It's like saying "Let's play rock, paper, scissors. You go first."

@kentoutcourt

4 жыл бұрын

I'm pretty sure that would be 100% "probabilty" of winning, though

@Triantalex

8 ай бұрын

false.

This is going on my playlist of "Cool and useful things that I will never use"

@novagate19

7 жыл бұрын

how is it useful if you never use it?

@salmjak

7 жыл бұрын

+NovaGate For instance it can be very useful if you want to scam somebody, but you wouldn't use it due to the moral and legal aspects of said scam.

@Dima-ht4rb

7 жыл бұрын

I dont find it cool neither useful, too many stuff to do and to clanky to play, doesn't even looks like a game.

@Dima-ht4rb

7 жыл бұрын

+NovaGate box with screwdrivers for each type of screw is useful, even if you would never use it.

@IanWorris

7 жыл бұрын

This actually is quite useful to teach probability first, also it might be used in other ways once you start generalizing the Head/Tails as an arbitrary binary sequence and compare likelyhoods of different sequences to appear, another way it's useful is because many of these sequence actually have, in a vacuum, the same likelyhood to appear, and yet that changes when you see how more likely one is to appear before a certain other.

"It's like one of those situations where you have a baker called Mr. Baker, or a mathmetician called Dr. Sexy"

This is the *perfect* game for teachers to play with students to introduce them to ideas like probability and sequences.

@007RAJKOify

7 жыл бұрын

I hate those classes.

@AKhoja

7 жыл бұрын

? What does BLM have to do with anything?

@ilidenstrmrege987

7 жыл бұрын

my school is too poor to afford a coin, so forget that

@remivannier9931

7 жыл бұрын

Personnally, I like to use "Grime's dice" for my teaching (you'll find them in Numberphile)

@Woodside235

7 жыл бұрын

@ChainReaction! What, is mathematics racist (for some convoluted reason) as well?

"a mathematician called Dr. Sexy" that killed me XD

@GreRe9

7 жыл бұрын

+

@dariusduesentrieb

7 жыл бұрын

+

@billywhizz09

7 жыл бұрын

+

@guiltyapollyon8085

7 жыл бұрын

-

@dariusduesentrieb

7 жыл бұрын

TheWaves_ | |

This video makes me feel like I'm getting scammed somewhere in my life in some way, and I don't even know it.

@psytaatysp2564

7 жыл бұрын

you probably are

@galesx95

7 жыл бұрын

+Psyta atysP hahaha totally

@noredine

7 жыл бұрын

Banks would know about them

@MrMayur1210

7 жыл бұрын

Most probably in everything related to gambling.

@MrZeyami

7 жыл бұрын

Welcome to probability and statistics

Cool game! I did an experiment with a computer program to see how this extends to sequences of length 4 and the result is pretty interesting. The same pattern holds for the last three bits of the second player's sequence: you just copy the first three of the first sequence (e.g first player picks HTTT then second player has to pick XHTT). For the first bit of the second sequence, you need to flip the third bit from the first sequence unless the first three bits are alternating (like HTH or THT) then it's the fourth one flipped. (e.g HTTT -> HHTT and HTHH -> THTH)

lesson learned, don't take a mathematician's wager

@Simpson17866

7 жыл бұрын

You're sure about that ;)

@dan_tr4pd00r

7 жыл бұрын

[insert comment about Pascal's wager]

@4myzelf

7 жыл бұрын

Hi Ho Wolverhampton he's a great mathematician, that wager on the other hand is flawed as it makes some bold, unsupported assumptions and fails to consider other variables

@Cythil

7 жыл бұрын

Also how you make sure to win against a mathematician. One use there assumptions about probability against them... and rig the game. One have to think out of the box to win.

It's because the "winning" sequence contains the beginning of the "losing" sequence

@eliakimrodrigues

3 жыл бұрын

Hey he could have explained that

@zeldajerk

3 жыл бұрын

@@eliakimrodrigues I totally agree. It makes sense now.

that last sentence. LOL

Interesting. Just like Grime's dice, there's no best choice, but unlike the dice, there are worst choices. I didn't expect so asymmetric a network to come up so naturally!

