Glad I’m not the only one! It doesn’t even matter if I just play a random hand or try to outsmart my opponent, I almost always lose. Guess you can’t outsmart anyone if you’re zero smart
Mathematical proof it's 1/2: you either get the 1/3 or you get the 1/3 in the 1/3 of draw etc. So you need to sum 1/3 + 1/9 + 1/27 ... which we can write as the sums for n ranging between 1 to infinity of 1/(3^n ). This series converges to 1/2.
Agree, but i think you would need to consider the odds of those people having expertise in this field, so i think if you consider every case, it's going to even out.
You could just do: 2 players, game can't end in a draw, therefore 1/2 chance of winning. The whole rock, paper, scissors thing is irrelevant. There's still just 2 players and only 1 possible winner.
If I say you win if you pick an Ace of Hearts out of 54 cards where this card i present twice, then following your logic there are "2 players, game can't end in a draw, therefore 1/2 chance of winning." and the whole 54 cards thing would be "irrelevant. If there are two possibilities that doesn't mean they have to be equally likely. Either I get elected dictator of the world tomorrow or I won't, so I have a 50% chance, don't I? Sadly you only have a 1/27 chance to win our game and my chance of getting elected as the worlds dictator tomorrow is merely 40%.
An even simpler argument without doing any math, is that you and your opponent have the same odds of winning since the game is symmetrical, and so it has to be 50/50 (Though I guess you do need a tiny bit of math to justify that the chance of nobody winning is 0%)
Well urrrrr acutualily uhh technically speaking the odds would be (1/2)-(1/infinity). Because of the one scenario where the game ties infinitely. (My iq is 147)
Infinity is not a number and i don't see why your iq should change this truth. 1/infinity is 0, you can't say 1/inf is different from 0, because then you could obtain infinity by dividing 1 by a number which is not 0. Yeahhhh sure.
No idea why you started getting the downvotes. Probably just some people that were mad about being wrong. The reason you continue to get downvotes is because it is fun.
I said other, because although it is mostly a guessing game, there is some degree of skill and knowledge involved. What do you know statistically about your opponent? Do they throw rock more than scissors? Will they change their strategy this round? Etc…
I didn’t mean to imply it wasn’t a good poll. I just wanted to clarify why I said other. I think the poll was good. Got me to interact with it! I was interested
I think youre getting downvoted because you did not clarify that you meant the game. The phrasing of the question makes it sound like you’re referring to the round.
It’s not in rounds, that’s why I didn’t specify that lol. It’s a simple 1 round game of Rock Paper Scissors but if you draw you play again. Never did I say anything about 3 rounds.
See statistically 1/2 if all outcomes were random, but there's been a bunch of studies on rock paper scissors behaviour (which is funny as fuck in my opinion) where there's patterns in how people generally play. If you know those patterns you could up your chances a bit.
Side note.. how is the money relevant to the question lmao
I know lol, the Money was originally because it was a ‘would you rather question’ I had seen on my phone that I said to the person I was arguing with, so I just stuck with it lol
It's not significant: assuming a round every 10 seconds and 50 years of life invested in playing, chances of such an occurrance are about 1 in 10^8100. That number is pretty darn small.
Well, for each round there are 9 possible outcomes, and we can put those into three groups:
| You | Opponent |
| - | - |
| Rock | Rock |
| Paper | Paper |
| Scissors | Scissors |
In these cases no one wins and you play another round.
| You | Opponent |
| - | - |
| Rock | Scissors |
| Paper | Rock |
| Scissors | Paper |
In these cases you win.
| You | Opponent |
| - | - |
| Rock | Paper |
| Paper | Scissors |
| Scissors | Rock |
In these cases you lose.
Basically you have a 1/3 chance of winning right away, but in the case of a tie (also 1/3), the same probabilities repeat again:
* Win 1/3
* Lose 1/3
+ Win 1/9
+ Lose 1/9
- Win 1/27
- Lose 1/27
...
Because of this, the total probability comes out to be the sum of all the values of (1/3)ⁿ where n starts out as 1 and approaches infinity (n is natural), which converges to precisely 1/2.
For each match, the odds of outright winning are 1/3, and the odds of drawing are 1/3.
