £16 000 represents 12 Months Salary after tax to yourself and you have very little or no savings.)

[MikeL05]

I'd pass and walk away with my 16,000. Unless I felt VERY strongly that this question was an aberration and that I had a very high likelihood of getting the next one(s).

[Hybrid_11]

Well we can take this to an EV approach. I believe the next level is 32000 which is twice that. So given you have a 50/50 chance of getting the right answer and well 50% of the time you make 16000 and 50% of the time you lose the EV value of guessing is 0 but you also have the option to walk away not answer the question and take 16000 so Im assuming the best value would be to walk away assuming you have no clue as to what the answer would be and it is a pure 50/50 guess

[Siegmund]

Whether or not a 50-50 guess is advisable from an EV standpoint depends on the level. The size of prizes doesn't always exactly double with each question, and getting a question wrong doesn't send you home with nothing except at the very lowest levels. According to Rule 6 (http://www.millionairetv.com/rules.html) on the official website, a 50-50 guess is:

EV-neutral on the $200 and $1000 questions;
-EV on the $300, $500, and $25000 questions;
+EV on $4k, $8k, $16k, and $50k-$1M questions;
a no-risk +EV freeroll on the $2k and $50k.

On the $16k question, for instance, you can either pass for a sure $8,000, or take a gamble with EV 8500 and SD 7500.

The "right" strategy for the game as a whole depends on how risk-averse you are and how linear your utility function for moderately large sums of money is.

[AlphaWice]

Reply above is correct.

Let me also add, that since the 32000 level is guaranteed, you get a free guess. So if you gamble and are right, you have an EV of higher than 32000.

[BlueBear]

This is where many players in the gameshow get it horribly wrong. If it is a pure 50-50 guess at the $16000 stage, a player should gamble at this point because the downside is $1000 (in the Australian version, probably the same in UK) and the potential upside is unlimited up to a million dollars.

Only an extremely risk adverse person (and very foolish in my opinion) would not gamble here.

[dondarias]

If the player guesses correctly he will be entitled to a free 1 in 4 shot at he £32000 question. Guessing here is +EV but interestingly nearly any (non poker playing) person who I ask about this situation would not guess. As is the case for most people faced with this stuation on the show. I can only think the majority of the population is highly risk adverse. Ironically insurance companies take advantage this inherent risk aversion to sell –EV positions that people are more than happy to gamble on.

If guessing here meant gambling with your entire bankroll is the edge big enough for you to guess? Or would bankroll management considerations dictate you fold…..

[AlphaWice]

Funny how, the choice of whether to gamble or not hinges on how smart you are (at trivia questions.)

[Laddy]

It certainly is a question of bankroll, and general wealth of the contestant. If they're a student with debt of $20,000, then they should certainly take the $16,000 and run. I think the idea is that EVEN if they had 60-40 to win $32,000 but would HAVE to take the $32,000 and not go further, someone in this financial situation should take the $16,000 and run. This is because to someone with this amount of money, winning $32,000 would not nearly be twice as "good" as winning $16,000, even though the money is twice as much!

Anyone else agree? Sometimes the most +EV decision will not always be the best option to take, it depends on the bankroll. On the WWTBAM gamewshow, a millionaire should ALWAYS take the gamble from $16 to $32.....but a student with large debt in my opinion should certainly not....

Comments?

Laddy...

[OrangeKing]

You're right. For most people, a game of WWTBAM is the equivalent of one of us playing at a limit way above their comfort zone. It's not surprising (or even wrong) for them to be risk adverse, as the additional money that earn with each correct answer may not have nearly the utility of the money they've already won.

[cursha]

thats just rubbish.... you gamble, have a punt, take a guess, pull on the straws.... Whats the point of living without risk.... Bring it on !

(some people call me a 'Lag' what does that mean ?)

[d10]

Strange. I haven't watched this show in years but it happened to be on a few days ago as I was flipping through the channels. I watched it for a bit and started thinking about all kinds of different situations where random guessing would be theoretically correct.

As others have mentioned, if you win the 16,000 question, you get a free shot at 64,000. This is the only reason why I would take a guess here if I was on the 16,000 question. Although if you miss the 16,000 question I still think you're guaranteed 1000 or something like that, so you're risking 15k to win 16k with a 1:1 chance of winning or losing. Slightly +EV but the variance is too high to take that risk. However when you consider that by guessing correctly you win 16k plus a free shot at winning another 32k on top of that, which is worth at a minimum 8k in EV (in actuality it's worth more since often you'll know enough about the question to make a better than random guess, but it's impossible to determine exactly how much more), this becomes too great a value to pass on.

[HigherAce]

+ev or not, if I get on a game show with a million dollar prize im either coming home with it all or the door prize... /images/graemlins/grin.gif

[TheHammer24]

On the 16k you have a 50:50 shot at 32k. So it's slighlty EV right there to guess. Plus, as others have mentioned, you get a 25% chance of getting the 64k right, plus the chance of knowing ht answers to all of the other questions. Gotta go for it. I find myself yelling at the TV when they walk away with only two answers on the board.

[EverettKings]

There's a small problem of semantics. Has he won 16k and is guessing for 32k, or has he won 8k and is guessing for 16k?

I'm gonna assume he has 16 and is guessing for 32. Unless he will starve without the 16k, he should take it. Half the time he drops and wins 1k. Half the time he gets to a GUARANTEED 32k level where he can at least have a 1/4 shot at 64k. Also he's probably smart to be on here so he might just know the answer and have a 90-100% chance of getting another 32k on top. You get the idea.

The possibility of knowing the next question makes it worth a little gamble if he can afford it. I know the 16k is a lot to him, a year's salary, but that's not enough to retire on and will just help him along. Should he get the question right and know the next coupld and walk home with 128k.... then his life is in amazing shape.

If I were him I would physically pull out a quarter on the set, flip it, and pick.

Everett