A brain teasing probability puzzle

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Hoss

Hoss

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Tuco_sl said:
Hehe that's a good question. I didn't see it before. I'll have to think about it.

At first glance I'd say no. The probability that contestant A or B picked the correct door is 1%. So you don't improve your odds by choosing a different door.

At second glance a huge difference between the previous question is that the host picks all the doors not chosen, which means that one of the contestants picked correctly. This would happen only 2% of the time making the entire game show very silly. But given that this only happens 2% of the time I'd still be confident in not changing.
Click to expand...
i originally asked it with just 3 doors, which would make for a better game show. But I liked the examples that used 100 doors to bring your odds of winning on a switch up to 99%. So I modified it. I'm pretty sure I also originally said that the 2 contestants didn't know about each other so as to preserve the dynamic of all the other doors being unchosen and being able to be lumped together. But I forgot that part.
 
DiddleySquat

DiddleySquat

Bronze Knight of the Realm
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Hoss_sl said:
This thread does have a proper paradox that I don't think anyone answered.

You have 100 doors, 1 prize, a host and 2 contestants. Each contestant picks a door, and the host opens up 98 doors to reveal the prize is not behind any of them. Will both contestant increase their odds of winning the prize by switching?
Click to expand...
It does not matter, the chances to win for each contestant is 50%.

Edit:
Let me explain a bit: each contestant has an initial 1 in 100 chance to pick the winning door. Practically speaking, the host will have to reset the experiment in 98% of the cases (by having the contestants repick a door until one of them has the prize door selected - which only the host knows of course) because the prize must be behind one of the contestants' doors to get to the scenario where he can open all 98 other doors and not reveal the prize. Anyway, the opening of the 98 doors only gives as info "one of the two remaining doors contains the prize", nothing more, so either door has a 1 in 2 chance.
 
Tuco

Tuco

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DiddleySquat_sl said:
It does not matter, the chances to win for each contestant is 50%.

Edit:
Let me explain a bit: each contestant has an initial 1 in 100 chance to pick the winning door. Practically speaking, the host will have to reset the experiment in 98% of the cases (by having the contestants repick a door until one of them has the prize door selected - which only the host knows of course) because the prize must be behind one of the contestants' doors to get to the scenario where he can open all 98 other doors and not reveal the prize. Anyway, the opening of the 98 doors only gives as info "one of the two remaining doors contains the prize", nothing more, so either door has a 1 in 2 chance.
Click to expand...
yeah this is how I feel too.
 
Hoss

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What if the contestants don't know about each other? Do they then both have a 98% chance of winning if they switch?
 
Tuco

Tuco

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Hoss_sl said:
What if the contestants don't know about each other? Do they then both have a 98% chance of winning if they switch?
Click to expand...
Yup. Even if they think that the host took out 98 doors and knows where the door is, it doesn't matter, they still have a 50% chance of having the right door.

But really they'd probably get tired after being told to pick a door ~25 times because both contestants kept not picking the right door.
 
Melvin

Melvin

Blackwing Lair Raider
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The Ancient_sl said:
I found an explanation that's better than any I could make:
Click to expand...
I liked that video until ~3:30, and then it started rustling my jimmies and I could only stand to watch about a minute more after that.

If the problem being discussed is a two envelope problem, then the probability (from the perspective of the player) of the contents of the sealed envelope is 100% uncertain. Claiming that the probability is anything other than 100% uncertain is an incorrect description of reality. If you use math that assigns P = .5 to the dollar value of the sealed envelope, your math is now incongruous with the actual problem being discussed.

It seems like a small subtle thing to get rustled about, but it's important.

Try this: create an experiment where you truly are offered a 50/50 chance of either doubling or halving your current dollar value. You will have created the same problem as neither 2 sealed envelopes, nor 1 sealed and 1 opened envelope.
 
Tuco

Tuco

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Melvin_sl said:
Try this: create an experiment where you truly are offered a 50/50 chance of either doubling or halving your current dollar value. You will have created the same problem as neither 2 sealed envelopes, nor 1 sealed and 1 opened envelope.
Click to expand...
I would take the money and run assuming that $1/2 = 0 or $0.01/2 = 0!

