Can you solve the monster duel riddle? - Alex Gendler
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Date: 2020-12-08
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Comments and reviews: 9
Raen
The bonus question is the nicest of all three:
1st round: There are two possibilities for any disk you pick. Because the opponent is going to pick according to your pick, we are going to consider only the lowest winning odds (the opponent will choose in order to minimize your odds. For A this is 51%. For B this is 44%. For C this is 38. 22%.
2nd round: The video explains this well. Just considering the second round, the odds of A winning is 28. 56%. For B this is 33. 22%. For C this is 38. 22%.
3rd round: In order to get the odds of A winning this round, one must multiply A1 and A2, which gives 14. 57%. Multiplying B1 and B2 give 14. 62%. C1 and C2 give 14. 61%.
We see that all three disks have incredibly similar odds, with B just barely coming out on top.
(You can correct me if I missed anything)
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The bonus question is the nicest of all three:
1st round: There are two possibilities for any disk you pick. Because the opponent is going to pick according to your pick, we are going to consider only the lowest winning odds (the opponent will choose in order to minimize your odds. For A this is 51%. For B this is 44%. For C this is 38. 22%.
2nd round: The video explains this well. Just considering the second round, the odds of A winning is 28. 56%. For B this is 33. 22%. For C this is 38. 22%.
3rd round: In order to get the odds of A winning this round, one must multiply A1 and A2, which gives 14. 57%. Multiplying B1 and B2 give 14. 62%. C1 and C2 give 14. 61%.
We see that all three disks have incredibly similar odds, with B just barely coming out on top.
(You can correct me if I missed anything)
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MGD313
See, normally if you go one-on-one with another Diskymon, you got a 50/50 chance of winning. But my Burgersaur is a genetic freak, and it's not normal, so you got a 25% at best at beating me! And then you add a Churrozard into the mix? Your chances of winning drastically go down. See, in the three-way, you got a 33 1/3 chance of winning. But I got a 66 2/3 chance of winning, cause the Churrozard knows he can t beat me, and he s not even gonna try. So, Wartortilla, you take your 33 1/3 chance, minus my 25 percent chance, and you got an 8 1/3 chance of winning! But then you take my 75 percent chance at winning if we was to go one-on-one, and then add 66 2/3 percents, I got a 141 2/3% chance of winning! See, the numbers don t lie, and they spell disaster for you at the Diskymon League Finals!
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See, normally if you go one-on-one with another Diskymon, you got a 50/50 chance of winning. But my Burgersaur is a genetic freak, and it's not normal, so you got a 25% at best at beating me! And then you add a Churrozard into the mix? Your chances of winning drastically go down. See, in the three-way, you got a 33 1/3 chance of winning. But I got a 66 2/3 chance of winning, cause the Churrozard knows he can t beat me, and he s not even gonna try. So, Wartortilla, you take your 33 1/3 chance, minus my 25 percent chance, and you got an 8 1/3 chance of winning! But then you take my 75 percent chance at winning if we was to go one-on-one, and then add 66 2/3 percents, I got a 141 2/3% chance of winning! See, the numbers don t lie, and they spell disaster for you at the Diskymon League Finals!
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Mark
My thought process (Part 1): If I choose disc A, my opponent s only option is to pick disc C, and I will have a 51% chance of winning. If I choose disc B, I will have a 44% chance of winning if opponent chooses disc A, and if my opponent chooses disc C, not only does my opponent have a 51% chance of losing and I have a 49% chance of winning, but if my opponent rolls a 5, I need to roll a 6 to win, so 22% x 49% = 10. 78% chance of winning. 10. 78% + 49% = 59. 78% chance of me winning. Finally, if I choose disc C and my opponent chooses disc A, I have a 49% chance of winning, but if my opponent chooses disc B, he has a 51% chance of winning and 49% x 78% = 38. 22% chance of me winning.
Worst Case Scenarios
Disc A: 51%
Disc B: 44%
Disc C: 38. 22%
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My thought process (Part 1): If I choose disc A, my opponent s only option is to pick disc C, and I will have a 51% chance of winning. If I choose disc B, I will have a 44% chance of winning if opponent chooses disc A, and if my opponent chooses disc C, not only does my opponent have a 51% chance of losing and I have a 49% chance of winning, but if my opponent rolls a 5, I need to roll a 6 to win, so 22% x 49% = 10. 78% chance of winning. 10. 78% + 49% = 59. 78% chance of me winning. Finally, if I choose disc C and my opponent chooses disc A, I have a 49% chance of winning, but if my opponent chooses disc B, he has a 51% chance of winning and 49% x 78% = 38. 22% chance of me winning.
