The Game Show Host says, “Let’s see where we are.
You’ve got the jet ski package and the car,
The Cancun cruise, the autographed baseball…
Looks like a lucky day for you so far.”
The Lovely Lucy, made up like a doll,
Approaches, and the Host says, “That’s not all!
The Lovely Lucy has a bonus stored
Behind this curtain, if you make the call.”
The Lovely Lucy grasps the braided cord
And draws the drape aside. What unexplored
Frontier of TV avarice awaits?
The curtain, drawn, reveals a wall, three-doored.
“You’ve had some luck,” the Host reiterates.
“Here’s one last chance for you to best the Fates.
One door will lead you to Your Private Isle,
The other two, goats eating paper plates.”
You survey all three doors, and slyly smile.
The odds are one in three you’ll own an isle!
Of course, there’s twice the chance you’ll get your goat,
But one in three? Beats Vegas by a mile.
You tell the Host, “Door A.” He clears his throat
And asks you, “Are you sure?” He smooths his coat
And cracks a joke about you liking cheese
More than a home surrounded by a moat.
But then he says, “Would you indulge me, please?
You chose Door A. That leaves me these two keys.
Let’s use one on a door you didn’t pick….”
Door C reveals a goat with knobby knees.
(You’re so relieved you think you may be sick.)
The Game Show Host says, “Would you rather stick
With your first choice, Door A, or make a switch
And take what’s back of B?” Is this a trick?
You had one chance in three to wind up rich,
And now it’s one in two, right? After all,
With only two doors left, no matter which
You choose, it’s even odds. So, what’s your call?
If it’s a coin flip now, why change your mind?
You took Door A to start with. Might as well
Just trust your gut, because you’re flying blind.
If you should switch, and lose? That would be Hell.
“I’m staying with Door A,” you say. Baa’d move:
You’re twice as likely, now, to get the goat.
No, really! Run the numbers and they’ll prove
That you just took your boot off Kismet’s throat.
Consider: Starting odds were one in three
That Door A hid the island. Nothing’s changed
Because you’ve seen the Capricorn in C;
The odds on A are fixed, not rearranged.
Why, then, should you have modified your guess?
Because you’re picking A against the field
And now the field’s been cut in half, so yes,
Door B’s odds changed when Door C was revealed.
Look at it this way: There’s a two-thirds chance
The island wasn’t where you first surmised.
The goat behind Door C cannot enhance
A’s one-third chance, but B’s odds rise. Surprised?
You started with one A, and two “Not-A”
(The first “Not-A” was B, the second, C).
“Not-A’s” odds are two in three, okay?
Despite the goat, “Not-A’s” still two in three.
The odds on Door C, though, have dropped to nil
Since we’ve all seen the goat. So, to recap,
It’s one-third A, two-thirds “Not-A.” You will
By now, of course, have tumbled to the trap:
The odds on C are zero out of three,
But “Not-A’s” odds remain two-thirds, ergo
The whole two-thirds are now installed in B!
The Lovely Lucy wraps your goat to go.
Prompted by November PAD Chapbook Challenge 2011 – Day 30