simulation:
Times to hit zero: 213 maxValue: 102400
Times to hit zero: 75 maxValue: 12800
Times to hit zero: 29 maxValue: 3200
Times to hit zero: 23 maxValue: 400
Times to hit zero: 249 maxValue: 12582912
Times to hit zero: 381 maxValue: 50331648
Times to hit zero: 329 maxValue: 419430400
Times to hit zero: 119 maxValue: 2048
Times to hit zero: 25 maxValue: 50
Times to hit zero: 113 maxValue: 8192
Times to hit zero: 29 maxValue: 400
Times to hit zero: 981 maxValue: 1610612736
Times to hit zero: 578 maxValue: 1677721600
Times to hit zero: 19 maxValue: 200
Times to hit zero: 41 maxValue: 384
Times to hit zero: 178 maxValue: 1677721600
Times to hit zero: 19 maxValue: 200
Times to hit zero: 123 maxValue: 196608
Times to hit zero: 87 maxValue: 12288
Times to hit zero: 247 maxValue: 409600
Times to hit zero: 529 maxValue: 104857600
Times to hit zero: 79 maxValue: 400
Times to hit zero: 9 maxValue: 200
Times to hit zero: 588 maxValue: 1073741824
Times to hit zero: 463 maxValue: 268435456
Times to hit zero: 51 maxValue: 51200
Times to hit zero: 13 maxValue: 200
Times to hit zero: 61 maxValue: 400
Times to hit zero: 47 maxValue: 400
Times to hit zero: 95 maxValue: 200
Times to hit zero: 225 maxValue: 25600
Times to hit zero: 353 maxValue: 100663296
Times to hit zero: 19 maxValue: 50
Times to hit zero: 57 maxValue: 800
Times to hit zero: 593 maxValue: 1610612736
Times to hit zero: 125 maxValue: 2048
Times to hit zero: 194 maxValue: 1677721600
Times to hit zero: 129 maxValue: 102400
Times to hit zero: 119 maxValue: 6144
Times to hit zero: 141 maxValue: 24576
Times to hit zero: 43 maxValue: 384
Times to hit zero: 375 maxValue: 6553600
Times to hit zero: 63 maxValue: 800
Times to hit zero: 169 maxValue: 24576
Times to hit zero: 79 maxValue: 12800
Times to hit zero: 81 maxValue: 25600
Times to hit zero: 93 maxValue: 6400
Times to hit zero: 51 maxValue: 12800
Times to hit zero: 229 maxValue: 6144
Times to hit zero: 37 maxValue: 384
Times to hit zero: 211 maxValue: 102400
Times to hit zero: 531 maxValue: 2097152
Times to hit zero: 103 maxValue: 12800
Times to hit zero: 214 maxValue: 1677721600
Times to hit zero: 93 maxValue: 25600
Times to hit zero: 21 maxValue: 400
Times to hit zero: 163 maxValue: 819200
Times to hit zero: 33 maxValue: 192
Times to hit zero: 69 maxValue: 1600
Times to hit zero: 181 maxValue: 1610612736
Times to hit zero: 145 maxValue: 12288
Times to hit zero: 247 maxValue: 65536
Times to hit zero: 11 maxValue: 50
Times to hit zero: 350 maxValue: 1073741824
Times to hit zero: 115 maxValue: 6400
Times to hit zero: 275 maxValue: 3145728
Times to hit zero: 97 maxValue: 1600
Times to hit zero: 15 maxValue: 200
Times to hit zero: 107 maxValue: 6144
Times to hit zero: 41 maxValue: 3072
Times to hit zero: 604 maxValue: 1073741824
Times to hit zero: 57 maxValue: 3072
Times to hit zero: 13 maxValue: 50
Times to hit zero: 365 maxValue: 1572864
Times to hit zero: 169 maxValue: 409600
Times to hit zero: 295 maxValue: 786432
Times to hit zero: 47 maxValue: 384
Times to hit zero: 25 maxValue: 200
Times to hit zero: 178 maxValue: 1677721600
Times to hit zero: 25 maxValue: 800
Times to hit zero: 581 maxValue: 1610612736
Times to hit zero: 762 maxValue: 1610612736
Times to hit zero: 283 maxValue: 1638400
Times to hit zero: 11 maxValue: 50
Times to hit zero: 21 maxValue: 50
Times to hit zero: 59 maxValue: 400
Times to hit zero: 115 maxValue: 512
Times to hit zero: 197 maxValue: 1610612736
Times to hit zero: 163 maxValue: 51200
Times to hit zero: 171 maxValue: 1610612736
Times to hit zero: 19 maxValue: 200
Times to hit zero: 618 maxValue: 1677721600
Times to hit zero: 909 maxValue: 419430400
Times to hit zero: 242 maxValue: 1677721600
Times to hit zero: 11 maxValue: 100
Times to hit zero: 422 maxValue: 1073741824
Times to hit zero: 121 maxValue: 6400
Times to hit zero: 9 maxValue: 50
Times to hit zero: 231 maxValue: 24576
Times to hit zero: 59 maxValue: 6400
Times to hit zero: 47 maxValue: 400
Times to hit zero: 329 maxValue: 1610612736
Times to hit zero: 11 maxValue: 50
Times to hit zero: 129 maxValue: 12288
Times to hit zero: 31 maxValue: 100
Times to hit zero: 693 maxValue: 419430400
Times to hit zero: 154 maxValue: 1677721600
Times to hit zero: 77 maxValue: 3200
Times to hit zero: 11 maxValue: 50
Times to hit zero: 33 maxValue: 50
Times to hit zero: 23 maxValue: 400
Times to hit zero: 288 maxValue: 1677721600
Times to hit zero: 81 maxValue: 768
Times to hit zero: 61 maxValue: 1600
Times to hit zero: 37 maxValue: 6400
Times to hit zero: 25 maxValue: 200
Times to hit zero: 205 maxValue: 1638400
Times to hit zero: 51 maxValue: 192
Times to hit zero: 111 maxValue: 3200
Times to hit zero: 61 maxValue: 1536
Times to hit zero: 325 maxValue: 262144
Times to hit zero: 893 maxValue: 1677721600
Times to hit zero: 43 maxValue: 3200
Times to hit zero: 380 maxValue: 1677721600
Times to hit zero: 73 maxValue: 1600
Times to hit zero: 900 maxValue: 1073741824
Times to hit zero: 67 maxValue: 1600
Times to hit zero: 73 maxValue: 384
Times to hit zero: 95 maxValue: 3200
Times to hit zero: 41 maxValue: 800
Times to hit zero: 55 maxValue: 100
Times to hit zero: 175 maxValue: 24576
Times to hit zero: 35 maxValue: 1600
Times to hit zero: 471 maxValue: 25165824
Times to hit zero: 133 maxValue: 409600
Times to hit zero: 39 maxValue: 25600
Times to hit zero: 11 maxValue: 50
Times to hit zero: 29 maxValue: 800
Times to hit zero: 65 maxValue: 768
Times to hit zero: 81 maxValue: 25600
Times to hit zero: 15 maxValue: 50
Times to hit zero: 7 maxValue: 50
Times to hit zero: 291 maxValue: 98304
Times to hit zero: 201 maxValue: 786432
Times to hit zero: 119 maxValue: 1600
Times to hit zero: 19 maxValue: 100
Times to hit zero: 17 maxValue: 200
Times to hit zero: 29 maxValue: 800
Times to hit zero: 249 maxValue: 1610612736
