TWCP OTD - 15th of March, 2017
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BEST CHANCE A man has $300 to take home. A friend offers him a bet to double the money. He has to roll dices... Rolling one to get a 4 or better, rolling two and get 5 or better on one of them at least or rolling 3 and getting 6 on one of them at least... Wont't get the result he looses the $300... Which one our man should choose?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
Take the dice and go home. Upon reconsideration... offer the "friend" the same wager. ;P I may be way off here, but if my probability-fu hasn't entirely failed me...One die for a 4 or 5 or 6 == 3:6 , 50% , to win even money == "fair game"
Two dice for at least one 5 or 6 == 8:36 , 22% , to win even money == about a 55% house edge?
Three dice for at least one 6 == 7:216 , 3% , to win even money == about a 94% house edge?One die for a 4 or 5 or 6 == 3:6 , 50% , to win even money == "fair game"
Two dice for at least one 5 or 6 == 20:36 , 55% , to win even money == -11% house edge?
Three dice for at least one 6 == 91:216 , 42% , to win even money == about a 16% house edge?Not playing is still the best option.
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BEST CHANCE A man has $300 to take home. A friend offers him a bet to double the money. He has to roll dices... Rolling one to get a 4 or better, rolling two and get 5 or better on one of them at least or rolling 3 and getting 6 on one of them at least... Wont't get the result he looses the $300... Which one our man should choose?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
Bash his friend over the head and take the money.
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Bash his friend over the head and take the money.
I thought of that myself immediately, but decided I like my friends ... :laugh:
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...
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BEST CHANCE A man has $300 to take home. A friend offers him a bet to double the money. He has to roll dices... Rolling one to get a 4 or better, rolling two and get 5 or better on one of them at least or rolling 3 and getting 6 on one of them at least... Wont't get the result he looses the $300... Which one our man should choose?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
Rolling two.
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BEST CHANCE A man has $300 to take home. A friend offers him a bet to double the money. He has to roll dices... Rolling one to get a 4 or better, rolling two and get 5 or better on one of them at least or rolling 3 and getting 6 on one of them at least... Wont't get the result he looses the $300... Which one our man should choose?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
- 1 dice, 4, 5, or 6 wins: 3/6 = 50% 2) 2 dice, 5 or 6 wins: (1 - (4/6)^2) = 55.6% 3) 3 dice, 6 wins: (1 - (5/6)^3) = 42.1% So the best options in order are 2, 1, then 3 :thumbsup: EDIT: Including just leaving with $300 (option #4), the option order is 2 > 1 = 4 > 3.
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- 1 dice, 4, 5, or 6 wins: 3/6 = 50% 2) 2 dice, 5 or 6 wins: (1 - (4/6)^2) = 55.6% 3) 3 dice, 6 wins: (1 - (5/6)^3) = 42.1% So the best options in order are 2, 1, then 3 :thumbsup: EDIT: Including just leaving with $300 (option #4), the option order is 2 > 1 = 4 > 3.
These are the chances to go home with $600, but there is the option - of 100% - to take home $300!
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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These are the chances to go home with $600, but there is the option - of 100% - to take home $300!
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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You asked for the best option which would be option #2 statistically speaking - 55.6% to double your money. This can easily be shown with a sample set: 100 rolls, double or nothing @ 55.6% = $333.6 100 rolls, $300 @ 100% = $300
Double or nothing means you can not have $333.6... It is either $600 or $0! So 55.6% of $600 is much worst than 100% of $300...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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- 1 dice, 4, 5, or 6 wins: 3/6 = 50% 2) 2 dice, 5 or 6 wins: (1 - (4/6)^2) = 55.6% 3) 3 dice, 6 wins: (1 - (5/6)^3) = 42.1% So the best options in order are 2, 1, then 3 :thumbsup: EDIT: Including just leaving with $300 (option #4), the option order is 2 > 1 = 4 > 3.
If I'm not mistaken... There are 36 outcomes from rolling 2 standard dice, and only 8 of them are winners. -- 20 winning outcomes There are 216 outcomes from rolling 3 standard dice, and only 7 of them are winners. -- 91 winning outcomes What did I miss? Edit: I was mistaken. I missed a whole bunch of winning outcomes.
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If I'm not mistaken... There are 36 outcomes from rolling 2 standard dice, and only 8 of them are winners. -- 20 winning outcomes There are 216 outcomes from rolling 3 standard dice, and only 7 of them are winners. -- 91 winning outcomes What did I miss? Edit: I was mistaken. I missed a whole bunch of winning outcomes.
PIEBALDconsult wrote:
What did I miss?
That the outcome of each dice is independent, as there is no meaning of the order or on which dice you got the winner number...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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PIEBALDconsult wrote:
What did I miss?
That the outcome of each dice is independent, as there is no meaning of the order or on which dice you got the winner number...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
Yes, I understand that, but I see where I went wrong -- I have since decided to graph it out...
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Double or nothing means you can not have $333.6... It is either $600 or $0! So 55.6% of $600 is much worst than 100% of $300...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
That's to show general value per roll. Each value is 0 or 600 (double or nothing). (55.6 x 600)/100 = 333.6. Since it's all or nothing, you could also do (600 x .556). Both calculate the same thing - the average value per roll. The point is that the per-roll evaluation of $333.6 is greater than the $300 evaluation (300 x 1.0). This isn't to show the money you earn but to weight and compare the options. If you'd like to include personality, monetary situation, and other per-person variables then even though you will statistically get more value out of the 55.6% option the guaranteed $300 may seem more appealing depending on the relative value of $300 to that individual.