@pablogriswold421

7 жыл бұрын

THH and HTT are better than most if you are forced to go first.

@okuno54

7 жыл бұрын

By "best" is meant a choice such that your opponent (who chooses second) cannot select a move which has better than even odds of winning.

@Fematika

7 жыл бұрын

You should a space between "a" and "symmetric" because right now it means the exact opposite of what you intended.

@okuno54

7 жыл бұрын

Fematika Actually, I did intend to say asymmetric. Yes, there are symmetries, but it's far less symmetric than e.g. rock-paper-scissors. In fact, with that space it would just be ungrammatical.

@pablogriswold421

7 жыл бұрын

+Rackergen Huh, just wondering how you got that. HTH on the diagram at least doesn't beat anything. What unshown matchups does it win and why?

"TRY IT OUT ON YOUR ENEMIES, SO YOU CAN BEAT THEM"!! omg i'm dying XD

I'd make a joke about it being called Penney's game, but it probably wouldn't make any cents

@johnkent2754

6 жыл бұрын

Brilliant

@firefish111

5 жыл бұрын

Great. Now what?

@Dazzletoad

4 жыл бұрын

😂🤣👏🏻

@Triantalex

8 ай бұрын

??

That joke at the end was horrible..... 10/10 tell more

@oz_jones

7 жыл бұрын

Agreed, it was sinfully bad.

@slickerius

7 жыл бұрын

That was pretty unexpected though.

@bartlankheet9026

7 жыл бұрын

I thought I missed it at the sponsor thingy but then it hit me

@DaOstMan

7 жыл бұрын

Russell Jarrett h

@toniokettner4821

4 жыл бұрын

but true

Another thing that makes this game counter-intuitive is that you give your victim first choice on selecting his sequence before you select yours. In many games, the person going first has an advantage, so he thinks he has the edge. In this game, it is just the reverse.

You: THH Me, an intellectual: TTH

@djedg10

6 жыл бұрын

HTT

@NipunChamikaraWeerasiri

6 жыл бұрын

THT

@thatoneguy9582

6 жыл бұрын

DJEdg10 HHT

@cubing3211

5 жыл бұрын

@@thatoneguy9582 THH

@caleblewis8169

5 жыл бұрын

@@cubing3211 TTH

Can we get this elusive Dr. Sexy in Numberphile? What is his area of expertise?

@schadenfreudebuddha

7 жыл бұрын

macrosexonomics.

@frankotto3134

7 жыл бұрын

his expertise is the 4-dimensional shape of reproductive organs, seducing you in a non-existing dimension :)

@WilliametcCook

7 жыл бұрын

He studies sets of primes that are 6 apart.

Probability may be the most counter-intuitive branch of mathematics. Similar to the "non-transitive" coin flipping game in this video are "non-transitive dice", covered in another Numberphile video. Then you've got the "Monty Hall Problem", as well as the "Bertrand Paradox", both of which can be found in a quick Internet search. I recall another youtube video about an experiment which indicated that birds, pigeons in particular, seem to have better intuition than people in situations rather like the Monty Hall Problem.

7/8 is exactly 87.5%

@potato-hj9nm

7 жыл бұрын

he also said 3/4 is about 75%

@ar_xiv

7 жыл бұрын

well it will always be "about" those numbers because you can never get a sample size big enough for it to be exactly one probability or another

@katzen3314

7 жыл бұрын

That's the whole point of probabilities Pocari, It's the chance of winning a game, not the ratio of wins to games in a finite selection.

@styvensbelloge1703

7 жыл бұрын

"There a three kind of Mathematician. the one who know how to do computation. and the one who don't" - A Mathematician

@katzen3314

7 жыл бұрын

***** With you falling into the last category I presume?

“It's this weird circular pattern… that I'm not going to explain!” What is this, factoidaphile? I have so many questions! What's the best choice if there's 8 people playing? How is it possible for it to be circular? Why does swapping the middle one work? Are there other worst choices that give you a smaller chance but still a high expected value?