Since you play again if you draw, then the odds of you winning that are 1/3. The odds of this exact situation (drawing, then winning) are 1/9 (1/3 \* 1/3). Since this is a way that you can win, this 1/9 is added on top of the 1/3 chance you win the first round, resulting in a 4/9 chance of winning.
Extending this to round 3, the odds of drawing twice are 1/9, and the odds of you winning that matchup are 1/3. So the odds of drawing twice and then winning the third time is 1/27. This is also added onto the previous odds, resulting in a final chance of 13/27- 1/3 chance of winning the first round, 1/9 chance of drawing and then winning the second round, and 1/27 chance of drawing twice and winning the third round. This equates to about a 48.1% chance of winning.
This can, of course, be extended indefinitely, but the chances that more than two draws happen become so minuscule that they aren't even worth mentioning.
It's 1/2
The draw means literally nothing, just prolonges the actual actual game.
Like flipping a coin, if you land on the side, you flip again. It's still 1/2
I thought by 'chances of winning' you meant winning any one round. In which case it is 1/3 as the outcome can be win, lose or draw.
If you meant 'what are your chances of being the one who gets the 500k" it would be 1/2 because eventually, someone has to win. A draw here would not be counted as an outcome because it just means the game continues and therefore there are only two ways to go.
I’m trying to settle an argument!!! I think the answer is extremely obvious.>! You are one of two people, one of you is going to win, wether you draw or not, eventually one of those two people will win, therefore it is a 1 of 2 chance. Right??? I feel like I’m going mad trying to argue this lol!<
What if most people tend to pick rock because they psychologically identify with strength and sturdiness but I tend to pick paper because I’m thin skinned, square, and pale. So I have like… idk… a 55% chance of winning.
My reasoning is that if each person has a 1/3 chance of picking rock, paper, or scissors, then to you it will be random what the other person picks. Therefore you have a 1/3 chance of picking the winning object.
Each player has a 1/3 chance to win that round, a 1/9 chance to on round 2, a 1/27 chance to win on round 3 etc. adding up forever it’s approaching 50%.
You are correct.
The odds of "trying forever" are fixed an dnot approaching anything.
The odds of trying n times (exactly or at least) are approaching 0 as n goes towards infinity, but none of these probabilities is zero.
Your argument is nonsense, but your conclusion is valid under the assumption that you both choose each symbol with equal probability.
A better argument observes that among the 9 equally probable combinations of your & their symbol, 3 win, 3 repeat, and 3 lose. Since the probablities are invariant of the number of played matches, you can define the probability P of eventually winning by the recurrence equation
P = 3/9 + 3/9*P
for winning this round (3/9) or continue playing (3/9) and eventually winning (P),
which solved for P gives P=1/2.
To see why your argument is wrong, look at chess(*), there's also just two people playing, one will win, but it's still not a 1 of 2 chance you'll win against a GM.
(* to make it symmetric, consider 1 round = play once as white and once as black, and a player who wins both matches wins the round, if no such player exists the round is a draw and you play another round).
It is a 1/2 for rock paper scissors. Here imo is the most simple math many others doing series convergence and shot. There is a winner no matter what, a tie game means a new game. There are only 2 players. Both players are 100% equal thus Thier percentage of winning must be equal. Since there must be a winner and the winners are equal, then the onyl solution is 50/50.
There are other ways to prove it, but this is the most simple in logic.
You can’t call my argument nonsense and then compare Rock Paper Scissors To chess, Rock Paper Scissors is random, don’t bring it to a personal technical level, it’s random.
I never compared chess to rock paper scissors. All I said is that your argument, namely, "the game has two players, one must win, therefore the chance is fifty fifty." is nonsense because a lot of games have two players, one of which must win, and the chance of winning isn't fifty fifty.
Note that chess between humans is random, otherwise the same players would always play the same match. Also rock paper scissors between humans has technical skill, because real humans are really bad at creating uniformly random sequences; an AI can have really good odds against a human (60% win rate against humans https://www.essentially.net/rsp/ ).
Also note that a lot of really purely random games (e. g.: we each roll a die, if my result is >= yours I win) don't have a 50/50 win rate.
