/lit/ - Literature

Starting second is the winning strategy.

>>16409087
OP here. That's wrong. Whether you should start depends on how many coins there are in each pile. The question is how.

>>16409098
Actually, you're wrong. If you had an IQ over 110 you'd understand.

>>16409098
No one is going to answer your question because of the shitpost image. Only a low IQ individual would be stupid enough to make this classic error. So you clearly have the wrong answer.

>>16409102
>>16409117
cope

>>16409078
If one pile has 2 or more extra coins, I think I'd go second, otherwise first.

>>16409146
Explain why.

>>16409078
If you take the first you shouldn't be greedy.

>>16409146
If that is a condition you can just go first and take enough for coins for the first pile to have 2+ extra coins. It is the same starting situation as if letting the other go first on pile that meet the criteria.
n and m don't matter in this case because the strict boundary is taking one single coin and using that to eliminate a pile. The first person to clear a pile loses.
The final syllogism to this is to go first and taken all but two coins out of one pile (n-2),, and all but one coin out of the other pile when it is your turn again (m-1)
There are exceptions for cases where piles n or m start near the boundary 1.
I don't know why you think this question is over 60 iq. The strategy is easier than tic-tac-toe.

>>16409098
If n=2x, m=2x-1, go second, otherwise go first

>>16409319
Wrong, idiot. If youre so confident why dont we play it out.
The starting position is (12,17). Your move.

>>16409404
I take 17 from the right pile

>>16409331
Let's play.
The starting position is (9,15). According to your strategy, you should be able to win if you go first. Your move.

>>16409426
I take 12 from the left pile and win. Idiot. Cant you think 1 move ahead?

>>16409435
Ok, I take 12 from the left pile instead

>>16409443
Then I take 17 from the right pile and win.

>>16409451
How?
You said you win if you take 12?

>>16409454
Wait, I misread the rules.
I take 12 from both piles.
Checkmate ;)

>>16409460
Then I take the rest of the coins on the right pile and win.

>>16409078
You should go second only if the stacks are equal. To win give opponent equal stacks every turn until you can give him 1 2 (or 2 1).

>>16409479
Lets play. Start with (9,15). Your move.

>>16409490
9,9

>>16409493
I take 9 from both piles and win.

>>16409498
gratz my strategy failed

>>16409475
I take no coins.

>>16409503
Thats not allowed. Read the rules again.

>>16409172
You want to force a situation of 2,1 for the other person essentially

>>16409506
I take 12 from both piles, you take one from the remaining pile, then I take the rest.

>>16409146
>>16409172
>>16409331
>>16409404
>>16409426
>>16409431
>>16409435
>>16409443
>>16409451
>>16409454
>>16409460
>>16409475
>>16409479
>>16409490
>>16409493
>>16409498
>>16409502
Samefagging schizoposter, FUcCK OFFFFFFFFFF

>>16409514
Moron. I take all of the pile because I want to win.

>>16409078
When you post shit like this I can't concentrate because I'm overwhelmed with the desire to procreate because of the woman in the picture

>>16409515
I've got 3 (You)s in that list, I don't know about the rest though.

>>16409544
I got three as well

>>16409431
Ok. (10,9)

>>16409479
If you go second on equal stacks your opponent will take both stacks on the first turn

>>16409573
(2,1)

>>16409573
(2,1)

>>16409515
Fuck (you) shut up no.

>no one has posted a solution yet
/lit/ is all sub 110 IQ midwits, isnt it?

>>16409674
I'm almost there wait just a little

>>16409479
>>16409678
retry here, I want to give opponent n,2n config, if it's not in that config I go first otherwise I go second.

>>16409587
Screw it, fogot about this. So losing positions are (2,1), (3,5), (4,7), (6,10), (8,13), (9,15) etc.
>>16409426
This should lose because I can play (8,13) next then

>>16409701
(8,13) Go

>>16409713
5,10

>>16409727
(5,3)

>>16409734
oh shit

>>16409741
I have to do some more thinking I'll get this

>>16409710
>So losing positions are (2,1), (3,5), (4,7), (6,10), (8,13), (9,15) etc.
How did you find these?

>>16409078
Yes, Plato and specifically his Phaedrus I believe.

>>16409741
>>16409710
I think I solved it here

>>16409078
Take all of the coins of one pile except for 1.

