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Ok, to get things straight first. I am not claiming to be the first one to ever think of this and actually a quick search on this very forum for "Monty Hall" reveals that it has been discussed here several times (allthough some of the results might be due to the map Monty Hall), but the last time was over a year ago. I do believe that there are many people here who really haven't thought about this before, so I figured it was time to pay good old Monty Hall another visit. If you're all tired of this thing coming up again, please feel free to delete the thread.
So here goes what I had actually planed to say. Consider this scenario, you are playing zerg and scouting with your overlord on a four-player map. After your tenth drone or so, you send out a drone just to make sure that you scout your opponent quickly. When the drone is halfway on his way to the enemy base, your overlord reaches his destination spawn location and reveals no enemy base. You now have the choice of continuing with your drone to the destination where it was headed, or you could switch and instead scout the other unknown location. Now most people (and in general common sense) tells us that it really doesn't matter since you have a 50/50 chance either way. This however is wrong. Statistically, it will always be beneficial to switch the drone scouting target! Basically this is due to the fact that initially, before knowing anything, you had a 1/3 chance of hitting your enemy with your scouting drone. This does not change after you have mis-scouted with your overlord. If you however switch scouting destination with your drone, you will have a 2/3 chance of hitting him.
Now I know that most people will simply reject this statement, claiming it to be false, but rest assured that it is a proved scientific fact. This is known as the Monty Hall problem, and more elaborate explinations on why it is true is given in the wikipedia-article.
And lets face it, as a zerg player this is a very common situation be in, but usage of this strategy is very rarely seen, even in high level play. You might see the exact propsed scenario in this game between IdrA v LzGamer where at 1:56 he really should have switched scouting target for his drone. Yes, I do know that in this particular case he happened to actually scout correctly, and you will in 1/3 of the times that you don't change target, but this is statistically not the optimal strategy.
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There are other considerations to take into account. For example, you'd want to scout the closest locations to you first in case of a possible cheese. This would be a much lesser concern if you spawned crossmap from your opponent due to the travel time.
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Yeah bro, your math is flawed. You do not get a higher chance of switching targets. When your overlord is in another main and its empty, you have a 50/50 chance of finding the guy with your scouting drone. I don't care what Mr Monty hall said, and will remain unconvinced until you actually explain it in a logical way.
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8751 Posts
I don't think your Overlord/Drone example is a true reconstruction of the Monty Hall problem. At least, the decisions of the Overlord and the game show host, as well as the decisions of the Drone and the contestant, are not analogous. It seems to me the disanalogy is significant but I'll just wait for a math/comp sci/stat person to weigh in...
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I think you have misunderstood the problem and the logic that resides within it.
There is no guarantee that the overlord will find them or not. If it was always so that the overlord would not scout him, then Monty Hall would apply. The basis of the Monty Hall thing is that the show host (Overlord) always will chose not to open a door (Scout a base) since he knows what is behind the curtain (fog of war). That makes it more likely for the other door of the two left to be the right one. This is due to the fact that you have two chained possibility things, not one and your odds therefore increase.
Whereas in SC2, the Overlord is no Godly being able to know where bases reside, so your statement is false.
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Isnt it the other way round? That when you send your Overlord you should switch it to another position when you scout with your Drone? Because its about the first choice (Overlord) being changed when you have better odds (Drone scouting empty position). But since Overlords are so slow anyway this is not useful at all.
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I'm familiar with the Monty Hall problem and I believe this is a misapplication of it, since you will never consider sending your drone to the same base as your overlord. In addition, part of the time your overlord will see the base.
edit: beaten, think of it this way:
It would be the Monty Hall problem if, say, your overlord was always sent to a wrong base, but you didn't know which base it was sent to until after your drone scout is on the way.
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This is a misinterpretation of the Monty Hall problem. Under your interpretation, if I understand it correctly, the Overlord would have to always reveal an incorrect base. Even then, I'm not sure if your example is strictly analogous.
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United States2822 Posts
On April 20 2010 03:35 FortuneSyn wrote:
Yeah bro, your math is flawed. You do not get a higher chance of switching targets. When your overlord is in another main and its empty, you have a 50/50 chance of finding the guy with your scouting drone. I don't care what Mr Monty hall said, and will remain unconvinced until you actually explain it in a logical way.
Then you are wrong and misinformed. Monty Hall is a famous problem and it takes nothing more than a Google search for you to find any number of proofs on it.
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flawed math FTL (misinterpretation of the Monty Hall problem)
always scout the closest bases to you first, and then look for cheese (if their base shows signs of it).
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I don't think Monty Hall applies here.
I'll try to explain why not, apologies if I don't succeed 
In the original MH problem, the game show hosts is guaranteed to open a non-winning door, thereby making the door left unopened "suspicious".
However, the overlord isn't guaranteed to find an empty base.
The zerg scouting problem would be equivalent to the game show host always opening the same door.
