EPTEfficient drone scouting and probability theory - Page 2
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yB.TeH
Germany419 Posts
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m3rciless
United States1476 Posts
On April 20 2010 03:48 Koltz wrote: lol unless youre a stats major and have created an entire thesis disproving the monty hall problem, i'd say you need to do some more research. But im going to bet that you arent a stat major, to which i say, the reason why the monty hall problem is famous is because it is so hard for people to understand, and is counter intuitive. Math > logic. Look at gabriel's horn (an object with finite volume and infinite surface area), or consider the worm on the rubber band (an application of the harmonic series divergence). Nonetheless, this isnt an application of the monty hall problem, there is no 'game show host' Either way, sometimes its more beneficial to make sure theyre not close positions with you. Consider this; 12 hatch in ZvT, and the opponent is bunker rushing. It is more beneficial to find this out if they are close positions, because even if you scout both close positions and do not find anything, you still have a better chance of defending the bunker rush overall. LOL NINJA EDIT. This post used to say that MH did have application on maps like gaia, and now it says the opposite. Classy, i must say. | ||
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ComradeDover
Bulgaria758 Posts
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Genesis128
Norway103 Posts
So this needs some tweakin then. However I actually do believe that this does not really falsify my claim. If you initially scout right with your overlord, then you just retreat your scout since you've already succesfully scouted. If you mis-scout then you are in the MH-case since the overlord obviously didn't scout right. Basically this means that you are only forced to make the decision of continuing/switching in the case where the overlord indeed does not hit right, giving the overlord the power of the game host in the MH-problem Now I realize that this is the MH-problem with a twist, so I can no longer link the proof to an article, but do believe that it actually still will hold. | ||
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zomgzergrush
United States923 Posts
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Oracle
Canada411 Posts
On April 20 2010 03:51 m3rciless wrote: LOL NINJA EDIT. This post used to say that MH did have application on maps like gaia, and now it says the opposite. Classy, i must say. it has applications, i just didn't wanna get into an argument about it :p i realized it would be a mistake to bring mathematical analysis here | ||
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EverDawn
Sweden91 Posts
In the original problem the game host removes a "miss" door, because he knows which door is correct, but in the perspective of scouting, the overlord is also sent at random, so I'm not sure if this act in the same way as in the Monty Hall problem by having none random elimination of one of the options? Probably it's the same thing and the Monty Hall problem ablies, but i just wanted a clarification  And of course, for this to be interesting at all the scouting locations have to be equal in distance and tactical value, right? And sorry, I'm not that good at English and it really shows when I'm supposed to to discuss something a little more complicated  ---------- Edit: Wow, I'm a slow typer Never mind. *reading thread instead* | ||
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Grend
1600 Posts
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Orpheos
United States1663 Posts
On April 20 2010 03:52 Genesis128 wrote: OK, after some thinking, then yes (most of you) are right. The Monthy Hall analogy does not completely hold since the initial overlord-scouting it random and will not always miss the enemy base as is required by the MH-problem. So this needs some tweakin then. However I actually do believe that this does not really falsify my claim. If you initially scout right with your overlord, then you just retreat your scout since you've already succesfully scouted. If you mis-scout then you are in the MH-case since the overlord obviously didn't scout right. Basically this means that you are only forced to make the decision of continuing/switching in the case where the overlord indeed does not hit right, giving the overlord the power of the game host in the MH-problem Now I realize that this is the MH-problem with a twist, so I can no longer link the proof to an article, but do believe that it actually still will hold. actually ilnp made a post that disproves this Cute effort, but as the result of whether the overlord finds a base or not is indeed random (that is, sometimes the overlord would find a base), the monty hall problem does not apply in this case. You can find verification of this in allknowing wikipedia, here: This difference can be demonstrated by contrasting the original problem with a variation that appeared in vos Savant's column in November 2006. In this version, Monty Hall forgets which door hides the car. He opens one of the doors at random and is relieved when a goat is revealed. Asked whether the contestant should switch, vos Savant correctly replied, "If the host is clueless, it makes no difference whether you stay or switch. If he knows, switch" (vos Savant, 2006). | ||
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crate
United States2474 Posts
You choose randomly where to send your overlord, then choose randomly where to send your drone (these are not actually the case, but they work out). 1/6 of the time you send your overlord left and your drone right 1/6 of the time you send your overlord left and your drone bottom etc. I'll call the six cases LR, LB, etc. with the overlord position first. All six are equally likely. Let's assume you pick L for your overlord. 1/3 your opponent is at L; LR and LB both send your drone to the wrong place. 1/3 your opponent is at R; LB is wrong but LR is correct. 1/3 your opponent is at B; LR is wrong but LB is correct. These are all equally likely. For Monty Hall: You choose a door. Let's say you choose L. There is a correct door, chosen at random from LRC. 1/3 the correct choice is L. 1/6 the host opens C, 1/6 the host opens R. 1/3 the correct choice is C. 1/3 the host opens R. 1/3 the correct choice is R. 1/3 the host opens C. As you can see, there are only four possibilities instead of the six we have in the scouting problem, so the analogy fails. | ||
