I dont get it. Why the hell would the outcome of one coin affect the other? If you had a hundred pistols in front of you and were told that at least 99 are empty and the last one can be either full or empty with 50% probability, and you were told to to play russian roulette with each, what is the chance that you walk out alive? It all obviously depends on the one uncertain gun.
@hollamonm Says:
I HATE the fact that I knew that the answer doesn't change regardless of the situation, but that when and how you specify does change the sample size that you're dealing with and that the
'probably' in this case is, I don't know if it's an actual term but I'd say depending on the way you specify things and present it the "objectivity" changes to where you only need to consider the worlds that meet those parameters and to loop this back around to the "idk if the actual term" I'd call it 'subjective' probability with the variables and constants...
And it's this subjectivity that REALLY makes me hate probability in general. Like, if I could kill a thing in Math (and I've taken through calculus for fun), I'd kill probabilities 100% of the time. To eliminate the possibility of probability ever existing as a concept we need to account for, it would be either "it will" or "it won't" just because it is a blight on Math and a pox upon the subject as a whole. Yes, I do feel that strongly about probability. However, it helps me in video games where I'd survive shit that I have no right surviving in a JRPG, so I guess I'll not try and find a genie to give me the power to wipe out all probability on the conceptual level of the universe.
@ililililili5968 Says:
This seems rather like a distinguishability problem: once the lights are turned off, the coins become impossible to tell apart, and HT and TH stop being two distinct outcomes (to be precise, writing HT and TH separately will no longer make any sense at all). The way out is to realise that the indistinguishability is temporary: the coins *will* eventually be distinguishable again as the lights are turned back on, so it should be possible to prove the whole thing a pseudo-paradox by treating left-hand reveals and right-hand reveals separately.
To me, this problem is a tame version of Gibbs' Paradox where everything is still nice and reconcilable because coins are macroscopic objects that are hardly ever indistinguishable.
@artyruch7028 Says:
Whem you reveal that one coin is tails (without the positioning just one one of the two coins you are holding is tails) probability already drops to 50/50 as it does not matter which one there are now 2 posibilities where you have 2 coins as tails and 2 where one heads other tails. Yiu have two hands and other coin can be in one of two positions
@OskiRedd Says:
To avoid ambiguity, I like to specify the difference between probability and chance. Probability never changes, but chance changes depending on constraints or revealed information.
@markusbrunolsen6461 Says:
I originally thought of propability purely outcome based, but it seems that when modelling propabilistic systems one must consider the entire chain of events as a part of the space.
@giacatnguyen9635 Says:
Quibble with the 1/6 probability for each choice of tails: why is this the case?
Assuming a coin flip is tails 1/2 of the time is fair because we usually specify that it's a fair coin, but I don't see any mathematical reason for each hand choice to have equal probability, and in practical terms, I'm not sure how you'd even manage that short of secretly flipping a coin. Maybe the probability of picking my right hand given that both coins are tails is greater than 50%.
Anyway, this goes to show why a basic probability book needs to be careful with how toy examples are phrased, since if you aren't careful you introduce a second random variable and you have to deal with the joint probability. That second variable, of course, is the speaker revealing information about the first variable.
Suppose in the cases with both coins tails that I choose my right hand 2/3 of the time and my left hand 1/3 of the time. Then if I say the coin in my right hand is tails, the new probabilities are (1/3)/((2/3)*(1/3) + (1/3)) = (1/3)/(5/9) = 3/5 and (2/3)*(1/3) /((2/3)*(1/3) + (1/3)) = 2/5. So in that case saying right hand is tails means the other one is tails 2/5 of the time!
More generally, P(TT) = (1/3) *P(R)/ ((1/3)*(1 + P(R))) = P(R)/(1 + P(R)) where P(R) is the probability that I choose my right hand in the double tails case.
So you can see that P(TT) is a function of P(R) with range [0,1/2].
Edit: OOH, and for more fun, we could include the probability that you're lying and the probability of how you'd like (or tell the truth) given each outcome of the coin flips. I'll bet Raymond Smullyan (one of my heroes!) could write a fun book about that.