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If I'm not mistaken... There are 36 outcomes from rolling 2 standard dice, and only 8 of them are winners. -- 20 winning outcomes There are 216 outcomes from rolling 3 standard dice, and only 7 of them are winners. -- 91 winning outcomes What did I miss? Edit: I was mistaken. I missed a whole bunch of winning outcomes.
PIEBALDconsult wrote:
There are 36 outcomes from rolling 2 standard dice, and only 8 of them are winners.
How did you get 8 winning combinations? If the first die already wins (in twqo out of six cases), the second one is irrelevant in any case. These already are twelve winning combinations. And then those cases where the first die 'misses', but the second one wins are added. Chance that the first one wins: 2/6. Chance that the first one mises, bt the second one wins: 4/6 * 2/6 = 8/36 (probably what you thought) Total chance 2/6 + 8/36 = 12/36 + 8 /36 = 20/36 = 0,56 (rounded).
PIEBALDconsult wrote:
There are 216 outcomes from rolling 3 standard dice, and only 7 of them are winners.
Similar calculation: Chance that the first one already wins: 1/6 Chance that the second one wins if the first fails: 5/6 * 1/6 = 5/36 Chance that the third one winds when the first two fail: 5/6 * 5/6 * 1/6 = 25/216 Adding it all up: 1/6 + 5/36 + 25/216 = (36 + 30 + 25) / 216 = 71/216 = 0,33 (rounded).
The language is JavaScript. that of Mordor, which I will not utter here
This is Javascript. If you put big wheels and a racing stripe on a golf cart, it's still a fucking golf cart.
"I don't know, extraterrestrial?" "You mean like from space?" "No, from Canada." If software development were a circus, we would all be the clowns. -
PIEBALDconsult wrote:
There are 36 outcomes from rolling 2 standard dice, and only 8 of them are winners.
How did you get 8 winning combinations? If the first die already wins (in twqo out of six cases), the second one is irrelevant in any case. These already are twelve winning combinations. And then those cases where the first die 'misses', but the second one wins are added. Chance that the first one wins: 2/6. Chance that the first one mises, bt the second one wins: 4/6 * 2/6 = 8/36 (probably what you thought) Total chance 2/6 + 8/36 = 12/36 + 8 /36 = 20/36 = 0,56 (rounded).
PIEBALDconsult wrote:
There are 216 outcomes from rolling 3 standard dice, and only 7 of them are winners.
Similar calculation: Chance that the first one already wins: 1/6 Chance that the second one wins if the first fails: 5/6 * 1/6 = 5/36 Chance that the third one winds when the first two fail: 5/6 * 5/6 * 1/6 = 25/216 Adding it all up: 1/6 + 5/36 + 25/216 = (36 + 30 + 25) / 216 = 71/216 = 0,33 (rounded).
The language is JavaScript. that of Mordor, which I will not utter here
This is Javascript. If you put big wheels and a racing stripe on a golf cart, it's still a fucking golf cart.
"I don't know, extraterrestrial?" "You mean like from space?" "No, from Canada." If software development were a circus, we would all be the clowns.Yes, I already found and corrected my error.
CDP1802 wrote:
Chance that the first one mises, bt the second one wins: 4/6 * 2/6 = 8/36 (probably what you thought)
Nope.
CDP1802 wrote:
Adding it all up: 1/6 + 5/36 + 25/216 = (36 + 30 + 25) / 216 = 71/216 = 0,33 (rounded).
Recheck your math.
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PIEBALDconsult wrote:
There are 36 outcomes from rolling 2 standard dice, and only 8 of them are winners.
How did you get 8 winning combinations? If the first die already wins (in twqo out of six cases), the second one is irrelevant in any case. These already are twelve winning combinations. And then those cases where the first die 'misses', but the second one wins are added. Chance that the first one wins: 2/6. Chance that the first one mises, bt the second one wins: 4/6 * 2/6 = 8/36 (probably what you thought) Total chance 2/6 + 8/36 = 12/36 + 8 /36 = 20/36 = 0,56 (rounded).
PIEBALDconsult wrote:
There are 216 outcomes from rolling 3 standard dice, and only 7 of them are winners.
Similar calculation: Chance that the first one already wins: 1/6 Chance that the second one wins if the first fails: 5/6 * 1/6 = 5/36 Chance that the third one winds when the first two fail: 5/6 * 5/6 * 1/6 = 25/216 Adding it all up: 1/6 + 5/36 + 25/216 = (36 + 30 + 25) / 216 = 71/216 = 0,33 (rounded).
The language is JavaScript. that of Mordor, which I will not utter here
This is Javascript. If you put big wheels and a racing stripe on a golf cart, it's still a fucking golf cart.
"I don't know, extraterrestrial?" "You mean like from space?" "No, from Canada." If software development were a circus, we would all be the clowns.The easier way to calculate this imo is to calculate what loses then subtract that from 1. This way the second example is simply 1 - (5/6)^3 = 0.4213... ~ 42.1%. Also in the last step of the second example, (36 + 30 + 25)/216 = 91/216 ~ 42.1% not 71/216 ~ 33% :thumbsup:
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The easier way to calculate this imo is to calculate what loses then subtract that from 1. This way the second example is simply 1 - (5/6)^3 = 0.4213... ~ 42.1%. Also in the last step of the second example, (36 + 30 + 25)/216 = 91/216 ~ 42.1% not 71/216 ~ 33% :thumbsup:
Oooops. It was late. :-)
The language is JavaScript. that of Mordor, which I will not utter here
This is Javascript. If you put big wheels and a racing stripe on a golf cart, it's still a fucking golf cart.
"I don't know, extraterrestrial?" "You mean like from space?" "No, from Canada." If software development were a circus, we would all be the clowns.