Times to hit zero: 151 maxValue: 1610612736
Times to hit zero: 199 maxValue: 13107200
Times to hit zero: 263 maxValue: 819200
Times to hit zero: 309 maxValue: 1610612736
Times to hit zero: 77 maxValue: 400
Times to hit zero: 39 maxValue: 800
Times to hit zero: 129 maxValue: 204800
Times to hit zero: 51 maxValue: 400
Times to hit zero: 159 maxValue: 102400
Times to hit zero: 15 maxValue: 200
Times to hit zero: 108 maxValue: 1677721600
Times to hit zero: 27 maxValue: 800
Times to hit zero: 47 maxValue: 200
Times to hit zero: 55 maxValue: 1600
Times to hit zero: 29 maxValue: 200
Times to hit zero: 269 maxValue: 1610612736
Times to hit zero: 113 maxValue: 6400
Times to hit zero: 61 maxValue: 768
Times to hit zero: 285 maxValue: 1610612736
Times to hit zero: 229 maxValue: 26214400
Times to hit zero: 103 maxValue: 400
Times to hit zero: 177 maxValue: 1638400
Times to hit zero: 15 maxValue: 400
Times to hit zero: 17 maxValue: 50
Times to hit zero: 21 maxValue: 50
Times to hit zero: 129 maxValue: 12288
Times to hit zero: 313 maxValue: 196608
Times to hit zero: 157 maxValue: 25600
Times to hit zero: 572 maxValue: 1677721600
Times to hit zero: 41 maxValue: 3200
Times to hit zero: 81 maxValue: 800
Times to hit zero: 189 maxValue: 819200
Times to hit zero: 73 maxValue: 12800
Times to hit zero: 13 maxValue: 50
Times to hit zero: 171 maxValue: 800
Times to hit zero: 87 maxValue: 1536
Times to hit zero: 575 maxValue: 1610612736
Times to hit zero: 47 maxValue: 800
Times to hit zero: 15 maxValue: 200
Times to hit zero: 41 maxValue: 200
Times to hit zero: 55 maxValue: 12800
Times to hit zero: 249 maxValue: 1610612736
Times to hit zero: 277 maxValue: 419430400
Times to hit zero: 49 maxValue: 1600
Times to hit zero: 13 maxValue: 50
Times to hit zero: 481 maxValue: 1610612736
Times to hit zero: 23 maxValue: 400
Times to hit zero: 13 maxValue: 100
Times to hit zero: 55 maxValue: 800
Times to hit zero: 489 maxValue: 1610612736
Times to hit zero: 55 maxValue: 800
Times to hit zero: 15 maxValue: 50
Times to hit zero: 367 maxValue: 786432
Times to hit zero: 707 maxValue: 1610612736
Times to hit zero: 507 maxValue: 1610612736
Times to hit zero: 67 maxValue: 768
Times to hit zero: 31 maxValue: 50
Times to hit zero: 35 maxValue: 400
Times to hit zero: 51 maxValue: 800
Times to hit zero: 75 maxValue: 128
Times to hit zero: 13 maxValue: 200
Times to hit zero: 21 maxValue: 400
Times to hit zero: 268 maxValue: 1677721600
Times to hit zero: 399 maxValue: 1610612736
Times to hit zero: 13 maxValue: 100
Times to hit zero: 37 maxValue: 3200
Times to hit zero: 127 maxValue: 3072
Times to hit zero: 285 maxValue: 1610612736
Times to hit zero: 21 maxValue: 200
Times to hit zero: 705 maxValue: 1610612736
Times to hit zero: 43 maxValue: 800
Times to hit zero: 61 maxValue: 200
Times to hit zero: 49 maxValue: 96
Times to hit zero: 179 maxValue: 13107200
Times to hit zero: 49 maxValue: 1600
Times to hit zero: 103 maxValue: 98304
Times to hit zero: 133 maxValue: 102400
Times to hit zero: 261 maxValue: 6291456
Times to hit zero: 83 maxValue: 400
Times to hit zero: 681 maxValue: 1677721600
Times to hit zero: 19 maxValue: 200
Times to hit zero: 827 maxValue: 6553600
Times to hit zero: 23 maxValue: 400
Times to hit zero: 127 maxValue: 204800
Times to hit zero: 55 maxValue: 6400
Times to hit zero: 129 maxValue: 1600
Times to hit zero: 13 maxValue: 200
Times to hit zero: 1135 maxValue: 536870912
Times to hit zero: 45 maxValue: 1600
Times to hit zero: 399 maxValue: 3145728
Times to hit zero: 23 maxValue: 800
Times to hit zero: 69 maxValue: 400
Times to hit zero: 51 maxValue: 1600
Times to hit zero: 73 maxValue: 12288
Times to hit zero: 89 maxValue: 4096
Times to hit zero: 195 maxValue: 3072
Times to hit zero: 339 maxValue: 1610612736
Times to hit zero: 201 maxValue: 102400
Times to hit zero: 145 maxValue: 3072
Times to hit zero: 105 maxValue: 512
Times to hit zero: 33 maxValue: 800
Times to hit zero: 7 maxValue: 50
Times to hit zero: 51 maxValue: 3200
Times to hit zero: 45 maxValue: 384
Times to hit zero: 73 maxValue: 3072
Times to hit zero: 9 maxValue: 200
Times to hit zero: 55 maxValue: 768
Times to hit zero: 19 maxValue: 1600
Times to hit zero: 647 maxValue: 209715200
Times to hit zero: 17 maxValue: 400
Times to hit zero: 379 maxValue: 1610612736
Times to hit zero: 181 maxValue: 1610612736
Times to hit zero: 460 maxValue: 1677721600
Times to hit zero: 347 maxValue: 65536
Times to hit zero: 267 maxValue: 1048576
Times to hit zero: 748 maxValue: 1677721600
Times to hit zero: 165 maxValue: 1610612736
Times to hit zero: 171 maxValue: 25600
Times to hit zero: 53 maxValue: 6400
Times to hit zero: 171 maxValue: 131072
Times to hit zero: 159 maxValue: 1610612736
Times to hit zero: 11 maxValue: 50
Times to hit zero: 177 maxValue: 98304
Times to hit zero: 270 maxValue: 1677721600
Times to hit zero: 17 maxValue: 50
Times to hit zero: 13 maxValue: 100
Times to hit zero: 409 maxValue: 13107200
Times to hit zero: 19 maxValue: 50
Times to hit zero: 23 maxValue: 50
Times to hit zero: 45 maxValue: 6400
Times to hit zero: 49 maxValue: 1600
Times to hit zero: 41 maxValue: 200
Times to hit zero: 49 maxValue: 384
Times to hit zero: 19 maxValue: 50
Times to hit zero: 229 maxValue: 8388608
Times to hit zero: 89 maxValue: 3072
Times to hit zero: 31 maxValue: 400
Times to hit zero: 721 maxValue: 1677721600
Times to hit zero: 151 maxValue: 12800
Times to hit zero: 207 maxValue: 3276800
Times to hit zero: 13 maxValue: 50
Times to hit zero: 9 maxValue: 50
Times to hit zero: 119 maxValue: 102400
Times to hit zero: 61 maxValue: 1600
Times to hit zero: 493 maxValue: 1610612736
Times to hit zero: 9 maxValue: 50
Times to hit zero: 381 maxValue: 6291456
Times to hit zero: 151 maxValue: 409600
Times to hit zero: 19 maxValue: 100
Times to hit zero: 313 maxValue: 2097152