Edit 2: Now all the comments are talking about Monty Hall, so I'm thinking of strategies Monty Hall could use to trick contestants into losing, and now THAT is making me think of those iterated rock/paper/scissors algorithm contests and Iocaine Powder, and I guess I'm not going to get any work done tonight, am I?
@Hollow_light Says:
you way over complicated this
@buckcherry2564 Says:
is the question after revealing one tails just "what are the odds of the unknown coin being tails"? The revealed one could be a ham sandwich, it wouldnt impact probability at all.
"Dont believe everything you see on the internet" Quoye atributed to Euclid
@ronnieripz Says:
Is this the Scott Steiner promo
@sashangovender5327 Says:
This is good. Proablities always confused my. But this video emphasizes the fact that to make sense of probabilities comes down to understanding the sample space. Enumerating the possible outcomes is a good way to do this.
@GoldenBeans Says:
now explain it to a sonic fan
@FastGunner2040 Says:
Weird seeing this guy be serious.
@001variation Says:
If you mute the video it looks like he's challenging you to box him 😂
@hello_there3718 Says:
"This one's tails"
What are we missing.
You're missing that I lied about this one being tails.
[Oh, I was right.]
@ibtastico Says:
is it weird that I completely understand monty hall but i just cannot understand this 💀
@Eagle_Punch Says:
He always sounds as if he is making a joke. No matter what he says, he always sounds like it´s sarcasm or a joke.
@ultrazombieYT Says:
What is worse is when you realize that whatever will happen always had a 100% chance of happening once it happened, and anything that does not happen always had a 0% chance of happening.
@isaacdebord7812 Says:
There is a higher chance at getting tails then heads due to weight
@samsibbens8164 Says:
This is counter-intuitive to the point of being headache inducing xD
@book19118 Says:
Make a video on DFT and FFT
@brianthesnail3815 Says:
This happens because you are categorizing options that have two characteristics. The first characteristic is 'Tails' the other is 'Which Hand'.
@SciFiFactory Says:
I ... don't like statistics ...
@v.prestorpnrcrtlcrt2096 Says:
Thanks for yelling
@Dabislav Says:
I think that coin thingy is misleading. Because with cards, suit and value are important, and if you revile suit and value, percentage will change. But with coins, the only thing that is important is value (beeing heads or tails). When adding left or right hand in a mix, we are adding something that is not important. It is just "the other hand". There will always be 50-50 chances that in "the other hand" is another tail. The only time that percentage will change is if you need to name the starting hand with a tail...at least that is my logic 😁
@Griede26 Says:
perspective.
@julietschwab5876 Says:
his ad placement is always genius but this might be my favorite
@Not_Zebby Says:
my head hurts and i havent even started the vidio yet
@ArwenAreYouOK Says:
You didn’t reveal anything the time the screen went to black. We just heard words. In the first ‘actual’ reveal you reduced the combos, but not the blank screen reveal
@boodiabed6414 Says:
not nice ad segway
@gJonii Says:
Probability for both being tails could be 0%, 100%, or anything inbetween, given you say "one of them is tails".
Usually with these, there is implicit or explicit procedure for reveal. Like, scenario A) I ask you "was either of them tails?", you check the coins, and answer truthfully "yes", the probability both are tails is 33%.
Scenario B) You throw two coins again, and then check one, and only one, result, remarking "huh, it came up tails". Probability of two tails, 50%
Scenario C) You decided to flip coins. After checking both, you say "I got one tails", because you got inspired by a a Youtube video. But the trick is, you checked that you did get one, and only one, tails. If there were two, or zero, you wouldn't have said anything. Propability of two tails, given your remark, 0%.
Scenario D), 100%, is left as an exercise for the reader.
@matthewpublikum3114 Says:
At 4:30 why does he write another set of ht,th,tt?
@KaiSong-vv7wh Says:
I just treated myself to some fun: I asked an AI to decide by finite toss of coin to decide equally between three doors. It alternated between the prohibited solutions of favoring odds of either door or retossing. It failed to acknowledge that now power of 2 is divisible by 3. Who would claim that AI is not trivially failing the Turing test?