@pablogriswold421

7 жыл бұрын

Best choice for 8 people is htt or thh (really the same) but yeah, I would have liked to know the odds of different matchups that are non adjacent here that could happen if you have to choose first.

@austinmitchell8846

7 жыл бұрын

I think about it this way: Each pairing of 3-sequences (lets call them 3-s) is a different kind of game, so there are actually choose(8, 2), or 28 different games you can play. What he's doing is for each set of 3-s, he's picking the game that it has the lowest chance of winning against given an infinitely long game that ends on the first pattern that appears I'm not sure about the math/logic on the center coin copy-flip, I'm still thinking about it. It seems like you're trying to make it so if their pattern appears somewhere, yours is likely to have just appeared before it (as you have 2/3 of their sequence, and the rest of your sequence happens at the end) What happens when 8 players play? Well, the number of different games you have is choose(8, 8), or 1 game (where every 3-s is picked), and each player has a 1/8 chance of winning, as one 3-s has to appear on the very first 3 coin flips and given only 3 coin flips any 3-s has an equal chance of winning. The key is the game continuing changes the probability.

@Ordoct

7 жыл бұрын

I piece to the explanation of why certain sequences beat others is that (and you can see this by the swapping the middle on thing) any sequence is beaten by a sequence who's last two are the same as the first sequence's first two. That was an awkward description to follow so what I mean is either sequence staring with HH, for example, is beaten by THH or both sequences starting with TH are beaten by TTH. Sequences whose last two are the first sequence's first two. It makes sense that that would be the case because the winning sequence sort of blocks the losing one. For the losing one to ever show up, you must first get the last two parts of the winning sequence to show up. Then, as long as the flip before that is the one you want, you do not proceed on to a third flip to complete the losing sequence.

@pablogriswold421

7 жыл бұрын

+Ordoct Yup, he mentioned that. However, there are more complex ones, like how you choose HHT if the enemy chose HTH. If you start H, both are going ok. Another H guarantees a win for HHT. A T second leaves hope for HHT though. Starting with T is irrelevant because neither go Txy, so from there we can tell why that is favorable.

@liambadalamenti7593

7 жыл бұрын

+Pablo Griswold wrong. each choice is equally likely to win in an 8 person game. no matter what, the game ends after 3 turns. in a two player game, this would also be the case if after the third coin flip you started fresh ignoring the previous coin flips.

A mathematician called Dr Sexy. xD

Huh... This principle could also be used in reverse. You could use it to rig a game in the users favor, like as a videogame's luck stat. This way the actions are perceived as just being lucky at a 50-50 game, when in reality they have a boosted chance of winning. I wonder if there is any version of this game where the increased odds of winning is the same for all possible choices.

Great video. Another way to remember this patter is to note the first two picks. If they are identical (HH or TT), you inverse your first pick and repeat those two picks (THH or HTT). For an alternate sequence (TH or HT), follow the one-one-two pattern (TTH or HHT).

You could say that the "Best Choice" would be THH or HTT because you have the best chance of not losing to someone who knows the trick.

I used to watch all Numberphile videos but now I only watch the ones with James :) I love that guy

I LOVE watching Grime explaining math stuff.

This is really cool. Thanks for sharing!

James is a really consistent coin flipper.

I always like seeing Dr. Grime

James you are the smartest person on this channel.

Somewhat surprisingly, this topic came up in the 2012 ARML Local team round (which I did recently for practice with some others). The question was the probability of the sequence HTH showing up before HHT. We first assumed it was 1/2 for a while, but then realized that it was in fact 2/3 (I believe, I am not sure if I remember it properly)! If only we had seen this video first.