In other words, following this process will almost inevitably brings you to a zero value.
 
Melvin

Melvin

Blackwing Lair Raider
1,399
1,168
Tuco_sl said:
I would take the money and run assuming that $1/2 = 0 or $0.01/2 = 0!

simulation:
Times to hit zero: 213 maxValue: 102400
Times to hit zero: 75 maxValue: 12800
Times to hit zero: 29 maxValue: 3200
Times to hit zero: 23 maxValue: 400
Times to hit zero: 249 maxValue: 12582912
Times to hit zero: 381 maxValue: 50331648
Times to hit zero: 329 maxValue: 419430400
Times to hit zero: 119 maxValue: 2048
Times to hit zero: 25 maxValue: 50
Times to hit zero: 113 maxValue: 8192
Times to hit zero: 29 maxValue: 400
Times to hit zero: 981 maxValue: 1610612736
Times to hit zero: 578 maxValue: 1677721600
Times to hit zero: 19 maxValue: 200
Times to hit zero: 41 maxValue: 384
Times to hit zero: 178 maxValue: 1677721600
Times to hit zero: 19 maxValue: 200
Times to hit zero: 123 maxValue: 196608
Times to hit zero: 87 maxValue: 12288
Times to hit zero: 247 maxValue: 409600
Times to hit zero: 529 maxValue: 104857600
Times to hit zero: 79 maxValue: 400
Times to hit zero: 9 maxValue: 200
Times to hit zero: 588 maxValue: 1073741824
Times to hit zero: 463 maxValue: 268435456
Times to hit zero: 51 maxValue: 51200
Times to hit zero: 13 maxValue: 200
Times to hit zero: 61 maxValue: 400
Times to hit zero: 47 maxValue: 400
Times to hit zero: 95 maxValue: 200
Times to hit zero: 225 maxValue: 25600
Times to hit zero: 353 maxValue: 100663296
Times to hit zero: 19 maxValue: 50
Times to hit zero: 57 maxValue: 800
Times to hit zero: 593 maxValue: 1610612736
Times to hit zero: 125 maxValue: 2048
Times to hit zero: 194 maxValue: 1677721600
Times to hit zero: 129 maxValue: 102400
Times to hit zero: 119 maxValue: 6144
Times to hit zero: 141 maxValue: 24576
Times to hit zero: 43 maxValue: 384
Times to hit zero: 375 maxValue: 6553600
Times to hit zero: 63 maxValue: 800
Times to hit zero: 169 maxValue: 24576
Times to hit zero: 79 maxValue: 12800
Times to hit zero: 81 maxValue: 25600
Times to hit zero: 93 maxValue: 6400
Times to hit zero: 51 maxValue: 12800
Times to hit zero: 229 maxValue: 6144
Times to hit zero: 37 maxValue: 384
Times to hit zero: 211 maxValue: 102400
Times to hit zero: 531 maxValue: 2097152
Times to hit zero: 103 maxValue: 12800
Times to hit zero: 214 maxValue: 1677721600
Times to hit zero: 93 maxValue: 25600
Times to hit zero: 21 maxValue: 400
Times to hit zero: 163 maxValue: 819200
Times to hit zero: 33 maxValue: 192
Times to hit zero: 69 maxValue: 1600
Times to hit zero: 181 maxValue: 1610612736
Times to hit zero: 145 maxValue: 12288
Times to hit zero: 247 maxValue: 65536
Times to hit zero: 11 maxValue: 50
Times to hit zero: 350 maxValue: 1073741824
Times to hit zero: 115 maxValue: 6400
Times to hit zero: 275 maxValue: 3145728
Times to hit zero: 97 maxValue: 1600
Times to hit zero: 15 maxValue: 200
Times to hit zero: 107 maxValue: 6144
Times to hit zero: 41 maxValue: 3072
Times to hit zero: 604 maxValue: 1073741824
Times to hit zero: 57 maxValue: 3072
Times to hit zero: 13 maxValue: 50
Times to hit zero: 365 maxValue: 1572864
Times to hit zero: 169 maxValue: 409600
Times to hit zero: 295 maxValue: 786432
Times to hit zero: 47 maxValue: 384
Times to hit zero: 25 maxValue: 200
Times to hit zero: 178 maxValue: 1677721600
Times to hit zero: 25 maxValue: 800
Times to hit zero: 581 maxValue: 1610612736
Times to hit zero: 762 maxValue: 1610612736
Times to hit zero: 283 maxValue: 1638400
Times to hit zero: 11 maxValue: 50
Times to hit zero: 21 maxValue: 50
Times to hit zero: 59 maxValue: 400
Times to hit zero: 115 maxValue: 512
Times to hit zero: 197 maxValue: 1610612736
Times to hit zero: 163 maxValue: 51200
Times to hit zero: 171 maxValue: 1610612736
Times to hit zero: 19 maxValue: 200
Times to hit zero: 618 maxValue: 1677721600
Times to hit zero: 909 maxValue: 419430400
Times to hit zero: 242 maxValue: 1677721600
Times to hit zero: 11 maxValue: 100
