Late last year, I asked you (a number of times … just like Howie Mandel) …
…. Deal or No Deal?!
What would you have done [AJC: if you haven’t yet ‘cast your vote’, please go back to this post and drop a comment]?
We know that Ms Tomorrow Rodriguez (sounds like a character out of a James Bond movie) said “No Deal!” to the miserly Banker’s’ offer that only paid out 1-in-3 for a 50/50 chance …
… Vote 1 for the ‘math kings’!
But, look at the situation that she’s faced with right now (in the photo above):
4 suitcases left: 3 of them contain ONE MILLION DOLLARS and 1 contains only $300!!
Ms Rodriguez – with the odds clearly stacked in her favor – has two choices:
1. Take the Banker’s Offer of $677,000
2. Say “No Deal” and select just one more suitcase (then she will be presented with another offer)
Deal or No Deal?
Let’s examine the options:
1. Take the $677k and run!
OK, the banker has offered $677,000 but there are 4 suitcases left of which three contain $1 Million and one is a (virtual) blank.
That smells like a 75% chance of $1 Million to me … ‘worth’ $750,000 (any maths whizzes out there to counter this?) … seems to me that the Banker is short-changing Tomorrow Rodriguez by $73,000 buckaroos!
2. Select just one more suitcase and see what happens next (after all, she can’t lose on the next turn)
Well, here is the problem … unlike any of the lead-up turns, this time there is only ONE non-million case left; so, there are actually two possible outcomes here:
i) Tomorrow selects the one suitcase containing the blank (i.e. $300) which means that she automatically wins (there are only 3 suitcases left … since each would then have to contain $1 Mill. she can’t lose)
ii) Three times more likely, Tomorrow selects one of the three suitcases that contain $1 Million and the chance of winning on the next round drops from 75% to 67% (3 suitcases left: 2 contain $1 Million and 1 contains $300 only)
From this round on, the Banker Deals can only get worse, because the next round after this one would leave just 2 suitcases (assuming that she hadn’t won by then) … or, a 50/50 chance (and, we’ve already seen how much the Banker will rip her off on that)
In fact, Tomorrow is effectively paying for each ‘roll of the dice’ from here on in … whether she realizes it or not …
So, if she turns down $677,000, Tomorrow is really saying: “$1 Million or Bust … I’m going all the way, Baby!” … because she will surely turn down the later, much lower offers (been there, done that!) as well.
So, Ms Rodriguez really has just two practical alternatives:
1. A guaranteed $677,000 if she walks away right now
2. A 75% chance of winning $1 Million AND a 25% chance of walking away virtually empty-handed
Deal or No Deal?
Just like last time, make a vote & drop your vote into the comment section below (I’d love to hear your reasons) … next week, we’ll check out what our readers had to say … it should be interesting!
In the meantime, do you want to know what Ms Rodriguez chose? Do you agree?
I picked deal.
I admit that I cannot make truly rational (from a pure mathematical/economics standpoint) decisions in cases where the stakes exceed around 5x my income. If you divided all the amounts by 10, I’d say no deal without too much thought. But 677k is probably going to be 400k or so after taxes (projecting future bracket changes for 2009). that leaves me enough to put my entire financial house in order AND have well over 300k left over as a foundation for the future.
I say no deal. 3 out of 4 to me is pretty good odds that I would open up one of the 1 mil suitcases. If I lose entirely, well, 677k isn’t going to break my spirit or my financial plans in the next 10 years or so and my life’s purpose requires a LOT more than that. I say GO FOR IT!
I would say no deal. The odds are in her favor, a situation which doesn’t happen a lot in life. Much like blackjack, when you have an eleven and dealer is showing a six, double down and wager as much as possible when the odds are in your favor.
Take advantage of the situation while there is a situation to be taken advantage of.
I’d take the $677,000 and run.
The Expected Value is ($3,000,300)/4 = $750,075 (you are close enough with 750k, esp if you happen to be on stage doing this in your head).
The banker offered $677,000, a 9.7% ‘discounted’ offer. Lower than the expected value and therefore not a good deal.
You have a 75% chance of losing a $1M suitcase and then the expected value drops to $666,766 (surprisingly close to the bankers current offer).
You only have a 25% chance of losing the $300 case, in which the expected value (actually the guaranteed value) is $1,000,000.
Even though the banker is not offering the best deal; when buying stocks, houses, or a new pair of jeans, etc, we’ve all paid a premium at times. Getting screwed by 10% isn’t so bad when considering that it is free money, i.e., the risk-free rate of return is infinite. And the odds are better.
Take the deal – you’re getting FREE MONEY from a game show for doing NOTHING!
Wow … some great arguments, both for and against; and we’re split right down the middle (50% voting FOR and 50% voting against) …. c’mon we need a LOT MORE VOTERS to see where this will end up.
Then, at least some of you might be surprised at how I might ‘vote’ … 😉
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I said no deal… but would take the next deal offered. It’s a bit of a gamble, but it wasn’t really my money or my winnings so it’s easy to gamble. 🙂
But, more importantly, what DID she do and what did she get?!
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As Steve Miller would say:
“Go on, take the money, and run. Woo hoo hoo”
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I think that I’m with Julie on this one…I would take the next offer. I think I would try to get just a little more out of the banker and if it doesn’t go my way then definitely pull the plug. If the Wealthy Canadian number’s are correct I would really only lose about $10,000 for an opportunity to increase the pot by $323,000 (a guaranteed win).
If they offer 10% less than the expected value then going again is risking a loss of $77K to gain $323K with a 75% chance of success. I would definitely try again!
If I was wrong again, then the offer goes down to $600,000, there are 2 $1 million cases and 1 $300 case left.
Going again is risking $150K for $400K gain with a 66% chance of success. I would go again.
If I was wrong again the offer drops to
$450,000 with 1 $1 Million and 1 $300 case.
At that point it’s risking $449,700 to make $550,000 with only a 50/50 shot at success. Mathematically it seems to make sense to go one more time, but I wouldn’t.
Why? The utility of the additional money is NOT linear for me. Getting $450K would make huge changes in my life. However, I don’t think that the $1M would result in even twice as much of a difference. Because of that I would not be willing to risk the $450K and would take the sure thing.
I think it all depends on the effect the money will have on the person, her life, and her plan. If the banks offer is enough money to be a game changer, then take the deal. If the amount is too low to really make a difference, then go for the million.
As for me, I’d take the deal. An extra $677k would push me ahead on my journey about 4 or 5 years… truly a game changer for me.
But, Rick has a point. Maybe $677k makes just as much a difference as $450k, so why not go for the million? Still, for me, I’d take the $677k.
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I chose deal, I don’t know how I would have gotten to that point in the first place, but $677k is better than walking away with only say $300.00 suit case.
I could make great use of that 677k , so the extra few dollars(if I would have hit the million) wouldn’t matter that much.
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