@KaiSong-vv7wh Says:
Haven't watched any of the vids, but successfully identify this as a "w.l.o.g." principle: I will just assume *without loss of generality* that the designated coin is in your left hand. In conclusion, the probability of the other coin being heads or tails is 50%. Likewise, for the Monty-Hall the wlog is that I always initially choose door 1 and hence never take it in the end because I switch.
@mahinshahrier7022 Says:
Zach, you should know better than this. Many statements are in illogical order, and you should definitely specify that, in the scenario presented at the very beggining, that a hand chosen as tails was done randomly. It may be implicit but because of how you decided to explain things later on, it actually isn’t so clear.
@cj82-h1y Says:
The reveal was dependent upon the knowledge of the states of the coins. If you had no idea about the right hand, then observed the left hand, and said "the left hand is tails", then the probability is 50/50... but you knew both, and the knowledge of the states of the coins influenced your reveal. The fact is, that although it seems as though you revealed additional information, you didn't: There is no situation where you don't reveal the tails, so therefore there's no change to your sample space. So treat it as 1/3.
If on the other hand, you said "one of them is tails" but you had no idea which, then you looked at the left hand, and revealed "the left hand is tails" - then, this IS adding more information, since there was a possibility that the left wasn't tails before you revealed it. - Since there is a situation where the reveal didn't result in tails, there is additional information being added by knowing that it is: Additional information then means a change in probability.
@refeying2698 Says:
When you showed the black screen when" revealing" a tails, i just got pissed. I knew immediatly what was going on and I didnt like it
@grahamjackson846 Says:
This is utter bollocks. If you state that one coin is tails, then the odds of TT are 50/50, NOT 1 in 3.
@philliberatore4265 Says:
If I understand correctly, the statement is "I have two coins, one is T. What is the probability the other is T". The answer is always 50%. HT and TH is the same outcome case in this problem.
Furthermore, revealing the T coin doesn't impart any additional information on the second. You still have either TH/TH or TT.
This is the reason roulette wheels always list the previous outcomes: to make people overthink the game trying to get an edge.
@gregaldr Says:
I didn't think you understand it yourself. There are two ways to play this game. In one case, that two coins are considered equivalent (interchangeable) which means for example that TH=HT and the are exactly 3 possible outcomes. However, another way to play this is to add the notion of position such that TH != HT. I'm this case, there are exactly 4 possible outcomes. For the game to make any sense, this must be clearly articulated at the beginning. There is no paradox as you are simply not specifying the equivalence (or non-equivalence) of the coins) up front and then conflating the two cases to present the APPEARANCE of a paradox where none exists. Perhaps this was intentional but if so the results are meaningless and the game uninteresting.
@LuigiGamingLounge Says:
I wrote a comment on your last video (the one about the three obvious questions that actually aren't) I wrote a lot about this last question, and how saying that the probability changes when one is revealed from when you just knew that one of them was tails had some faulty reasoning. Then I was recommended this video (which was made 2 weeks ago at the time) and I watched through this video and was glad to see your clarification of how the "probability" in a mathematical sense changes, but in in a "probability" sense. As strange as that sounds, thank you for making this follow-up video. Very good work, brother!
@jeremyashford2145 Says:
So far so good, then blahblahblahblahblahblahblah...
@Thori45 Says:
Seems to be connected to the Goat Problem just the otherway around...
@TheJDanley Says:
The odds do change.
The original situation is that at least 1 hand contains tails. Since the second hand could also be tails we have a third possible outcome so the odds of any hand being tails is 2/3.
The situation where we know which hand has the tails is the situation where we have already resolved the first situation. It has always been fifty-fifty that the coin opposite the one we know is tails would be tails.
It is two seperate probabilities involving two seperate coins.
Additionally probabilities are tied to perspective. If I close my eyes while you reveal something then it has not been revealed to me and the revelation does not change my calculation.
@Airsoftdude1100 Says:
This can be easily explained by probability theory , using filtrations and sigma algebra
@CutleryChips Says:
2min and I know he doesn’t even have coins in his hands. See how tightly closed it is
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