Times to hit zero: 422 maxValue: 1073741824
Times to hit zero: 121 maxValue: 6400
Times to hit zero: 9 maxValue: 50
Times to hit zero: 231 maxValue: 24576
Times to hit zero: 59 maxValue: 6400
Times to hit zero: 47 maxValue: 400
Times to hit zero: 329 maxValue: 1610612736
Times to hit zero: 11 maxValue: 50
Times to hit zero: 129 maxValue: 12288
Times to hit zero: 31 maxValue: 100
Times to hit zero: 693 maxValue: 419430400
Times to hit zero: 154 maxValue: 1677721600
Times to hit zero: 77 maxValue: 3200
Times to hit zero: 11 maxValue: 50
Times to hit zero: 33 maxValue: 50
Times to hit zero: 23 maxValue: 400
Times to hit zero: 288 maxValue: 1677721600
Times to hit zero: 81 maxValue: 768
Times to hit zero: 61 maxValue: 1600
Times to hit zero: 37 maxValue: 6400
Times to hit zero: 25 maxValue: 200
Times to hit zero: 205 maxValue: 1638400
Times to hit zero: 51 maxValue: 192
Times to hit zero: 111 maxValue: 3200
Times to hit zero: 61 maxValue: 1536
Times to hit zero: 325 maxValue: 262144
Times to hit zero: 893 maxValue: 1677721600
Times to hit zero: 43 maxValue: 3200
Times to hit zero: 380 maxValue: 1677721600
Times to hit zero: 73 maxValue: 1600
Times to hit zero: 900 maxValue: 1073741824
Times to hit zero: 67 maxValue: 1600
Times to hit zero: 73 maxValue: 384
Times to hit zero: 95 maxValue: 3200
Times to hit zero: 41 maxValue: 800
Times to hit zero: 55 maxValue: 100
Times to hit zero: 175 maxValue: 24576
Times to hit zero: 35 maxValue: 1600
Times to hit zero: 471 maxValue: 25165824
Times to hit zero: 133 maxValue: 409600
Times to hit zero: 39 maxValue: 25600
Times to hit zero: 11 maxValue: 50
Times to hit zero: 29 maxValue: 800
Times to hit zero: 65 maxValue: 768
Times to hit zero: 81 maxValue: 25600
Times to hit zero: 15 maxValue: 50
Times to hit zero: 7 maxValue: 50
Times to hit zero: 291 maxValue: 98304
Times to hit zero: 201 maxValue: 786432
Times to hit zero: 119 maxValue: 1600
Times to hit zero: 19 maxValue: 100
Times to hit zero: 17 maxValue: 200
Times to hit zero: 29 maxValue: 800
Times to hit zero: 249 maxValue: 1610612736
Times to hit zero: 151 maxValue: 1610612736
Times to hit zero: 199 maxValue: 13107200
Times to hit zero: 263 maxValue: 819200
Times to hit zero: 309 maxValue: 1610612736
Times to hit zero: 77 maxValue: 400
Times to hit zero: 39 maxValue: 800
Times to hit zero: 129 maxValue: 204800
Times to hit zero: 51 maxValue: 400
Times to hit zero: 159 maxValue: 102400
Times to hit zero: 15 maxValue: 200
Times to hit zero: 108 maxValue: 1677721600
Times to hit zero: 27 maxValue: 800
Times to hit zero: 47 maxValue: 200
Times to hit zero: 55 maxValue: 1600
Times to hit zero: 29 maxValue: 200
Times to hit zero: 269 maxValue: 1610612736
Times to hit zero: 113 maxValue: 6400
Times to hit zero: 61 maxValue: 768
Times to hit zero: 285 maxValue: 1610612736
Times to hit zero: 229 maxValue: 26214400
Times to hit zero: 103 maxValue: 400
Times to hit zero: 177 maxValue: 1638400
Times to hit zero: 15 maxValue: 400
Times to hit zero: 17 maxValue: 50
Times to hit zero: 21 maxValue: 50
Times to hit zero: 129 maxValue: 12288
Times to hit zero: 313 maxValue: 196608
Times to hit zero: 157 maxValue: 25600
Times to hit zero: 572 maxValue: 1677721600
Times to hit zero: 41 maxValue: 3200
Times to hit zero: 81 maxValue: 800
Times to hit zero: 189 maxValue: 819200
Times to hit zero: 73 maxValue: 12800
Times to hit zero: 13 maxValue: 50
Times to hit zero: 171 maxValue: 800
Times to hit zero: 87 maxValue: 1536
Times to hit zero: 575 maxValue: 1610612736
Times to hit zero: 47 maxValue: 800
Times to hit zero: 15 maxValue: 200
Times to hit zero: 41 maxValue: 200
Times to hit zero: 55 maxValue: 12800
Times to hit zero: 249 maxValue: 1610612736
Times to hit zero: 277 maxValue: 419430400
Times to hit zero: 49 maxValue: 1600
Times to hit zero: 13 maxValue: 50
Times to hit zero: 481 maxValue: 1610612736
Times to hit zero: 23 maxValue: 400
Times to hit zero: 13 maxValue: 100