Or maybe I just take all the coins from both piles in equal number because it doesn't stop me?

>>16409753
OP here, I think you did. Care to explain how you got the losing positions?

>>16409750
(1) n and m can't repeat, e.g. (2,4)>(2,1); (4, 15)>(4,7)
(2) m-n (difference between m and n) can't repeat either, e.g. (3,4)>(1,2), (11, 13)>(3,5)

>>16409791
Congratz, your IQ is at least 110.

>>16409078
Take every coin from both piles

>>16409087
>Dem beens

Also for reference, this is a beginner level question from the WAIS-IV (2013) full-scale IQ test. The goal is to reach the solution within 20 seconds to reach the cutoff for above 110 for this particular subtest.

So, if you didn't, you have a processing speed deficiency, which can made up for with other things like spatial intelligence.

>>16409791>>16409885
You're supposed to write all this in 20s? Doubtful

>>16409791
nice, to flesh it out and see if I understood:
For (n,m):
0. (1,2) is losing
1. Any (n,m) such that n and m both aren't present in a losing configuration is losing
2. Any (n,m) where abs(n-m) isn't present in a losing configuration is losing

Is this correct?

>>16409885
Wow that's brutal, I have a bachelor in physics and imagined I was comfortably above 110. I honestly find it hard to believe that over 10% of the general pop can do this in less than 20.

>>16409919
not "present" but "equal to" ugh

>>16409919
Believing the post you responded to means you have an IQ below 110. I'm very sorry.

>>16409919
Shitposting aside, keep in mind that a score of 110 in this one subtest (out of 5 or so) for PS doesn't mean that your PS score is a 110. You'd probably have a much easier time with digit span. I found the 20 sec time limit hard to believe as well.

Test

>>16409078
>>16409479
The winning strategy is to always take from the bigger stack, leaving both stacks with a 1 coin difference. It doesn't matter if you make it have 1 coin more or 1 coin less, but you must never be the one to leave the stack with 2 coins or less. Once your opponent leaves 2 coins in a stack (or 1), you leave 1 coin in the other stack (or 2). Whatever he does next move, you win.

>>16409078
It depends on the value of M and N.

>>16409919
You're replying to a funpost, this is called "Wythoff's Nim".

>>16410260
Thanks for the name!

>>16410242
That doesn't mean you can't propose a plan.

>>16409885
wtf I literally can't solve it I'm i doomed?

>>16410466
It took me time an I have 3 years of training in this kind of problem solving.
This training and not any gift of intellect made me plot it as a grid like a chess board and go from there. Think of t as a queen trying to reach the corner.

>>16409078
>Let pile n = 15
>Let pile m = 18
There are two possible moves,
>(1) to take an even number of coins from each pile
>(2) or to take a whole pile
The winning strategy is to make move (1) and be the first player to move so long as you take the whole larger pile. If you take the whole larger pile while playing move (1) then you must take the smaller pile also. Therefore you end up taking the last coin, winning the game even though doing so makes pile n = -3, a non-natural number.

If the rules are that you cannot exploit the game by finishing the game with a non-natural number in either pile, then you end up with a game that will be longer and more indecisive, except that whoever takes the last coin from the smaller pile loses the game, or whoever makes m equal to n on their turn also loses the game.

I hate these questions because the answer is always so lame

So in summary taking first or second move won't guarantee a advantage, and turn out just a boring counting game, am I right?

>>16410662
Unless you can exploit the game by taking all the coins in the first move. Just take the whole bigger pile and say you want an even amount of coins from the other pile. Nobody said at the outset that because each pile started as a natural number that I can't end the game with negative coins in a pile.

>>16410662
No, https://en.wikipedia.org/wiki/Wythoff%27s_game
You can know if any given config is winning or losing and start/go second accordingly. You can know this also for big n and m by the method in the wiki article.

:( OP's question never got answered.
>thinking fast and slow
>make it stick
>deep work

It is a dumb question. There is no straight answer. The only answer is: every (n,m) is either winning or losing. If you're lucky enough to go first on a winning position, make a move that takes them to a losing position. That's all it is. Winning and losing are defined recursively out of losing when facing (0,0)

>>16409508
this

>>16409078
Try to understand things you have a hard time understanding. Throw yourself into the middle of a complicated subject rather than starting at the beginning.

