Probability Lesson 3: The Monty Hall Problem

The Monty Hall Problem.

Game show, there are three doors, a new car behind one, and nothing behind the other two.

You pick one door. They reveal one door that didn't have a prize, you then have the option to switch doors before a potential prize is revealed behind the door of your choice.

Does your probability stay the same if you switch?

my first thought is no, as you chose from a 1/3 chance, and they just showed you that one of your passed-on choices happens to not have the car. that doesn't mean the odds are any different, just that you may have chosen correctly cause the car wasn't that other door they opened.

Absolutely not.

1st choice -- you have 2/3 chance to be wrong, 1/3 chance to be right

if you choose at random you are now sitting at 1-2 odds. When the bad door is revealed, you are still sitting at the fact that you only had at a 1 third chance of having been right. Assuming that you were wrong in your initial choice (66.7% chance) than you should switch. Since there is still that 66.7% chance that the Prize Door is the unrevealed one you didnt choose and only a 33.3% chance its the one you did choose.



Now I have a probability question for you. If you roll 1,000,000 dice all in one go and chart the results, how far do you think you will be from each column having 166,667 results?

Yes, it does increase if you change your choice.

gluvzer wrote:Yes, it does increase if you change your choice.

Ryan's the big winner. If you switch your choice, you have a 66% chance of winning the game, instead of a 33% chance.

canadin wrote:
Now I have a probability question for you. If you roll 1,000,000 dice all in one go and chart the results, how far do you think you will be from each column having 166,667 results?

The probability would be very low that it would stray too far from 1/6th in each.

Of course, with numbers so high, you'd be testing the natural variability of the dice, whether or not the dice in question "roll true".

To make the math easier, Adam, you could calculate the probability based on 30 die rolls, and you wouldn't even need to roll them "all in one go". The rules of your question preclude the dice rolls being independent, as you are interested in the collection of rolls, and not one individual, isolated event. (30 is the "magic number" in statistics where the law of large numbers is applicable)

Maybe I'm Luckier than you?

canadin wrote:Maybe I'm Luckier than you?

Confirmation bias. Calculate the standard deviation of the average total of 105 on a 30 dice roll. It's a pretty bell curve :-)

https://www.youtube.com/watch?v=mhlc7peGlGg

Explained via Youtube.

BUT I live based off of Confirmation biases.

If Plan A works, then Plan A harder;
If Plan A didn't work, then you didn't Plan A hard enough.

I accidentally my plan A, the whole thing. Should I be worried?

I fuxed up my math above too, LOL. Irony win.? 66% chance of winning if you switch, because it's not a new game, and still linked to the previous result.

The moral of the story though, is dice rolls are not linked. Not ever.

If you fail 5/5 3+ saves, the chance of you failing the next 3+ save is still 33%. (Well... ~34.1% because we roll on rounded GW dice! *laughs*)

If it helps; I do absolutely agree with your point that each independant dice roll has the equal chance to roll good or bad. And every set of dice rolls have equal chance to be good or sucky.

My initial argument of rolling more dice gives you better rolls is probably better said like this: Given that many of the units in Codex:CSM are rather cheap for the number of dice they let you roll, if one has a list where he gets to roll more dice than his opponent than he has more chances to get lucky vs that opponent.

And if it helps, I have been trolling you since you had an initial adverse reaction to my initial statement in regards to the luck of the dice. But if you like this game I can continue to come up with silly answers to your probability questions.

Oh I know :-)

The more dice you roll, the better chance that you'll have a good (or bad) effect. This is why I like Shoota Boyz in an Ork list.

When you take 38+6 shots (28 boyz with shootas, two with big shootas), you have a high probability of getting 1/3rd hit. You'd expect ~13S4 hits and ~2S5 hits.

However, there's a chance, whenever you roll those 44 dice, that you can do much better or much worse.

If you're playing Space Marines and shooting bolters, a lascannon, and a meltagun, you get 8+1+1 shots. The best you can do is 8S4 hits, 1S9 hit, and 1S8 hit. The probability of you getting 13S4 hits is 0 (unless you`re within 12``)

I understand your point of view, but applying it to multiple die rolls over the course of a game isn`t correct. The chance of your autocannons preforming better on turn two does not increase because they performed poorly on turn one.

The chance of my particle whip destroying wave serpents in subsequent turns is very low. But, after I`ve done it once, it reverts back to it`s one-of nature.

Every die roll is an independent event. However, every collection of die rolls to yield a wanted result isn`t. P(two destroyed waveserpents) is lower than P(one destroyed wave serpent). Because both the events are independent, after the first success, the second has the same chance as the first.

If you do your leadership rolls one die at a time, the chance you`ll roll 12 after rolling a 6 is a 6th. Always taken together, it is a 36th.

Huzzah :-)

canadin wrote: Given that many of the units in Codex:CSM are rather cheap for the number of dice they let you roll, if one has a list where he gets to roll more dice than his opponent than he has more chances to get lucky vs that opponent.

Wow, really? This is a whole other kettle of fish. What are these "cheap" units to which you're referring?

Khorne Daemon Prince with wings 140 points

Combi-Weapons on Tanks 10 points

but #1 is a basic Marine Marked to Khorne. 18 points a model, has a bolter, charges for 4 attacks.

How does a combi-weapon on a rhino let you "roll lots of dice for the points"? Khorne marked marines are overcosted and crappy. All daemon princes are good, but the Khorne one is the second-worst of the 4.

Actually the Khorne DP is the worst...no psychic powers (i.e. no lash, warptime or bolt), nothing that makes him better then the others (no toughness boost, ward save boost, etc...).

I guess we should be thankful that Canadin uses inferior choices, that way we all still have a chance!

Yeah, the Tzeench and Khorne ones would be about the same in my books. Although against certain lists the Tzeench one might be slightly better. I bet he takes them just so we do have a chance! He's a magnaminous sort of fellow.

Khorne is CHEAP aaand More atacks FTW. A top tier enemy list will most likely have great ability to both deter psychic powers as well as remove your daemon princes rather quickly. So paying less for just a khorne prince which is almost as good as the other ones saves my ass when he gets gunned down (vs Tau or Guard or Eldar or DE); big time. And when Shadow of the Warp, or Phychic Hood, or Runes of Warding are on the feild, all those phychic powers feel kinda silly.

Also I like Khorne more than Nurgle.

Also, for the combi's. I never used them in the past, but its effectively a super-sneak attack since few expect Rhinos to have anti-tank/anti-Monster/anti-character sshooting capability without s squad inside.

And for troops, +1 attack lets them win combat which in my mind is extremely important for not losing a squad to one's enemies's assault troops.

canadin wrote:

Also, for the combi's. I never used them in the past, but its effectively a super-sneak attack since few expect Rhinos to have anti-tank/anti-Monster/anti-character sshooting capability without s squad inside.

And for troops, +1 attack lets them win combat which in my mind is extremely important for not losing a squad to one's enemies's assault troops.

They are super-sneak attack if they're not modelled on your vehicles. Otherwise they are not.

A 30 point upgrade that makes your troops no more resilient to shooting is fail. When can marines ever assault out of a rhino? You assume your daemon princes will get shot to death so you keep them cheap but assume your marines will not get shot to death so you make them expensive? Your arguments make little sense.

Hehe, nothing gets by you Tim.

I think a Truthier answer would just be that I like the fluff around the Khorne Cult, but wuld like to at least have a beleif that is somewhat ignorent of gamestate to appease the tactical part of my brain. Nurgle would probabley be a better choice than Khorne game wise, but I've always loved the Angry Blood cult that yells KILL MAIM BURN!!!