Times to hit zero: 55 maxValue: 800
Times to hit zero: 489 maxValue: 1610612736
Times to hit zero: 55 maxValue: 800
Times to hit zero: 15 maxValue: 50
Times to hit zero: 367 maxValue: 786432
Times to hit zero: 707 maxValue: 1610612736
Times to hit zero: 507 maxValue: 1610612736
Times to hit zero: 67 maxValue: 768
Times to hit zero: 31 maxValue: 50
Times to hit zero: 35 maxValue: 400
Times to hit zero: 51 maxValue: 800
Times to hit zero: 75 maxValue: 128
Times to hit zero: 13 maxValue: 200
Times to hit zero: 21 maxValue: 400
Times to hit zero: 268 maxValue: 1677721600
Times to hit zero: 399 maxValue: 1610612736
Times to hit zero: 13 maxValue: 100
Times to hit zero: 37 maxValue: 3200
Times to hit zero: 127 maxValue: 3072
Times to hit zero: 285 maxValue: 1610612736
Times to hit zero: 21 maxValue: 200
Times to hit zero: 705 maxValue: 1610612736
Times to hit zero: 43 maxValue: 800
Times to hit zero: 61 maxValue: 200
Times to hit zero: 49 maxValue: 96
Times to hit zero: 179 maxValue: 13107200
Times to hit zero: 49 maxValue: 1600
Times to hit zero: 103 maxValue: 98304
Times to hit zero: 133 maxValue: 102400
Times to hit zero: 261 maxValue: 6291456
Times to hit zero: 83 maxValue: 400
Times to hit zero: 681 maxValue: 1677721600
Times to hit zero: 19 maxValue: 200
Times to hit zero: 827 maxValue: 6553600
Times to hit zero: 23 maxValue: 400
Times to hit zero: 127 maxValue: 204800
Times to hit zero: 55 maxValue: 6400
Times to hit zero: 129 maxValue: 1600
Times to hit zero: 13 maxValue: 200
Times to hit zero: 1135 maxValue: 536870912
Times to hit zero: 45 maxValue: 1600
Times to hit zero: 399 maxValue: 3145728
Times to hit zero: 23 maxValue: 800
Times to hit zero: 69 maxValue: 400
Times to hit zero: 51 maxValue: 1600
Times to hit zero: 73 maxValue: 12288
Times to hit zero: 89 maxValue: 4096
Times to hit zero: 195 maxValue: 3072
Times to hit zero: 339 maxValue: 1610612736
Times to hit zero: 201 maxValue: 102400
Times to hit zero: 145 maxValue: 3072
Times to hit zero: 105 maxValue: 512
Times to hit zero: 33 maxValue: 800
Times to hit zero: 7 maxValue: 50
Times to hit zero: 51 maxValue: 3200
Times to hit zero: 45 maxValue: 384
Times to hit zero: 73 maxValue: 3072
Times to hit zero: 9 maxValue: 200
Times to hit zero: 55 maxValue: 768
Times to hit zero: 19 maxValue: 1600
Times to hit zero: 647 maxValue: 209715200
Times to hit zero: 17 maxValue: 400
Times to hit zero: 379 maxValue: 1610612736
Times to hit zero: 181 maxValue: 1610612736
Times to hit zero: 460 maxValue: 1677721600
Times to hit zero: 347 maxValue: 65536
Times to hit zero: 267 maxValue: 1048576
Times to hit zero: 748 maxValue: 1677721600
Times to hit zero: 165 maxValue: 1610612736
Times to hit zero: 171 maxValue: 25600
Times to hit zero: 53 maxValue: 6400
Times to hit zero: 171 maxValue: 131072
Times to hit zero: 159 maxValue: 1610612736
Times to hit zero: 11 maxValue: 50
Times to hit zero: 177 maxValue: 98304
Times to hit zero: 270 maxValue: 1677721600
Times to hit zero: 17 maxValue: 50
Times to hit zero: 13 maxValue: 100
Times to hit zero: 409 maxValue: 13107200
Times to hit zero: 19 maxValue: 50
Times to hit zero: 23 maxValue: 50
Times to hit zero: 45 maxValue: 6400
Times to hit zero: 49 maxValue: 1600
Times to hit zero: 41 maxValue: 200
Times to hit zero: 49 maxValue: 384
Times to hit zero: 19 maxValue: 50
Times to hit zero: 229 maxValue: 8388608
Times to hit zero: 89 maxValue: 3072
Times to hit zero: 31 maxValue: 400
Times to hit zero: 721 maxValue: 1677721600
Times to hit zero: 151 maxValue: 12800
Times to hit zero: 207 maxValue: 3276800
Times to hit zero: 13 maxValue: 50
Times to hit zero: 9 maxValue: 50
Times to hit zero: 119 maxValue: 102400
Times to hit zero: 61 maxValue: 1600
Times to hit zero: 493 maxValue: 1610612736
Times to hit zero: 9 maxValue: 50
Times to hit zero: 381 maxValue: 6291456
Times to hit zero: 151 maxValue: 409600
Times to hit zero: 19 maxValue: 100
Times to hit zero: 313 maxValue: 2097152