Great video!

i'm SOOOO gonna use this

That diagram is wild. Now do it with 4 picks lol.

awesome ... saw this in the first hour... success

awesome ... saw a video in the first hour... success

Great video

7:23 He looks so smug... THAT WAS THE SECOND WORST CHOICE POSSIBLE YOU UTTER FOOL!

The prime number machine from Warning: Contains Numbers is behind James!

I like these videos, but they should be made in two parts. The first one like this one, to show the general idea behind the topic discussed. And the second one with the full-fledged math showing how the conditional probabilities play out. I mean, the key point here is that the two events the players bet on are correlated, although one would assume that they are not at first glance. People who are more used to math would enjoy this second part I think.

Great trick!

Dr James Grime is the best! :D

I think the real lesson here is *never gamble with Dr Grime*

James i only like to watch these vids ONLy when you make them , i like ur humor :)

james grime is the best guest hands down

I wonder what will happen if you play this with 3 friends and we all pick the inner circle...

@neropatti1504

7 жыл бұрын

Watch the video again. =)

@shelvacu

7 жыл бұрын

The people being pointed to have a higher chance to lose, I think. The interesting question is what happens with 4 people all on the inner circle.

@stensoft

7 жыл бұрын

Two of you (the ones who chose the sequences that are ¾ better than one of the others) would have higher probability than the other two to win. Those two would be 50:50 against each other, and so the other two.

@jakeglenn9690

7 жыл бұрын

haha thats what he was asking.. with 3 friends means with 4 people total XD

@DrGerbils

7 жыл бұрын

The 4 sequences in the inner circle are equally likely. The probabilities for the 2 player game apply only to the pair being compares. THH occurs 3 times as often as HHT in the long run, but in the 4 player version the long run will be cut short if TTH occurs.

What if 3 people played at the same time?

@ejesbd

7 жыл бұрын

Or, what if four people played simultaneously and chose the four choices shown in the circular portion?

@brokenwave6125

7 жыл бұрын

Then they would stand an even chance. You had to already know that so why did you ask?

@TP3200

7 жыл бұрын

Two of them might be more likely to win, since they have slightly higher chances of beating some of the others.

Is this possible with n-times H or T ? Will it always be the same possibility?

@orangemanatee39

7 жыл бұрын

Well it certainly doesn't work for n=1 or n=2. I'm pretty sure you could prove that it works for all natural numbers greater than 3 though.

@sas911

7 жыл бұрын

Partially works for N=2, but doesn't have a guaranteed higher probability of winning. TT loses to HT. HH loses to TH. TH and HT are 50/50 to each other.

Amazing!

I would call tossing throwing the coin up in the air to increase the randomness or spinning it on a desk to increase the randomness and to build up tension between "tosses".

Love all your videos, can you please explain Banach-Tarski?

Actually, it makes sense that there isn't a best choice, since every two equal-one different combination has the same probability to appear, but the best call would have to be more likely to appear, so have a higher probability (althought I'm not sure it's a valid demostration, but it is a pretty solid idea).

Love it!

i'm told that actually is how rock paper scissors got started, the original game was basically 'pick a number of fingers from 0 to 5' and because of the circular strategy, it ended up being that only 0, 2, and 5 were worthwhile choices.

@hebrewhammer770

7 жыл бұрын

Do you have a source for that strategy? There's a game called Horsengoggle that uses that principle and I'd be interested to learn about it.

@KairuHakubi

7 жыл бұрын

Taco Peligroso I can't remember where I heard it, I can't find it online, and wikipedia's origin of janken seems to contradict it.. but it sounded too plausible and detailed to be fraudulent. Something about every number beating the one above.. or below it? one of those two.. and thus 1 became useless because 2 did its own job better with less risk, and somehow it all worked out so that the only viable strategy was the 0, the 5, and the 2.. it all made sense but now that I say it out loud it sounds completely mad I think maybe the idea was to throw the lowest number of fingers, except 5 beats 0.. so then that would make more sense, 3 and 4 are pointless because you could just go with 2, 1 is an inferior version of zero, and 5 beats zero. something like that.