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Punk
United States35 Posts
On April 20 2010 03:52 Genesis128 wrote: So this needs some tweakin then. However I actually do believe that this does not really falsify my claim. If you initially scout right with your overlord, then you just retreat your scout since you've already succesfully scouted. If you mis-scout then you are in the MH-case since the overlord obviously didn't scout right. Basically this means that you are only forced to make the decision of continuing/switching in the case where the overlord indeed does not hit right, giving the overlord the power of the game host in the MH-problem Now I realize that this is the MH-problem with a twist, so I can no longer link the proof to an article, but do believe that it actually still will hold. Still doesn't work, and isn't the MH-case. | ||
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ComradeDover
Bulgaria758 Posts
On April 20 2010 03:52 Genesis128 wrote: OK, after some thinking, then yes (most of you) are right. The Monthy Hall analogy does not completely hold since the initial overlord-scouting it random and will not always miss the enemy base as is required by the MH-problem. So this needs some tweakin then. However I actually do believe that this does not really falsify my claim. If you initially scout right with your overlord, then you just retreat your scout since you've already succesfully scouted. If you mis-scout then you are in the MH-case since the overlord obviously didn't scout right. Basically this means that you are only forced to make the decision of continuing/switching in the case where the overlord indeed does not hit right, giving the overlord the power of the game host in the MH-problem Now I realize that this is the MH-problem with a twist, so I can no longer link the proof to an article, but do believe that it actually still will hold. No. It does fully falsify your claim. In order for Monty Hall to work, you need to not be informed if you've made the right choice or not until after you've made the decision to switch paths or not. Because you instantly know the if the base you've scouted with your overlord is right or not, there's no tension with the information. Furthermore, if you're sending out the drone before your overlord arrives, you have a 2/3 shot of being right with one of them anyway. To address your title and not the OP, the most efficient drone/overlord scouting is to send the overlord to the "close" position (Verticals on Kulas Ravine, northwest/southest on LT) and a drone to either of the "far" positions, and if both are wrong sending whichever is closer (depending on the map) to the last remaining spot. | ||
Carnivorous Sheep
Baa?21246 Posts
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segfix
United States32 Posts
This difference can be demonstrated by contrasting the original problem with a variation that appeared in vos Savant's column in November 2006. In this version, Monty Hall forgets which door hides the car. He opens one of the doors at random and is relieved when a goat is revealed. Asked whether the contestant should switch, vos Savant correctly replied, "If the host is clueless, it makes no difference whether you stay or switch. If he knows, switch" (vos Savant, 2006). This needs to be requoted for emphasis. | ||
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Drunken.Jedi
Germany446 Posts
Just imagine what the consequence would be if switching actually increased your chances of finding your opponent: if that were the case, then it would be advantageous to just switch to the other position right away as this would increase your chances if you find nothing with your overlord and wouldn't matter at all if you did actually find your opponent. However, using that same logic you could justify switching back to your original scouting plan, and so on, ad infinitum. Edit: wow, I really should learn to post faster^^ | ||
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Assault_1
Canada1950 Posts
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yB.TeH
Germany419 Posts
zerg scouting problem: you know 1 is revealed anyway (overlord) so you have only 2 locations your initial chance to scout correct with the drone in a true monty hall scenario would be 1/3, and increase to 1/2 because 1 of your options just disappeared.. in the scouting problem the option that disappeared didnt exist to begin with | ||
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Orpheos
United States1663 Posts
On April 20 2010 03:58 Carnivorous Sheep wrote: While faulty, I still appreciate the thought that went into this thread, cheers. this. i totally dig the monty hall problem. especially because it took me awhile to understand it(probably because the people who explained it to me didnt understand it themselves or were just bad at explaining) i love these counterintuitive things. like .9 repeating is the same as 1 | ||
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zomgzergrush
United States923 Posts
At the point your overlord reaches its first base, you can still use the monte python analogy, but you also need to factor in expected distance to travel to enemy base. Assume base A is the base your drone was originally going for. "don't change paths" E(distance to travel before scouting enemy) = [P(enemy = base A) x distance left to A] + [P(enemy = base B) x (distance left to A + distance from A to B)] "change paths" E(distance to travel before scouting enemy) = [P(enemy = base B) x distance to change paths from current drone scout position to base B] + [P(enemy = base A) x (distance to change paths from current drone scout position to base B + distance from B to A)] This would all come down to when you actually sent your drone scout out. You can, however, still plug in monte python values in for the probabilities. | ||
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goswser
United States3548 Posts
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