In other words, following this process will almost inevitably brings you to a zero value.
Click to expand...
Oh cool, I wasn't expecting anything that detailed at all. I'm just barely computer literate enough to hack together a version of your code that compiles on my system. As far as the output, I'm surprised that it always hits zero so quickly, and I'm also a little bit concerned about how consistent (predictable?) rand() is, but all in all thanks for putting together a simulation so quickly. It's nice to see some thorough math that produces real numbers instead of jumbles of words mixed with mostly related but half-formed maths.

username:~/bin$ g++ dorh.cc
username:~/bin$ ./a.out
Times to hit zero: 115 maxValue: 6400
Times to hit zero: 235 maxValue: 104857600
Times to hit zero: 47 maxValue: 100
Times to hit zero: 11 maxValue: 200
Times to hit zero: 45 maxValue: 800
Times to hit zero: 295 maxValue: 1610612736
Times to hit zero: 23 maxValue: 200
Times to hit zero: 21 maxValue: 200
Times to hit zero: 455 maxValue: 1610612736
Times to hit zero: 681 maxValue: 1677721600
Times to hit zero: 15 maxValue: 100
Times to hit zero: 167 maxValue: 800
Times to hit zero: 197 maxValue: 8192
Times to hit zero: 31 maxValue: 400
Times to hit zero: 81 maxValue: 1600
Times to hit zero: 131 maxValue: 393216
Times to hit zero: 55 maxValue: 6144
Times to hit zero: 61 maxValue: 3200
Times to hit zero: 15 maxValue: 200
Times to hit zero: 15 maxValue: 200
Times to hit zero: 113 maxValue: 6144
Times to hit zero: 41 maxValue: 400
Times to hit zero: 11 maxValue: 200
Times to hit zero: 239 maxValue: 51200
Times to hit zero: 268 maxValue: 1677721600
Times to hit zero: 61 maxValue: 200
Times to hit zero: 25 maxValue: 50
Times to hit zero: 21 maxValue: 400
Times to hit zero: 121 maxValue: 24576
Times to hit zero: 15 maxValue: 50
Times to hit zero: 17 maxValue: 96
Times to hit zero: 57 maxValue: 3200
Times to hit zero: 220 maxValue: 1677721600
Times to hit zero: 466 maxValue: 1677721600
Times to hit zero: 93 maxValue: 800
Times to hit zero: 199 maxValue: 1610612736
Times to hit zero: 29 maxValue: 200
Times to hit zero: 25 maxValue: 100
Times to hit zero: 228 maxValue: 1677721600
Times to hit zero: 93 maxValue: 768
Times to hit zero: 423 maxValue: 196608
Times to hit zero: 43 maxValue: 200
Times to hit zero: 23 maxValue: 800
Times to hit zero: 27 maxValue: 100
Times to hit zero: 390 maxValue: 1677721600
Times to hit zero: 45 maxValue: 3200
Times to hit zero: 471 maxValue: 13107200
Times to hit zero: 61 maxValue: 200
Times to hit zero: 29 maxValue: 400
Times to hit zero: 75 maxValue: 6144
Times to hit zero: 199 maxValue: 409600
Times to hit zero: 11 maxValue: 200
Times to hit zero: 153 maxValue: 12800
Times to hit zero: 25 maxValue: 200
Times to hit zero: 23 maxValue: 100
Times to hit zero: 119 maxValue: 24576
Times to hit zero: 17 maxValue: 50
Times to hit zero: 13 maxValue: 200
Times to hit zero: 125 maxValue: 1638400
Times to hit zero: 195 maxValue: 98304
Times to hit zero: 29 maxValue: 12800
Times to hit zero: 69 maxValue: 768
Times to hit zero: 295 maxValue: 786432
Times to hit zero: 85 maxValue: 25600
Times to hit zero: 31 maxValue: 200
Times to hit zero: 341 maxValue: 1677721600
Times to hit zero: 482 maxValue: 1677721600
Times to hit zero: 472 maxValue: 1677721600
Times to hit zero: 39 maxValue: 800
Times to hit zero: 23 maxValue: 200
Times to hit zero: 23 maxValue: 200
Times to hit zero: 17 maxValue: 100
Times to hit zero: 9 maxValue: 200
Times to hit zero: 383 maxValue: 13107200
Times to hit zero: 59 maxValue: 800
Times to hit zero: 13 maxValue: 200
Times to hit zero: 99 maxValue: 384
Times to hit zero: 17 maxValue: 50
Times to hit zero: 725 maxValue: 1610612736
Times to hit zero: 495 maxValue: 1572864
Times to hit zero: 631 maxValue: 26214400
Times to hit zero: 59 maxValue: 800
Times to hit zero: 81 maxValue: 12800
Times to hit zero: 333 maxValue: 524288
Times to hit zero: 269 maxValue: 1610612736
Times to hit zero: 11 maxValue: 50
Times to hit zero: 9 maxValue: 100
Times to hit zero: 160 maxValue: 1677721600
Times to hit zero: 244 maxValue: 1677721600
Times to hit zero: 95 maxValue: 12800
Times to hit zero: 79 maxValue: 102400
Times to hit zero: 349 maxValue: 12800
Times to hit zero: 35 maxValue: 400
Times to hit zero: 45 maxValue: 400
Times to hit zero: 121 maxValue: 98304
Times to hit zero: 212 maxValue: 1677721600
Times to hit zero: 33 maxValue: 50
Times to hit zero: 649 maxValue: 6553600
Times to hit zero: 29 maxValue: 1600
Times to hit zero: 9 maxValue: 50

I was actually thinking that someone might come up with a description of how this experiment would need to be carried out in the real world. Something like a player who hits or stands and a dealer that flips a coin to determine whether the pool is doubled or halved.
 
T

The Master

Bronze Squire
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Szlia_sl said:
That seems related to another paradox:St. Petersburg paradox - Wikipedia, the free encyclopedia

A casino offers you the following lottery: when you enter the game, there is a pot of $1. A coin is then flipped. For each head result, the pot is doubled. As soon as there is a tail result, you get the pot. Question: What would you consider to be a fair entry fee for this lottery?
Click to expand...
What never made sense to me about this problem is the expectation that you can somehow keep playing indefinitely. Assuming the Casino is behaving rationally, running a game that has a potentially infinite payout would be nonsensical. They'd limit the number of flips so the potential was non-infinite and set an entry amount at slightly higher than the average return from that number of flips. Meaning you'd eventually run out of money if you kept playing. Samuelson made a similar argument that the Casino would simply never offer such a game.

Also in the truly infinite scenario, the Casino never has to pay out, because you never stop playing.
 
Melvin

Melvin

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You'd also need to play a nearly infinite number of games before you get that perfect streak of lucky coin flips. If the person setting the price wasn't careless (and Vegas odds-makers aren't), you'd be losing money far more often than not. So as you're playing those nearly infinite number of games, you'd also be pretty consistently raising the bar for how much you needed to win just to break even. Woo gambling!
 
E

elidib

Vyemm Raider
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The Master_sl said:
What never made sense to me about this problem is the expectation that you can somehow keep playing indefinitely. Assuming the Casino is behaving rationally, running a game that has a potentially infinite payout would be nonsensical. They'd limit the number of flips so the potential was non-infinite and set an entry amount at slightly higher than the average return from that number of flips. Meaning you'd eventually run out of money if you kept playing. Samuelson made a similar argument that the Casino would simply never offer such a game.

Also in the truly infinite scenario, the Casino never has to pay out, because you never stop playing.
Click to expand...
huh?