@KairuHakubi

7 жыл бұрын

***** I think it's that that was a stage in its development, and then people started choosing 2 in order to beat 1 or 5 or whatever (whichever direction it worked in), and that ruined 1 as a choice, while 0 and 5 remained viable. Again it's bizarre I can't find any links to this now. It's way too specific a memory for me to have imagined it.

@KairuHakubi

7 жыл бұрын

***** Yeah you're right, I just vaguely remember "2 because it beats 1" but that would mean it was HIGHER numbers win, with 0 beating 5, but if that was the case youd expect 3, not 2.. plus it would mean the dynamic of rock-paper-scissors would have been FLIPPED at one point.

Hey Brady ! Big fan of your work here ! I was just wondering why you stopped posting on PhilosophyFile ? (I'm sorry, maybe you explained it somewhere else, but I didn't see it) Thank you for your work

I'm curious to know if a winning strategy could be made if you were playing with an n sided "coin." Could you have an edge if this were played with a 3 sided coin?

I came here because of your interview on Rafael's channel, from Brasil

How do you derive the strategy shown in the video that beats opponent's combination? It makes sense that you want the opponents first and second choices to be your second and third so that you have three correct when he has his first two, but how do you reason the strategy of flipping opponent's middle choice and putting it as your first in your sequence? Also in the middle circle HTT -> TTH -> THH -> HHT -> HTT. If you play with four players with each choosing one of these combinations, is everyone equally likely to win and how that can be if some combinations beat others?

Can you please do an episode on the math behind the game Battleship. I think that would be interesting.

A mathematician called Dr Sexy. That was pretty funny.

I've seen this before. I thought it was on one of Brady's channels. It had a bit more detail also.

I wanna play this game with my friends. It's like an advanced Rock-Paper-Scissors.

Can this be extended to 4 or 5 coin flips to give you even better odds? And is there an easy rule to remember what you should choose? Intuition tells me that you flip second to last coin, and put it up front.

I only watch the videos on this channel that have this guy. Anyone else?

@twiligtcrazygirl

7 жыл бұрын

Same.

@jaakkohintsala2597

7 жыл бұрын

he da real husbado...

@twiligtcrazygirl

7 жыл бұрын

+Jaakko Hintsala Literally bae amirite.

@RyanDB

7 жыл бұрын

Are you subbed to his personal channel?

@MD-pg1fh

7 жыл бұрын

You're missing out, mate.

Is it not better to just flip the first and copy the first 2? That way once your first coin shows up anywhere in the sequence you win. Example HTH T Copy the first and second HT->HT Ends with THT. Once a T appears you will in before them. (Unless there first coin shows up repeatedly at the start) Am I wrong?

if I use the rule, the sequence to beat HHT is THT instead of THH? seems the rule suggest not to change the last letter meaning a sequence will only be beaten by a sequence ending with the same letter. did I miss anything?

@kuroganeyuuji6464

6 жыл бұрын

you eliminate the 3 that is the T of HHT and make a copy of the second that is H, them put the copy in first and reverse it, making THH

This penny video was also on a channel called scam school where they did their version.

Someone challenged me with working out this game at a party. It was fun for 2 minutes, and better than the alcohol at most parties!

Wait since the action of flipping the coin is random and independent of the previous flip, any sequence should be equally likely as another right? Cause each flip is independent so each side has a chance of winning equally on each flip. Like the Law of Averages in stats

This was on a STEP paper a few years ago :).

That was interesting

This would be interesting if we were to look at choices of coin sequences that extend over 3 coins... so say if we were asked to pick a sequence of 4 coin faces instead of 3. How would it change mathematically, and is there still a strategic algorithm to ensure you have a higher chance of winning? :)

is it possible to use this strategy during a game of darts? each player would choose a triple color sequence and whenever a dart hits the target,they record the space's color...

