Imagine you're going to walk a ten mile distance. In every 1/10 of a mile mark there's a stack of gold coins in the ground. You know each stack has between 1 and 100 coins randomly. You can only see one stack at a time. Along the ten miles, you can only grab one stack with you, never turn back and never switch the stack once you have chosen one. You can only do this challenge once./Sci/entifically and mathematically speaking, what strategy should you use to secure the maximum amount of gold?
>>17032754Do you have a calculator with you or not?
>>17032754>randomlydefine how the stack value is determined
So, my original guess is that if you get a bag with 90+, you should just take that.In most iterations, there is a bag with 100 coins. Waiting for 100 and only 100 is good, but there is a chance you can end up with whatever is the last bag.What I've done is probabilistically calculate the chance that the bag you're on is the best bag. If it's better than 50/50, you keep the bag. In most cases, it's the best bag. It's mostly 100, and if it's not 100, then it's usually 97+. In very rare cases, you skip a 99 bag early when it's more likely to get a 100 bag, but then you keep a 97 bag when the 100 bag is rare, which there sometimes is or isn't. This method gives a few coins better result than picking the first 90 bag. You can check if it's worse than 100 only and sometimes getting last bag.
>>17032841Here is a nice sequence where there is no 100 bag and the statistical method gets a low last bag
>>17032841no dude. if the first stack is 99 and you take it, you'll most likely regret it.if there is only one stack left, you have no choice but to take it; the expected value is 50.5if there are two stacks left, you strategy would be, if the 2nd-to-last stack is 50 or lower, don't take it, take the chance of the last stack; otherwise take it. with this strategy the expected value of 2 stacks is 63.with 100 stacks in front of you, the expected value should be very close to 100.
>>17032935>if the first stack is 99 and you take it, you'll most likely regret itwhat? to put this in real terms, a 1oz gold coin goes for just over 4kso you're saying in this scenario you would give up 396,000 for a chance at 400,000?
step aside, nerds
>>17032935What? People who only read you must be very confused.
>>17032754Intuitively with 100 chances and a spread of 100 the chances of 100 are pretty good but only at the start. I believe the optimal strategy will be to set your acceptance limit that you adjust based on how many rolls you have left. Intuitively it probably should be something like "more than 50% chance of getting a better number than X in the future". With 100 pulls left the chance of a 100 is 63% so you probably only take the first pile if it's 100, the chance of 100 drops below 50% only at 68 rolls left so that would probably be the spot where you start going for 100 or 99, you continue that up to 34 at which point you swap to 100,99 or 98 and so on.If you don't swap your strategy then the highest expected value at the start is for picking 96 or above on sight but I don't think that's correct play overall.
>>17032754Probably has to do something with Euler's number so take the first stack that is higher than each of the first three stacks.
>>17033020Or rather take the first stack that is higher than each of the first 100/e % stacks that you see
>>17032754This is a good one gents, don't share solutions. Worth your time to solve and commit the concept to memory.Post 3 distance markers and stack size at each and whether you take or leave it and I will tell you if you are right or wrong. Also, distances and values you pick are more important than whether you take or leave btw. >>17032841>>17032848>>17032945Wrong>>17032954keep working at it.
You work your way backwards, starting with the tenth stack of coins. If you've reached the tenth stack and haven't selected yet, then you must. Your expected payout would be 50.5 coins at this point, and with that, you can work backwards. At the ninth stack, you should take if it has 51 or more coins. The expected utility here would be calculated by taking the average of what you're expected to get if you grab here or skip, which is going to be 51-100 (for grabbing) and 50.5 (for skipping). Average of 51-100 is 75.5, and if you average that with 50.5, and you get 63, which is the expected payout for playing at the ninth stack onwards. So, for the 8th stack, you should then grab at 64 or more coins. Continue this chain going all the way to the first stack, and you'll end up with the optimal strategy.
>>17033267it's a 10 mile walk with 100 stacks, not one mile and only 10 stacks, but the strategy still applies.
>>17033270ten miles? who's going to walk ten fucking miles? I'll take the first stack.
>>17032943Their greatest fear will be their gf will sell out for 396,001>>17033104Already ran off to murder-suicide? You can't come back to reply
>>17032943obviously (you) are not an average intelligent rational economic person, aka a jew.it's a fair point that people have different risk seeking/aversion profiles. but in this case, you are mistaken. you are not betting 396K for a 400K payout; you give up 396K in exchange of 99 more chances. and in the worst case you'll end up with $202K.
>>17033364since you niggers are so lazy, I'll do it. (using floating point so it may not be strict)1=50.50, 2=63.00, 3=70.03, 4=74.67, 5=78.01, 6=80.54, 7=82.53, 8=84.14, 9=85.48, 10=86.61, 11=87.57, 12=88.41, 13=89.14, 14=89.78, 15=90.36, 16=90.87, 17=91.33, 18=91.75, 19=92.14, 20=92.49, 21=92.81, 22=93.10, 23=93.38, 24=93.63, 25=93.86, 26=94.08, 27=94.29, 28=94.48, 29=94.66, 30=94.83, 31=94.99, 32=95.14, 33=95.29, 34=95.42, 35=95.55, 36=95.67, 37=95.79, 38=95.90, 39=96.01, 40=96.11, 41=96.20, 42=96.29, 43=96.38, 44=96.47, 45=96.55, 46=96.63, 47=96.70, 48=96.77, 49=96.84, 50=96.91, 51=96.97, 52=97.03, 53=97.09, 54=97.15, 55=97.20, 56=97.26, 57=97.31, 58=97.36, 59=97.41, 60=97.46, 61=97.50, 62=97.55, 63=97.59, 64=97.63, 65=97.68, 66=97.72, 67=97.75, 68=97.79, 69=97.83, 70=97.86, 71=97.90, 72=97.93, 73=97.96, 74=97.99, 75=98.02, 76=98.05, 77=98.08, 78=98.11, 79=98.14, 80=98.17, 81=98.19, 82=98.22, 83=98.24, 84=98.27, 85=98.29, 86=98.32, 87=98.34, 88=98.36, 89=98.39, 90=98.41, 91=98.43, 92=98.45, 93=98.47, 94=98.49, 95=98.51, 96=98.53, 97=98.55, 98=98.57, 99=98.59, 100=98.61, 101=98.63, 102=98.64, 103=98.66, 104=98.68, 105=98.69, 106=98.71, 107=98.73, 108=98.74, 109=98.76, 110=98.77, 111=98.79, 112=98.80, 113=98.81, 114=98.83, 115=98.84, 116=98.86, 117=98.87, 118=98.88, 119=98.89, 120=98.91, 121=98.92, 122=98.93, 123=98.94, 124=98.95, 125=98.96, 126=98.97, 127=98.98, 128=98.99, 129=99.00, 130=99.01,