The casino pays out as soon as you hit a tails and get the pot.

and absolutely a casino would rationally run a game with the expectation that you can keep playing infinitely... this is how they draw you in, their whole business model is predicated on this. The casino can bank on the probability that paying out a fortune is so unlikely that they will never have to do it. Even if someone gets really lucky and the casino does in fact lose money, OR if they set the price so low that most people are making money from this game, they will make it up on (a) other games, (b) concessions and drinks, (c) room rates, and (d) consider it an advertising cost because now you have someone yelling about how awesome it is they made so much easy money at xyz casino.

If you were super lucky and got heads over 10 times in a row before a tails, your payout would only be a bit over $1,000. That's not even a blip on the radar to a casino, and the likelihood that you're going to get that far is slim.

What would I consider a fair entry fee? fucking free, just a gimmick to get people in the door.
 
T

The Master

Bronze Squire
2,084
2
But the premise of the problem, mathematically, is that the game has an infinite value. But as long as the game has an infinite value, itnever actually ends.That is what the math tells you. You can't have the infinite value without having the game never end.

Missing the premise of the problem. If you say, for instance, $1 is a fair value to buy-in, you're always guaranteed to win $1. So you can play infinitely till you're ahead. No casino would run a game like that. Casinos only run games where the odds are in their favor, i.e, statistically they are going to make money. This doesn't qualify (which is kind of the point, that so many people miss the simple fact that almost any amount of money is worth buying in, because the return is infinite). Also casinos have laws that require them to have a certain amount of money on hand to deal with expected payouts which are based on those same statistical models. A game that has potentially infinite payout would mean they would need infinite money on hand,regardlessof if anyone even played the game or won an infinite amount of money. Hence my point no casino would ever run this game in real life, the way it is stated. So on the theoretical side, game never actually ends, on the practical side, no casino would ever run this as a game for any amount of money.
 
E

elidib

Vyemm Raider
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Theexpectedpayout, based on statistical models, is not infinite though, nor is it even very large, is my point. It's also possible that you could pull 777 on a slot machine an infinite number of times in a row, or guess that the ball will land on black an infinite number of times in a row. Does that mean the casino has to keep infinity dollars lying around? no. Because the payout isn't expected to be that huge. The coin-flipping game will end, and it will nearly always end in a reasonable amount of time for the casino to make money on it, even if they did price it at just $1 so that you're guaranteed to always win. Casinos give free shit away all the time.

What if they showed you ads before every coin flip? BAM they are making money while you are making money, win-win.

What if they had to flip everyone elses coins before they got back around to your second flip, taking over an hour to get to you because of the lines? Now they're giving out free shit, sure, but noone actually wants to dick around with it an "infinite" number of times.

My point is that there are, in fact, a myriad of reasons that a casino (or other entity in a different form) would run such a game, and still be highly profitable no matter what the entry fee was. The original question though, was how much would you consider it fair to pay yourself as an entrance fee to be on the player side. My answer is still $0, because even at $1 when I go to a casino I'm not going to stand there watching a croupier flip a damn coin all day just to make a buck here and there, since they certainly aren't going to manage the game in any reasonable amount of time to accommodate all of the people who would want to play.

They would need to provide me with some other incentive to play this game, or make it free so that *I* am getting some financial benefit from playing their game, not them.
 
Ambiturner

Ambiturner

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Not sure if you guys are understating how it works. If you pay $5 to play you'd need 3 heads in a row before you actually win anything. Odds are against that so the casino will win much more often.
 
F

foddon

Silver Knight of the Realm
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elidib_sl said:
Theexpectedpayout, based on statistical models, is not infinite though, nor is it even very large, is my point. It's also possible that you could pull 777 on a slot machine an infinite number of times in a row, or guess that the ball will land on black an infinite number of times in a row. Does that mean the casino has to keep infinity dollars lying around? no. Because the payout isn't expected to be that huge. The coin-flipping game will end, and it will nearly always end in a reasonable amount of time for the casino to make money on it, even if they did price it at just $1 so that you're guaranteed to always win. Casinos give free shit away all the time.

What if they showed you ads before every coin flip? BAM they are making money while you are making money, win-win.

What if they had to flip everyone elses coins before they got back around to your second flip, taking over an hour to get to you because of the lines? Now they're giving out free shit, sure, but noone actually wants to dick around with it an "infinite" number of times.

My point is that there are, in fact, a myriad of reasons that a casino (or other entity in a different form) would run such a game, and still be highly profitable no matter what the entry fee was. The original question though, was how much would you consider it fair to pay yourself as an entrance fee to be on the player side. My answer is still $0, because even at $1 when I go to a casino I'm not going to stand there watching a croupier flip a damn coin all day just to make a buck here and there, since they certainly aren't going to manage the game in any reasonable amount of time to accommodate all of the people who would want to play.

They would need to provide me with some other incentive to play this game, or make it free so that *I* am getting some financial benefit from playing their game, not them.
Click to expand...
I'm pretty sure you're wrong about this. Casinos have maximum bets for all table games and don't offer infinite parlays on roulette tables (meaning if you win a couple times in a row doubling your bet you're going to hit the max bet and not be able to double any longer). Slots are programmed to prevent from paying out too many jackpots AND have maximum bets so you could never double your winnings. Any sweepstakes they offer will be covered by insurance or available cash (no matter how remote the odds are).

I would imagine casinos are legally obligated to be able to cover any bet they offer. They wouldn't be able to cover this bet 100% of the time so they wouldn't be able to offer it. They would have to have a maximum number of doubles in the rules of the game.
 
Tuco

Tuco

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Szlia_sl said:
That seems related to another paradox:St. Petersburg paradox - Wikipedia, the free encyclopedia

A casino offers you the following lottery: when you enter the game, there is a pot of $1. A coin is then flipped. For each head result, the pot is doubled. As soon as there is a tail result, you get the pot. Question: What would you consider to be a fair entry fee for this lottery?
Click to expand...
From my model about $13
wink.png


output:
avgVal:[12.922964] avgIt:[1.999862] max:[33554432] maxTimeToTails:[26]

It would be a viable (if boring) casino game if they put a max (say 1024 or something) amount of gain from it, that'd likely drop the value dramatically.
 
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