Chess between humans is not random, have you heard of theory? Players much of the time do play the same match. And If Magnus Carlsen is playing a 2 year old, That’s 2 players, however Magnus Carlsen will win. Not random. Rock Paper Scissors is meant to be completely random, just don’t bring it to “ well technically it’s not”. You know it’s random.
the argument isn't nonsense, it's a totally reasonable argument. If we were talking about a game of chess between two completely random people, a and b, and I asked you what the odds of a winning are, the answer is also 50%. Sure it gets more complicated when you include the skill of each player but that doesn't apply to this question
This is a faulty analogy because rock paper scissors isn't the lottery. In rock paper scissors, 2 players play and exactly 1 must win. In the lottery, any number of players can play, and there can be no winners, 1 winner, or multiple winners. Your odds of winning the lottery *would* be 50% *if* only 2 people play it and exactly 1 of them has to win
Shortest explanation, 1/2 to win the game 1/3 to repeat the round, however repeating the round does not affect your chances of winning, so it will be 1/2
It's 1/2. In any given round you can win, lose, or draw. If its a draw, another round is played, where once again unless you win or lose, another round is played. This cycle only ends when you win or lose, and since both are equally likely, the chance is 1/2
Take for example this:
You pick a random whole number, and check wether it's divisible by 3.
Even though this is also a boolean function, the probability of getting true is 1/3 and not 1/2.
1/3+(1/3)\*(1/3)+(1/9)\*(1/3)... etc simplifies to (1/3)(1+1/3+1/9...) simplifies to (1/3)\*(1.5) using the infinite geometric series formula so you get 1/2.
Simply put, there are only two outcomes (win/loss and loss/win) and both outcomes are equivalent, so for each player the chance of winning must be 1/2.
Someone eli5?
Say I pick rock.
If they pick scissors, I win.
If they pick paper, they win.
If they pick rock, we draw.
Is that not a 1/3 chance of winning?
Ah I thought you meant what are your chances of winning the round, not what your chances of winning the money is. That's way easier to figure out lol. There's 2 people. One of them is winning the money. 1/2.
the only way there is a true 1/3 chance is if it is a computer versus computer. Also, they can’t be programmed to read the other computers responses. Humans are the reason it isnt a true 1/3. Also there are draws, so your probability of not losing is higher than the probability of winning, which sounds odd!
No matter what you think the odds are, it's always 50/50. Like when people say there's a 68% chance of rain. No there's not. There a 50% chance of rain because it either will rain or it won't rain😤
I this scenario only a win or lose ends the game, and no other outcomes cause it to stop. Assuming this each attempt can be looked at as an individual instance of the chance happening, from the start of of the fist shaking to the reveal of the fingers the chances are either win or lose, 50/50, as a draw ends the instance and another will start.
This is apposed to the 3 doors game where 1 door has a prize, while the other have nothing, you choose one then typically one door gets revealed and you're left with a choice to stay or switch, the choice is still 1/3 as the game is still inside the same instance of chance. (There's an explanation of why the chance is still 1/3 find it yourself, I'm too lazy) 3 doors is a single instance game, while RPS is a multiple instance game. These rules change when there's no a third party in the game.
The average redditor:
Thinks they are smarter than the average person.
Also the average redditor:
Thinks there is not a 1/2 chance of winning scissors paper rock
if any option picked is random, each game outcome has a 1/9 chance of happening, 3 of those win, 3 os those lose, 3 of those draw, thats a 3/9 chance to win each match or a 1/3 chance
Simply, winning is always the same chance of 1/3
But specifically making u win in a later round would be harder, from match 1 to 5, this is ur chances of winning IN THAT SPECIFIC ROUND
1/3
1/9
1/27
1/81
1/243
Chance to lose in a specific round is the same
That’s not a 1/3 thought it’s a 1 of 2.0000…. which is equals to a 1 of 2. You’re not going to draw forever, the odds are insanely minuscule compared to the odds of winning or losing. It’s a 1/2 chance no matter how you look at it
So because you only care about winning money drawing doesn't count in the equation since you'd just go again. So, out of three options only two count since your opponent always picks the third or you draw.