Awesome

The story about the origin of the name for this game is similar to that of the origin of how German chocolate cake got its name: It's not that it's made out of German chocolate (although I suppose you could use German chocolate in the recipe, but it's not specifically called-for) -- it's because the last name of the chef who came up with the recipe was German!

if i was told to go first, what kind of sequence would be best? 121, 112, 122, or 111? this assumes that the other person doesn't know about this.

I'm wondering if you could use this on a roulette table, playing sequences of even or odd numbers (or colors) based on the last 3 or 4 results of the table before betting. Do you then have an probable advantage over the casino (except for the zero on the wheel)?

so what would be the best to choose if you choose first

8 elements have 28 groups of 2. In your diagram you have measured only 8 relations. Are ALL the rest related by a 50% chance?. (Some of them, like TTT vs HHH or THT vs HTH are clear, but, what about the others?)

how do they interact otherwise? what about the probabilities of two entries which aren't linked by any arrows? is it equal for those?

Given the "trick", you don't actually care what the third selection is. You just care that TH beats HH, which beats HT, which beats TT, which beats TH. The pattern is THHTTH for the first two selections, and you just move one backwards to beat them.

here's how to fix the game. have all players pick theirs in private and reveal right before the game begins. this makes strengths and weaknesses happen more randomly, and there is always a chance that players will have random benefits. or just force all players to pick one of the 4 cardinal choices (TTT, HHH, THT, HTH) which leaves everyone with an equal probability.

Now does this extend? as in what would you say if you picked a sequence of 2,4,5, tec? (obviously, 3's already covered in this video) that would be an interesting video, and perhaps doing a numberphile2 video on the logic behind the new choices and an extendable fassion

@htmlguy88

7 жыл бұрын

they semi showed how to extend it with the examples they gave if the because if it right on the first n then some will never win against others.

That ending made me crack up

Anyone else thinking translation of mRNA to proteins?

One interesting side story on this - the discoverer of the principle Walter Penney was a high school student when he published the story in the Journal of Recreational Mathematics in 1969.

props to Brady for realizing his mistake

THH and HTT are the best options for the one who picks first. Because, at the worst, you lose with a 67%, but at the best, you win with an 87.5%.

What if the person who picks first can choose one other selection to be voided? How does that work out?

Wouldnt it be such that their first two should be your last two? In that situation, for their sequence to start, yours will have (at least had a chance at) ending, right?

from the thumbnail I thought it was going to be about at how you flip it.

I laughed quite hard when you said 7/8 is approximately 87.5%

@themobiusfunction

Жыл бұрын

With an error margin of "approximately" 0%

YES now I can challenge my enemy into a deadly duel of coin flipping !!

If you think about partition primes are ruling ends of number jumble which create probability.

@venkateshbabu5623

6 жыл бұрын

If you take 1 2 3 4 then given multiple of two as the occurring then 2 3 are primes so 2/4.

"Or a mathematician called Dr. Sexy" Grime, James - 2016

is the probability sequence rearranged with rinsed coins counterclockwise?

intersesting Video. But i still have one question. what if I choose the Opposition Sequenz to the Sequenz of my opponent? (For example they choose htt and I choose thh)

*If you choose the same as them you're sure you will win every time*

I'm like 99% sure Iv'e seen that before... if not here maybe on James' channel??

@Ruminations09

7 жыл бұрын

You might be thinking of Grime Dice, a set of dice that James made that are impossible to draw with, that go in a circle of giving each person a better chance of winning.

@madamerouge123

7 жыл бұрын

Scam School had this exact trick in one of their videos.

@L4Vo5

7 жыл бұрын

Yes there's a video about this on James' channel, actually 2 i think

@ediza.8485

7 жыл бұрын

Yes, he actually made a video explaining this on his channel called "singingbanana". It's like 3 or 4 years old though, which is why you might not completely remember it.

Hey Brady, I have a question : How often do you learn about mathematics/enjoy mathematics on your own compared to before you started this channel ? I would be very interested to see if making these videos helped you understand the world better (that's a big word), thank you.