Worst Case Scenarios
Disc A: 51%
Disc B: 44%
Disc C: 38. 22%
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Alex
For the third round solution:
For 1 on 1, your first opponent will always pick the disk that leaves you with worst odds possible.
If you pick A, you will win 1-vs-1 51% of the time (vs C, and battle royale 28, 56% of the time - the chance to win is multiplication, 14, 5656%
If you pick B, you will win 1-vs-1 44% of the time (vs A, and battle royale 33, 22% of the time - the chance to win is 14, 6168%
If you pick C, you will win 1-vs-1 38, 22% of the time (vs B, and battle royale with the same 38, 22% chance - the chance to win is 14, 607684%
Bottom line:
Pick B and pray to every god you know.
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For the third round solution:
For 1 on 1, your first opponent will always pick the disk that leaves you with worst odds possible.
If you pick A, you will win 1-vs-1 51% of the time (vs C, and battle royale 28, 56% of the time - the chance to win is multiplication, 14, 5656%
If you pick B, you will win 1-vs-1 44% of the time (vs A, and battle royale 33, 22% of the time - the chance to win is 14, 6168%
If you pick C, you will win 1-vs-1 38, 22% of the time (vs B, and battle royale with the same 38, 22% chance - the chance to win is 14, 607684%
Bottom line:
Pick B and pray to every god you know.
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Harrison
ok now B and C have a chance of summoning a higher level monster even though it's not as likely as the other choices, so you should switch. For A to beat B and C, both B and C need to land on the 2 and 1, and like in the frog riddle, that doesn't lead up to a good outcome, since those events are not dependent on each other. Now for B to win, it has to land on a 6 which has a better chance if C doesn't land on a 5, which adds up to a 33. 22% chance of winning. Now for C to win disk B has to land on a 4 or 2. with those facts C has a 38. 22% chance of winning so you should pick disk C.
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ok now B and C have a chance of summoning a higher level monster even though it's not as likely as the other choices, so you should switch. For A to beat B and C, both B and C need to land on the 2 and 1, and like in the frog riddle, that doesn't lead up to a good outcome, since those events are not dependent on each other. Now for B to win, it has to land on a 6 which has a better chance if C doesn't land on a 5, which adds up to a 33. 22% chance of winning. Now for C to win disk B has to land on a 4 or 2. with those facts C has a 38. 22% chance of winning so you should pick disk C.
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Inky
To answer the final riddle
Disk A has a 51% chance of winning first round and a 29% chance to win the second round
Disk B has a 44% chance of winning first round and a 33% chance to win the second round
Disk C has a 49% chance of winning first round and a 38% chance to win the second round
Which means Disk A s chances of winning are 51% x 29% = 14. 79% Disk B s are 44% x 33% = 14. 52% and Disk C s are 49% x 38% = 18. 62%
Meaning that the Disk most likely to win the extra round is Disk C
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To answer the final riddle
Disk A has a 51% chance of winning first round and a 29% chance to win the second round
Disk B has a 44% chance of winning first round and a 33% chance to win the second round
Disk C has a 49% chance of winning first round and a 38% chance to win the second round
Which means Disk A s chances of winning are 51% x 29% = 14. 79% Disk B s are 44% x 33% = 14. 52% and Disk C s are 49% x 38% = 18. 62%
Meaning that the Disk most likely to win the extra round is Disk C
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Adam
My answers:
1. A
2. C (I didn't calculate the probabilities, I just looked at the problem closely and made an intuitive, educated guess that it was better than A or B)
3. B (I didn't calculate the probabilities, I guessed it was B because the previous two were A and C. I have no idea what the actual answer is.
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My answers:
1. A
2. C (I didn't calculate the probabilities, I just looked at the problem closely and made an intuitive, educated guess that it was better than A or B)
3. B (I didn't calculate the probabilities, I guessed it was B because the previous two were A and C. I have no idea what the actual answer is.
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MEXICAN
I still pick 3 because playing individually and drawing vs two opponents can still be seen as two individual matches regardless of the probabilities of playing in a tournament of three. It's a matter of luck really but if the tournament repeats then yes, go with the higher percentage of winning in the final stages.
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I still pick 3 because playing individually and drawing vs two opponents can still be seen as two individual matches regardless of the probabilities of playing in a tournament of three. It's a matter of luck really but if the tournament repeats then yes, go with the higher percentage of winning in the final stages.
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Nasen
For the last riddle I've got:
In total 14, 56% of winning for choosing disc A, 14, 61% for disc B and 14, 60% for disc C
Given you have super clever opponents who would always choose the best counter disc in round A: )
Does anyone agree?
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For the last riddle I've got:
In total 14, 56% of winning for choosing disc A, 14, 61% for disc B and 14, 60% for disc C
Given you have super clever opponents who would always choose the best counter disc in round A: )
Does anyone agree?
reply
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