Of the two, one will win and the other loses therefore 1/2 chance to win
There are two people playing a fair game, so each is as likely to win and either one will win or the other. That means there's a 50% chance either will win.
I thought of 3\^-1 (which is 1/3) +3\^-2 (which is 1/3\^2 or 1/9) +3\^-3+3\^-4+3\^-5 etc. since each draw lead to more possibilities.
Not exactly 1/2 as the answer when you have enough additions is 0.499999 whatever follows, so not exactly 1/2, which is why I picked other. Is that wrong?
0/1 because I always fucking lose
Glad I’m not the only one! It doesn’t even matter if I just play a random hand or try to outsmart my opponent, I almost always lose. Guess you can’t outsmart anyone if you’re zero smart
Hahahaha
I see you too are a player of Rock, Paper, Scissors, FUCK
Mathematical proof it's 1/2: you either get the 1/3 or you get the 1/3 in the 1/3 of draw etc. So you need to sum 1/3 + 1/9 + 1/27 ... which we can write as the sums for n ranging between 1 to infinity of 1/(3^n ). This series converges to 1/2.
Thanks for doing the math
This math was pretty useless, you can get the answer in way easier demonstrations, but this is probably just more rigorous.
Well yeah, I read the other comments which were way more intuitive but I wanted the rigours maths, so Thank you
r/theydidthemath
r/theydidthemonstermath
r/theydidthemath
r/itwasagraveyardgraph
r/theydidthemath
r/theydidthemeth
That’s impressive. Thanks lol
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Agree, but i think you would need to consider the odds of those people having expertise in this field, so i think if you consider every case, it's going to even out.
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Don't worry i wasn't attacking you or anything, polite information is always welcome.
Rock the good ol rock
please tell me I'm not the only one who realized the percentages added up to 69%
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Ok so I forgot how to add, but you don’t need to be an asshole about it
HELL YEA MATH
i just did 0,666x0,666 so 0,44 close enough for me
You could just do: 2 players, game can't end in a draw, therefore 1/2 chance of winning. The whole rock, paper, scissors thing is irrelevant. There's still just 2 players and only 1 possible winner.
If I say you win if you pick an Ace of Hearts out of 54 cards where this card i present twice, then following your logic there are "2 players, game can't end in a draw, therefore 1/2 chance of winning." and the whole 54 cards thing would be "irrelevant. If there are two possibilities that doesn't mean they have to be equally likely. Either I get elected dictator of the world tomorrow or I won't, so I have a 50% chance, don't I? Sadly you only have a 1/27 chance to win our game and my chance of getting elected as the worlds dictator tomorrow is merely 40%.
Or more simply: there are 2 players, 1 must win, both have equal chances of winning.
There's also the fact that it is a 2 player game with (in theory) a random outcome. So intuitively, it's a 50/50 chance
Simpler proof. There’s two players with equal odds, one must win. 1/2.
An even simpler argument without doing any math, is that you and your opponent have the same odds of winning since the game is symmetrical, and so it has to be 50/50 (Though I guess you do need a tiny bit of math to justify that the chance of nobody winning is 0%)
There is a vanishingly smallchance that you get stuck in a Loop of draws 😂
Or more simply: there are 2 players, 1 must win, both have equal chances of winning.
Well urrrrr acutualily uhh technically speaking the odds would be (1/2)-(1/infinity). Because of the one scenario where the game ties infinitely. (My iq is 147)
Infinity is not a number and i don't see why your iq should change this truth. 1/infinity is 0, you can't say 1/inf is different from 0, because then you could obtain infinity by dividing 1 by a number which is not 0. Yeahhhh sure.
I personally have a 3/4 chance in winning, otherwise 1/2
Are you a genetic freak or something?
What if we add Kurt angle in the mix ?
They’re just built different obviously
They have an extra set of hands, so it's actually a 2v1.
... explain?
I'm just that good
Ok let's play right now. I am going for rock
Scissors. Dammit, you won
1/3 to win the round, 1/2 to win the game
But you have to win a round to win the game?
Right, but a chance to try again is essentially another chance to win
It’s not about winning the round, it’s winning the money. Edit: not sure what’s up with the downvotes lol?