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On April 20 2010 03:26 Genesis128 wrote:Ok, to get things straight first. I am not claiming to be the first one to ever think of this and actually a quick search on this very forum for "Monty Hall" reveals that it has been discussed here several times (allthough some of the results might be due to the map Monty Hall), but the last time was over a year ago. I do believe that there are many people here who really haven't thought about this before, so I figured it was time to pay good old Monty Hall another visit. If you're all tired of this thing coming up again, please feel free to delete the thread. So here goes what I had actually planed to say. Consider this scenario, you are playing zerg and scouting with your overlord on a four-player map. After your tenth drone or so, you send out a drone just to make sure that you scout your opponent quickly. When the drone is halfway on his way to the enemy base, your overlord reaches his destination spawn location and reveals no enemy base. You now have the choice of continuing with your drone to the destination where it was headed, or you could switch and instead scout the other unknown location. Now most people (and in general common sense) tells us that it really doesn't matter since you have a 50/50 chance either way. This however is wrong. Statistically, it will always be beneficial to switch the drone scouting target! Basically this is due to the fact that initially, before knowing anything, you had a 1/3 chance of hitting your enemy with your scouting drone. This does not change after you have mis-scouted with your overlord. If you however switch scouting destination with your drone, you will have a 2/3 chance of hitting him. Now I know that most people will simply reject this statement, claiming it to be false, but rest assured that it is a proved scientific fact. This is known as the Monty Hall problem, and more elaborate explinations on why it is true is given in the wikipedia-article. And lets face it, as a zerg player this is a very common situation be in, but usage of this strategy is very rarely seen, even in high level play. You might see the exact propsed scenario in this game between IdrA v LzGamer where at 1:56 he really should have switched scouting target for his drone. Yes, I do know that in this particular case he happened to actually scout correctly, and you will in 1/3 of the times that you don't change target, but this is statistically not the optimal strategy.
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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This is not analogous to the Monty Hall problem because the host of the game show knows what's behind the doors and always picks a wrong one. Your Overlord, on the other hand, has no prior knowledge.
edit: Beaten to the punch ^^
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Well, this seems the same as Monty Hall problem.
The Drone has the same role as the player (right click on location 1 = select door 1).
The Overlord has the same role as the game show host (reveals empty location=opens empty door).
(empty door=door with goat behind it)
But there is one difference - the game host must open an empty door, but it isn't nessecery, that the overlord finds empty location.
Let's see another example.
We have 100 doors, not 3. And only 1 wins.
We choose a door and the host opens another 98 doors. So 2 doors are closed.
It's obvious, that the better choice is to switch the door. The probability is 50:50. But before it was 1/100. So the chance, the chosen door to be winning is 1/100.
In starcraft: Let's have 100 expansions (100 posible enemy locations) and 98 overlords
You send each overlord to every location, and later a drone to the 99th location.
The difference is, that the chance, that every overlord finds an empty place is very small (1/50)
But in this case, the chance, that the enemy is on each of 2 remainig locations is 50:50
I think, that IN THIS case switching will be better.
The difference with Monty Hall is, that THIS case will happen in 1/50 times.
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8751 Posts
On April 20 2010 03:38 scintilliaSD wrote:Show nested quote +On April 20 2010 03:35 FortuneSyn wrote:
Yeah bro, your math is flawed. You do not get a higher chance of switching targets. When your overlord is in another main and its empty, you have a 50/50 chance of finding the guy with your scouting drone. I don't care what Mr Monty hall said, and will remain unconvinced until you actually explain it in a logical way. Then you are wrong and misinformed. Monty Hall is a famous problem and it takes nothing more than a Google search for you to find any number of proofs on it.
He didn't say the Monty Hall problem has no merit to it. He just said the OP was mistaken.
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Untrue. The key difference here is that the overlord scout is random. What makes the MH problem so counter intuitive is that the host always picks a goat, as others have said.
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<edit> Wow a million people beat me to this.
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On April 20 2010 03:35 FortuneSyn wrote:
Yeah bro, your math is flawed. You do not get a higher chance of switching targets. When your overlord is in another main and its empty, you have a 50/50 chance of finding the guy with your scouting drone. I don't care what Mr Monty hall said, and will remain unconvinced until you actually explain it in a logical way.
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.
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Yea so the reason why the monty hall problem works is that the game show host HAS to show you a wrong choice.
so if you picked the right door, there are two wrong doors left and he can pick either one of them.
But if you picked the wrong door, he HAS to pick the other wrong door, leaving the right door left.
so the reason why the problem is somewhat misleading is that not everything is random, namely the game show host's door he shows you is not random.
so in the first scenario of picking the right door first(which happens 1/3 of the time) switching will make you lose and not switching will make you win.
in the second scenario of picking the wrong door first(which happens 2/3 of the time) switching will make you win and not switching will make you lose.
now as for how much that helps with the drone scouting scenario im not sure whether the same scenarios work. my intuition is that the probability does not work out the same way because the overlord is sent to a "door" or base before you make your drone decision. that means when you make your drone decision you are only really picking between two "doors", namely those that were not scouted by the ovie.
then again i might be completely wrong(not about the monty hall problem, about the drone ovie scenario)
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While this indeed seems to be a flawed analogy I still appreciate it. Applying fairly abstract maths to something practical always is nice and even realizing that drone scouting is at least similar to the Monty Hall problem is not something everyone would do.
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EPT
