Knowing what is in one envelop changes the problem.
Let's see if there is a paradox. If you have a box in front of you and they show you the only other box contains $100 and tell you that your box has twice as much or half as much as the other do you keep the unknown amount or switch to the known $100 box? The math is still the same. You should still take the unknown amount.
Without knowing anything about what either box contains the same logic would have you endlessly switching to the other box as a better choice.
Lol I should have spoiled it. Two posts later and it was. It's an interesting problem and one more reason I wish I was better at probability math. I never did problems like this in high school, but then again the only math I took in high school was geometry my freshman year.
Sent from my SM-G955U using Tapatalk
i do not agree with the mathematical solutions.. neither box has ev of $125.. its either $50, $100, or $200, $125 is not a possible outcome. The math saying you should not switch is wrong as is the math saying you should switch is also. There is no advantage to switching.
the established facts are we know one box already opened has $100 and the other either has $50 or $200. and so the ev to switch or not switch is 0. and since we are card counters we dont typically risk money at 0% edge we should probably just keep the $100 and add it on top of our bet in a high count. on the other hand 100 bucks is not much money so most of us would switch anyway because we woukd hate not knowing what was in both boxes.
This paradox shows the danger of mathmaticians who proving themselves right with equations built around false assumptions.
Last edited by hypercube; 02-18-2018 at 05:49 PM.
LoL. Gram posed a different but similar situation. In the link they never revealed any information about what was in the box/envelop.
That created symmetry between the two choices creating a paradox. In Gram's query you knew what was in one box/envelop. That broke the symmetry that equated the two envelops and made switching the correct choice. He tricked those that were familiar wit the problem. I was thinking "S", the small bet wasn't the same so my logic was flawed but I didn't quite get it straight in my head until Miestro posted his thoughts that you should switch. When I read that for some reason it made me clear up what was bothering me and realize my mistake.
Bubbles, you got it right first.
neither box has ev of $125.. its either $50, $100, or $200, $125 is not a possible outcome.
Right, there are two possible outcomes. $50 and $200. The average of $50 + $200 is $125.
Look at it this way. If you switch, then you can either gain $100 or lose $50. Both of these results are equally likely. Since it is better to gain $100 than it is to lose $50 you should switch.
no this is wrong the ev of switching is $0 not +$25. and it is not better to gain $100 than lose $50 when you already have $100.
50% loss is exactly equal to 100% gain because if you lose that bet. now you need 100% gain yo get back to the origianl $100. ev to switch is 0, and the advantge in edge to switch is also zero. from that perspective of of a card counter we dont tend to like risking money without an edge so we should never switch.
Last edited by hypercube; 02-18-2018 at 06:02 PM.
Half the time you win $100. The other half of the time you lose $50. Assuming you won $100 one time and lost $50 the other time, which is what your long term expected result would be, you would have won $50 over two trials, or $25 per trial. The EV of switching is $25 or more specifically $125.
Last edited by Meistro123; 02-18-2018 at 06:03 PM.
sry i was still editing my post. here is my response.
it is not better to gain $100 than lose $50 when you already have $100.
50% loss is exactly equal to 100% gain because if you lose that bet, now you need 100% gain to get back to the original $100 and 400% instead of 100% to get to the $200 from the original $100 we had. The ev to switch is $0,not +$25 and the advantage in edge to switch is also exactly zero. $125 is not a possible outcome. From perspective of a card counter we dont tend to like risking money without an edge so we should never switch. but we all would anyway because its more fun and there zero positive or negative expectancy.
Bookmarks