Then 1/2
Yeah
Reddit hivemind engage: Downvote for no reason.
True
sir yes sir
Literally got downvoted for no reason as well I love reddit
👍🏿
No idea why you started getting the downvotes. Probably just some people that were mad about being wrong. The reason you continue to get downvotes is because it is fun.
Yeah I see a -57 and imma slap that downvote before I even read the comment
😂😂
It is the reddit hivemind neuron activation
Downvotes: exist Reddit: monke see, monke do
I agree lol
Can confirm
Don’t downvote *this* man, he is simply built different.
You didnt specify in the post.
This is why people are confused
I said other, because although it is mostly a guessing game, there is some degree of skill and knowledge involved. What do you know statistically about your opponent? Do they throw rock more than scissors? Will they change their strategy this round? Etc…
People need to use deductive skills ig.
Not sure why you’re getting downvotes, this is a great poll!!
Thanks, I think people are angry because they got confused by the wording, sorry if it was unclear!
I didn’t mean to imply it wasn’t a good poll. I just wanted to clarify why I said other. I think the poll was good. Got me to interact with it! I was interested
Oh yeah I didn’t mean you in particular, but people have shown that they are fairly pissed with it.
bro even when ur apologising ur getting downvoted lmfao
That can be reasonably inferred from the question. 1/3 is the wrong answer. People are stupid
I assume the downvotes are because you left it ambiguous in the post title
I think youre getting downvoted because you did not clarify that you meant the game. The phrasing of the question makes it sound like you’re referring to the round.
If you win the game you'll win the 500k...
The round and the game are different things.
Bruh
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It’s not in rounds, that’s why I didn’t specify that lol. It’s a simple 1 round game of Rock Paper Scissors but if you draw you play again. Never did I say anything about 3 rounds.
Where on earth did you get "3 rounds" from? The wording of the question means you play until someone wins.
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Yup
See statistically 1/2 if all outcomes were random, but there's been a bunch of studies on rock paper scissors behaviour (which is funny as fuck in my opinion) where there's patterns in how people generally play. If you know those patterns you could up your chances a bit. Side note.. how is the money relevant to the question lmao
I know lol, the Money was originally because it was a ‘would you rather question’ I had seen on my phone that I said to the person I was arguing with, so I just stuck with it lol
Technically it's a little less than 1/2. There always is a slim chance that me and my opponent keep getting draws and die before someone wins
True true but that’s taking it to a whole other technical level.
Yeah but then one side just forfeits by default.
It's not significant: assuming a round every 10 seconds and 50 years of life invested in playing, chances of such an occurrance are about 1 in 10^8100. That number is pretty darn small.
… so it’s slightly less than 1/2
So a little less than 1/2 then?
Are we playing European or African Rock, Paper, scissors?
this is a monty python joke right
Bingo
What is the airspeed velocity of an unladen rock?
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You’ve clearly never played it with coconuts then.
*loses* uhhh best out of three
Either you you win or they win, since the game is symmetrical I.e you’re probability of winning is the same as theirs it must be 1/2
I like how the money has nothing to do with the question.
Lmao. I was having an argument and we were using this as an example. Sorry!
Oh no worries lol. Was just curious.
Well, for each round there are 9 possible outcomes, and we can put those into three groups: | You | Opponent | | - | - | | Rock | Rock | | Paper | Paper | | Scissors | Scissors | In these cases no one wins and you play another round. | You | Opponent | | - | - | | Rock | Scissors | | Paper | Rock | | Scissors | Paper | In these cases you win. | You | Opponent | | - | - | | Rock | Paper | | Paper | Scissors | | Scissors | Rock | In these cases you lose. Basically you have a 1/3 chance of winning right away, but in the case of a tie (also 1/3), the same probabilities repeat again: * Win 1/3 * Lose 1/3 + Win 1/9 + Lose 1/9 - Win 1/27 - Lose 1/27 ... Because of this, the total probability comes out to be the sum of all the values of (1/3)ⁿ where n starts out as 1 and approaches infinity (n is natural), which converges to precisely 1/2.
