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# Jamie's darts

## Question

Good shot, said Davey, after Jamie's 1st dart.

Sorry, didn't mean to jinx you, he said, when the 2nd dart was farther from the bullseye.

Alex chimed in, I'll wager a pint your 3rd dart won't be better than your 1st.

You're on, said Jamie as he took aim.

Who is likely to win the bet? Or is it a tossup?

Assume Jamie aims for the center of the board all three times, and his skill is

the same for all 3 darts [not distracted or helped by the comments or the bet].

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At first glance, and again in a hurry; "sorry Cardinal Rule" as some guy in a big red hat whacks me with an incensce burner.

I would have to say his odds are lower since the body of the first dart covers a portion of the board Jaime likely needs to hit. Considering trajectories and the center of the circle.

This was all assuming he was going for the bull.

So tell me some more details Bonanova, were they playing cricket? was he shooting a low number when he hit the first mark? what was the coordinate of that first dart? Was the sun in his eyes? does he have a limp? How many pints has he had?

Peace

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Good shot, said Davey, after Jamie's 1st dart.

Sorry, didn't mean to jinx you, he said, when the 2nd dart was farther from the bullseye.

Alex chimed in, I'll wager a pint your 3rd dart won't be better than your 1st.

You're on, said Jamie as he took aim.

Who is likely to win the bet? Or is it a tossup?

Assume Jamie aims for the center of the board all three times, and his skill is

the same for all 3 darts [not distracted or helped by the comments or the bet].

I'm going to go with an easy answer....

Alex has a better chance of winning because Davey said "good shot" which indicates to me that it was better than Jamie's average shot. Meaning, that Jamie has a higher probability of hitting his average than he does of getting better than his "good" shot.

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I'm going with Jamie losing the bet, for reasons similar, but not exactly the same as bonanova's

Using his past throws to compute his average skill results in his average being somewhere between his first and second shot. Yes, it is a small sample to work from (2 shots), but it is all we have.

It is logical to expect the odds to be higher that his third shot will be closer to the average than for it to be outside the established high/low range.

Of course, none of this takes into account the point values on the board. If his first dart happened to hit the triple-twenty, then it doesn't matter where aims for, Davey wins the bet.

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This was all assuming he was going for the bull.

So tell me some more details Bonanova, were they playing cricket? was he shooting a low number when he hit the first mark? what was the coordinate of that first dart? Was the sun in his eyes? does he have a limp? How many pints has he had?

Peace

Going for the bull? Correct

Cricket? No. Morty keeps the place pretty clean.

Low number? I didn't notice.

Coordinates? 3 cm above and 2 cm right of bullseye.

Sun? No.

Limp? Yes. How did you know? People rarely notice. He covers it up so well.

Pints? Five.

The throws are independent events [neither aided nor hindered by the chatter]

The darts are aimed with equal skill at the center of the board.

The darts have equal likelihood of being closest to the center i.e. one chance in three.

The only way dart 3 is better than dart 1 is if it's closest i.e. one chance in three.

So the odds favor Alex 2 to one.

Alex has 2 chances in 3 of winning.

Arguing that the bet was made after it was already known that dart 2 wouldn't be closest

so it's between darts 1 and 3 therefore the odds are 50-50 will only lead to hurt feelings,

pouting and the receipt of the nightly whining and puling award.

Have a cold one on Alex and get on with your life.

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This was all assuming he was going for the bull.

So tell me some more details Bonanova, were they playing cricket? was he shooting a low number when he hit the first mark? what was the coordinate of that first dart? Was the sun in his eyes? does he have a limp? How many pints has he had?

Peace

Going for the bull? Correct

Cricket? No. Morty keeps the place pretty clean.

Low number? I didn't notice.

Coordinates? 3 cm above and 2 cm right of bullseye.

Sun? No.

Limp? Yes. How did you know? People rarely notice. He covers it up so well.

Pints? Five.

The throws are independent events [neither aided nor hindered by the chatter]

The darts are aimed with equal skill at the center of the board.

The darts have equal likelihood of being closest to the center i.e. one chance in three.

The only way dart 3 is better than dart 1 is if it's closest i.e. one chance in three.

So the odds favor Alex 2 to one.

Alex has 2 chances in 3 of winning.

Arguing that the bet was made after it was already known that dart 2 wouldn't be closest

so it's between darts 1 and 3 therefore the odds are 50-50 will only lead to hurt feelings,

pouting and the receipt of the nightly whining and puling award.

Have a cold one on Alex and get on with your life.

Thank you, I relish the opportunity to practice a little humility.

BTW I made it into MENSA

Military

Education

No

Special

Abilities

snicker snicker

Peace

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Thank you, I relish the opportunity to practice a little humility.

BTW I made it into MENSA

Military

Education

No

Special

Abilities

snicker snicker

Peace

Well ... I don't know whether you were wrong, or not.

The question was who will win the bet? Or is it a tossup?

Couldn't tell if you meant Jamie's odds or Alex's odds.

So, no, I'm not saying you're wrong.

And congratulations on the MENSA thing!! That's great.

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this is simular but not as good as another puzle that involes three doors with one prize

the contestant picks one and the host shows him one door that doesnt have the prize, is he beter of switching doors to the unopened on he doesnt have or staying the same

in this case he has a 1/3 chance if he stays but if he changes he basickly gets the two other doors giving him a 2 in 3 chance

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this is simular but not as good as another puzle that involes three doors with one prize

the contestant picks one and the host shows him one door that doesnt have the prize, is he beter of switching doors to the unopened on he doesnt have or staying the same

in this case he has a 1/3 chance if he stays but if he changes he basickly gets the two other doors giving him a 2 in 3 chance

Monty Hall = Dartboard?

O, I get it ... they both have the number 3 [doors and darts], and one of the 3 wins.

There are a lot of problems that have a 3, so let's dig a little deeper:

[1] In MH, the contestant had opened one door when the decision had to b made; in DB, Jamie threw two darts when the bet was made.

[2] In MH, MH opens one of the other doors; in DB nobody but Jamie throws a dart.

[3] In MH, MH lets the contestant give up his first choice; in DB Jamie keeps all of his darts.

[4] In MH, the contestant wins or loses; in DB a non-player - Alex - makes the winning bet.

[5] In MH, the last door has a better chance of winning; in DB the last dart has a poorer chance of winning.

[6] In MH, the winning door is predetermined: no matter what the contestant does, only door x can win; in DB, nothing is predetermined: any dart can be closest.

[7] In MH, the bet is basically two doors against one door; in DB it's one dart against one dart.

OK, there's more simularity than what I describe.

Just ragging on you a bit cuz you said DB wasn't as good as MH.

Even granting some simularity, what makes MH better?

But if you say that essentially MH = DB, then I guess you're thinking that Alex should have bet the third dart.

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