Implied Odds on Super Millionaire

[Sadat X]

I was just watching Super Millionaire on TV and I got into a discussion with my girlfriend on whether or not a contestant should answer the $100,000 question even if it is just a random guess. Here is the situation:

The contestant has won $50,000 and is going for $100,000. If he answers incorrectly, he drops to $5,000. If he answers correctly, he wins $100,000 and is gauranteed to leave with at least that much. More importantly, he gets two lifelines that all but assure he will get the $500,000 question correct.

In this situation, assuming that the contestant will reach the $500,000 level, he is getting 10-1 on a 3-1 bet. Shouldn't he just guess even if he has no clue, or am I missing something here?

[PairTheBoard]

If you're right about the $500,000 being nearly guaranteed then your conclusion seems pretty clear to me. It may be that some contestants don't think it's so likely they will get to the $500,000 from $100,000. Of course there's also the concept of Utility of Money. For example, if the $50,000 meant you could get a life saving operation which you couldn't get otherwise then you might not want to gamble for the extra money.

PairTheBoard

[MicroBob]

this is a different situation then just looking at the implied-odds.

in poker, you get to make these bets over and over again.

no matter how good the bet may happen to be...for most people, risking 50k on a single shot is beyond any level of comfortability.


if, however, you had a 300BB bankroll and got to play this millionaire-game over and over, then Yes...taking a wild guess would be the correct play.


i read an article similar to this where the author blasted those stupid millionaire-players for always backing off and not guessing even when they had supposedly appropriate odds.

well...there is a difference between the collective group of players winning more money from millionaire (as would be the case if they all played correctly) and the situation that a single-player faces when he's essentially risking 45k on a single-shot.


lets say someone gives you $50k.
he says you can either keep the 50k....or draw 1 card from a 3-card deck. if you draw the 1 card marked "Winner" then you get $160k and if not you forfeit the whole thing.

what if the game gave you only $151k if you won?? or $150.001k?? it's still +ev isn't it??


what if it paid 100-to-1 on your 50k on a 99-to-1 shot?? that's plus EV as well??


how about if it was a 50,000 card deck and there was only 1 card marked 'loser' and you get $2 if you pick any other card but have to forfeit the whole $50k if you get really really unlucky.
is that worth the risk even though it's +ev??


these +ev scenarios are not quite what they seem imo.


there is a different show on the game-show network called russian Roulette (very cool show...eliminated players drop through a hole in the floor).
the championship round involves answering 10 questions for $10k...and if you succeed there you have the option of pulling the russian-roulette handle one more time. you risk your $10k for a 1-in-6 chance to increase the winnings to $100k.
interestingly...most contestants walk with the $10k.
however...if you answer the 10 questions super-fast then it's actually a 1-in-3 chance of turning your $10k into $100k. a lot of players turn this down too...but some go for it. the 1-in-3 chance doesnt come up very often anyway.

disclaimer -
these are all the opinions of a total rank-amateur and i'm fairly certain i only kind of know what i'm talking about.

[David Steele]

I don't think the 500K is quite so certain, haven't a fair number lost it? That question tends to be quite obscure.

Some lost it by failing to use both lifelines even though they had some doubt about their answer. It is almost a fatal flaw of this Super structure that you should use both new lifelines on that 500K question unless you are nearly positive, since the payoff is such a big jump.

It would be perfectly fair to assume something like 75% chance to get it. The double-dip guarantees 50% and you or the experts may just know the answer. So I am sure it is +EV to guess. There is still more implied odds from the potential last questions.

Still the economic reasoning would correctly preclude many from gambling even with the great +EV.

D.

[Equal]

Interesting thread.