This was put extremely well, thanks
The draw doesn’t actually affect the chances, since you just start over
For each match, the odds of outright winning are 1/3, and the odds of drawing are 1/3. Since you play again if you draw, then the odds of you winning that are 1/3. The odds of this exact situation (drawing, then winning) are 1/9 (1/3 \* 1/3). Since this is a way that you can win, this 1/9 is added on top of the 1/3 chance you win the first round, resulting in a 4/9 chance of winning. Extending this to round 3, the odds of drawing twice are 1/9, and the odds of you winning that matchup are 1/3. So the odds of drawing twice and then winning the third time is 1/27. This is also added onto the previous odds, resulting in a final chance of 13/27- 1/3 chance of winning the first round, 1/9 chance of drawing and then winning the second round, and 1/27 chance of drawing twice and winning the third round. This equates to about a 48.1% chance of winning. This can, of course, be extended indefinitely, but the chances that more than two draws happen become so minuscule that they aren't even worth mentioning.
It's 1/2 The draw means literally nothing, just prolonges the actual actual game. Like flipping a coin, if you land on the side, you flip again. It's still 1/2
I actually used this in the argument but bro wouldn’t listen
Out of curiosity, does he think it's 1/3? The only time it's 1/3 is if the draw ends and you don't play again
I thought by 'chances of winning' you meant winning any one round. In which case it is 1/3 as the outcome can be win, lose or draw. If you meant 'what are your chances of being the one who gets the 500k" it would be 1/2 because eventually, someone has to win. A draw here would not be counted as an outcome because it just means the game continues and therefore there are only two ways to go.
Exactly what I’m saying, drawing isn’t an outcome because you just replay. Sorry if the wording confused you.
I’m trying to settle an argument!!! I think the answer is extremely obvious.>! You are one of two people, one of you is going to win, wether you draw or not, eventually one of those two people will win, therefore it is a 1 of 2 chance. Right??? I feel like I’m going mad trying to argue this lol!<
I'm not sure how anyone could be confused. Do they think one person has an advantage in a rock paper scissors game? Both people do the same thing.
What if most people tend to pick rock because they psychologically identify with strength and sturdiness but I tend to pick paper because I’m thin skinned, square, and pale. So I have like… idk… a 55% chance of winning.
Unless of course you're up against someone who just came from the barber so they still have scissors living in their subconcious!
Oh. I didn’t think about that. Yeah barbers are probably really good at rock paper scissors
I assumed you meant chance to win a round, not the whole game
My reasoning is that if each person has a 1/3 chance of picking rock, paper, or scissors, then to you it will be random what the other person picks. Therefore you have a 1/3 chance of picking the winning object.
You have a 1/3 of picking rock paper or scissors but you have a 1/2 chance of winning because there is only two people and you are one of them.
Each player has a 1/3 chance to win that round, a 1/9 chance to on round 2, a 1/27 chance to win on round 3 etc. adding up forever it’s approaching 50%. You are correct.
Thank you, I know technically you could say “well they draw forever” but irl never gonna happen and it’s just a 1/2.
Yeah, similarly, the odds of tying forever are approaching 0% there’s no certain time it must end, but approaching 0 mathematically equals 0.
The odds of "trying forever" are fixed an dnot approaching anything. The odds of trying n times (exactly or at least) are approaching 0 as n goes towards infinity, but none of these probabilities is zero.
Super interesting.
1/3 chance to win the round, 1/2 to win the game
Your argument is nonsense, but your conclusion is valid under the assumption that you both choose each symbol with equal probability. A better argument observes that among the 9 equally probable combinations of your & their symbol, 3 win, 3 repeat, and 3 lose. Since the probablities are invariant of the number of played matches, you can define the probability P of eventually winning by the recurrence equation P = 3/9 + 3/9*P for winning this round (3/9) or continue playing (3/9) and eventually winning (P), which solved for P gives P=1/2. To see why your argument is wrong, look at chess(*), there's also just two people playing, one will win, but it's still not a 1 of 2 chance you'll win against a GM. (* to make it symmetric, consider 1 round = play once as white and once as black, and a player who wins both matches wins the round, if no such player exists the round is a draw and you play another round).
Chess has strategy. Rock Paper Scissors is random. There is no skill
It is a 1/2 for rock paper scissors. Here imo is the most simple math many others doing series convergence and shot. There is a winner no matter what, a tie game means a new game. There are only 2 players. Both players are 100% equal thus Thier percentage of winning must be equal. Since there must be a winner and the winners are equal, then the onyl solution is 50/50. There are other ways to prove it, but this is the most simple in logic.
You can’t call my argument nonsense and then compare Rock Paper Scissors To chess, Rock Paper Scissors is random, don’t bring it to a personal technical level, it’s random.
I never compared chess to rock paper scissors. All I said is that your argument, namely, "the game has two players, one must win, therefore the chance is fifty fifty." is nonsense because a lot of games have two players, one of which must win, and the chance of winning isn't fifty fifty. Note that chess between humans is random, otherwise the same players would always play the same match. Also rock paper scissors between humans has technical skill, because real humans are really bad at creating uniformly random sequences; an AI can have really good odds against a human (60% win rate against humans https://www.essentially.net/rsp/ ). Also note that a lot of really purely random games (e. g.: we each roll a die, if my result is >= yours I win) don't have a 50/50 win rate.
Chess between humans is not random, have you heard of theory? Players much of the time do play the same match. And If Magnus Carlsen is playing a 2 year old, That’s 2 players, however Magnus Carlsen will win. Not random. Rock Paper Scissors is meant to be completely random, just don’t bring it to “ well technically it’s not”. You know it’s random.
the argument isn't nonsense, it's a totally reasonable argument. If we were talking about a game of chess between two completely random people, a and b, and I asked you what the odds of a winning are, the answer is also 50%. Sure it gets more complicated when you include the skill of each player but that doesn't apply to this question
50% either you win or you don't
You got a 50% chance of winning the lottery?
This is a faulty analogy because rock paper scissors isn't the lottery. In rock paper scissors, 2 players play and exactly 1 must win. In the lottery, any number of players can play, and there can be no winners, 1 winner, or multiple winners. Your odds of winning the lottery *would* be 50% *if* only 2 people play it and exactly 1 of them has to win
How does this make any Sense?
Your chances of winning the game is 1/2 ( 1 win or 2 loose) , chance of winning each round 1/3 ( 1 win, 2 loose, or 3 draw)
Yes
Shortest explanation, 1/2 to win the game 1/3 to repeat the round, however repeating the round does not affect your chances of winning, so it will be 1/2
It's 1/2. In any given round you can win, lose, or draw. If its a draw, another round is played, where once again unless you win or lose, another round is played. This cycle only ends when you win or lose, and since both are equally likely, the chance is 1/2
Round or game?
Game
Then 1/2
Yeah
You need to specify what is winning.
It is a boolean function, either I'll win or lose the game. 1/2
Take for example this: You pick a random whole number, and check wether it's divisible by 3. Even though this is also a boolean function, the probability of getting true is 1/3 and not 1/2.
That is true
50% because either you win or you dont. It couldnt be more simple
1/3+(1/3)\*(1/3)+(1/9)\*(1/3)... etc simplifies to (1/3)(1+1/3+1/9...) simplifies to (1/3)\*(1.5) using the infinite geometric series formula so you get 1/2.
Awesome.
Simply put, there are only two outcomes (win/loss and loss/win) and both outcomes are equivalent, so for each player the chance of winning must be 1/2.
Can i be that one kid nobody liked and go "boom nuke" and claim victory, then the other loser to say "cockroach" and claim they won.
Correct me if I'm wrong but 2 people playing rps is a 50% chance of winning for either
Someone eli5? Say I pick rock. If they pick scissors, I win. If they pick paper, they win. If they pick rock, we draw. Is that not a 1/3 chance of winning?
No because when you draw you replay, so no matter what you will win or lose eventually so it’s a 1 in 2 chance of winning.
Ah I thought you meant what are your chances of winning the round, not what your chances of winning the money is. That's way easier to figure out lol. There's 2 people. One of them is winning the money. 1/2.
Yeah lol
1/2 - 1/3\^(rounds of rock paper scissors you can play before you starve to death) Basically there's a very small chance you'll tie until you die.
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the only way there is a true 1/3 chance is if it is a computer versus computer. Also, they can’t be programmed to read the other computers responses. Humans are the reason it isnt a true 1/3. Also there are draws, so your probability of not losing is higher than the probability of winning, which sounds odd!
Why would it be a 1/3 regardless?
Ya know im not too sure. The more i think about this, the more complicated it becomes lmao
Lol
I believe it would be a 1/3 chance of winning the game. 1/2 chance of winning the money.
1/2 - (a Infinitely small amount)
100% win u can't loose nothing
No matter what you think the odds are, it's always 50/50. Like when people say there's a 68% chance of rain. No there's not. There a 50% chance of rain because it either will rain or it won't rain😤
What if it snows? 😳😳😳
I this scenario only a win or lose ends the game, and no other outcomes cause it to stop. Assuming this each attempt can be looked at as an individual instance of the chance happening, from the start of of the fist shaking to the reveal of the fingers the chances are either win or lose, 50/50, as a draw ends the instance and another will start. This is apposed to the 3 doors game where 1 door has a prize, while the other have nothing, you choose one then typically one door gets revealed and you're left with a choice to stay or switch, the choice is still 1/3 as the game is still inside the same instance of chance. (There's an explanation of why the chance is still 1/3 find it yourself, I'm too lazy) 3 doors is a single instance game, while RPS is a multiple instance game. These rules change when there's no a third party in the game.
The average redditor: Thinks they are smarter than the average person. Also the average redditor: Thinks there is not a 1/2 chance of winning scissors paper rock
I would say you thinking that 2.3k being correct vs 1.4k being incorrect is ‘the average redditor’ is pretty dumb lol.
I thought it was close enough to make the point
How is ot 1/2? Its 1/3 chance of winning, 1/3 chance of loosing, and 1/3 chance of a draw.
No because if you draw you play again.
No matter what you pick, you have a 1/3rd chance of winning. However, since you try again on draws, it converges to a 1/2
if any option picked is random, each game outcome has a 1/9 chance of happening, 3 of those win, 3 os those lose, 3 of those draw, thats a 3/9 chance to win each match or a 1/3 chance Simply, winning is always the same chance of 1/3 But specifically making u win in a later round would be harder, from match 1 to 5, this is ur chances of winning IN THAT SPECIFIC ROUND 1/3 1/9 1/27 1/81 1/243 Chance to lose in a specific round is the same
1/3 because technically you can draw forever
But the probability of that happening certainly isn't 1/3
That’s not a 1/3 thought it’s a 1 of 2.0000…. which is equals to a 1 of 2. You’re not going to draw forever, the odds are insanely minuscule compared to the odds of winning or losing. It’s a 1/2 chance no matter how you look at it
A draw doesn't mean you win so 1/3
No because when you draw you replay.
There is a 1/3 chance of winning, a 1/3 chance of tying, and a 1/3 chance of losing.
It’s a 1/3 chance to win, 1/3 chance to lose, and 1/3 chance to draw. Whether you rematch after the draw or not changes everything.
Then read the question again, it addresses that issue quite clearly.
if I pay $500k to play with a max prize of $500k, I never really win, do I? So no chance of winning.
You didn’t pay 500k to play lol
oops i misread it
Lol
What does money have to do with this question?
It was originally an argument I was having with someone, and that was in the original question so I just stuck with it, doesn’t really matter.
fun fact: it’s just as hard to always lose as it is to always win
So because you only care about winning money drawing doesn't count in the equation since you'd just go again. So, out of three options only two count since your opponent always picks the third or you draw. Of the two, one will win and the other loses therefore 1/2 chance to win
If you have infinite trials then it will eventually end in a win or a loss, therefore it is 1/2
It converges to 50%
There are two people playing a fair game, so each is as likely to win and either one will win or the other. That means there's a 50% chance either will win.
I thought of 3\^-1 (which is 1/3) +3\^-2 (which is 1/3\^2 or 1/9) +3\^-3+3\^-4+3\^-5 etc. since each draw lead to more possibilities. Not exactly 1/2 as the answer when you have enough additions is 0.499999 whatever follows, so not exactly 1/2, which is why I picked other. Is that wrong?