>>16409078
I have over 110 IQ but I don't get these concepts because I grew up in a ghetto and was heavily disillusioned around the time of middle school so my math education is garbage. IQ is a meme.

>>16409759
Depends on the number of coins in the remaining pile. You can easily calculate this but idk what the fuck you do if this isnt an option.

>>16409078
Well it depends, are there an equal amount of coins?

If yes then go first and take all the coins.

If no, bait your opponent into taking the last of one pile, then take the last of the 2nd pile and win.

>>16409078
either is fine.

>>16409078
If going first should always take equal amounts of coins of each pile every turn

>>16409078
Simply start taking from the bigger one until your opponent is forced into a 2vs1 position.

>>16414363
Based occultist polygamist

>>16409078
gonna answer without looking at replies. lets say N is greater than M. take an amount so that pile of M coins only has 1 left and N has however many more. now other player has to either take all of one of the piles or one from each. either way I win. thought about it for 1-2 minutes. Am smart?

>>16414959
You can't even read

>>16409078
Wouldn't it be: take all but one coin from one pile, and then the dude is screwed because either A: they divide their take between both piles, leaving a pile of 0 and a pile of X-1 (which you can take all from the former pile), or B take from as much as they want from the other pile, leaving this threat. You force them into a losing situation where they can't leave 1 coin in each pile, as then you can take both, but they can't take the single coin in the one pile, as then you can take all in the single remaining pile.
If their first turn does not result in instant victory on your second turn, then you take all but two in the second pile, forcing them into a situation whether any move they make leaves a coin for you to take.

Am I retarded?

>>16415027
what mean? im saying take an equal number from each pile so that there is 1 pile with 1 left and another with more than 1. now any move my opponent makes will necessarily remove the pile with 1 left and I can take all of the coins in the remaining pile.

>>16415092
u got it

>>16415109
That wasn't hard. I haven't looked at the thread because that's cheating, but what I did see from scrolling down to see your reply seems to be a bunch of fixation on detail over strategy. /lit/ is retarded confirmed

>>16409710
(3,5) is beatable because you take 2 from the three, forcing the opponent's hand. The only losing position is 2,1 and so your goal should be to get to this position.
I explained it here
>>16415092

>>16415118
i got it too :)

>>16415100
>now any move my opponent makes will necessarily remove the pile with 1 left
No it will not
Read again

>>16415118
You actually are retarded. If you leave a single coin in one pile, your opponent can take all but two coins in the other pile and force you into a losing position. Think harder midwit.

>>16415126
Then your opponent takes three from the five, leaving you with the (1,2) losing position.

>>16415204
I'm not my opponent.
The game is simple enough to be beat, meaning that any move has a perfect response. There is no perfect strategy. Any non-midwit knows that often enough it's ok to have a good enough strategy and then act.
>>16415213
I see.

>>16415178
oh
then this shit is b8

>>16409078
> I keep getting distracted from the logic problem by the drawing's tits
this has been more damaging for my ego and my identity than you ever could have hoped for.

>>16415092
He can just take X-2 from the larger pile left to force YOU into a losing scenario (2 - 1 is a losing combination for whoever's turn it is).

>>16414339
But that's why I said "Take all of the coins of one pile except for 1.", it would be the most sound choice not knowing how many coins there are until the end.

>>16415898
If you go first and reduce one pile to either 1 or 2, I will take all but 2 or all but 1 from the other pile, forcing you into a (2,1). It's probably the most efficient strategy to LOSE at this game beyond making the piles equal or reducing one to zero.

The objective is to force (2,1). Take all but 3 from one pile. If your opponent ever takes a coin from that pile -- 1,2, or 3 -- you win because you can either directly take all remaining coins or force him into a (2,1).

If he reduces it to 3, I take two threes. If he reduces it to 2 or 1, I take 2 from the 3. If he reduces it to zero, I directly take the 3.

The only question is how do you steer the game so he's the one to reduce the pile to 3 or less? I will think more on that and post when I solve it, but here's the groundwork.

>>16415944
"It" after the second line being the pile that I did not alter on my first move, sorry for any confusion.

(n1, m1) = initial numbers
(n2, m2) = number after you remove coins on both sides

if (n1, m1) is where (n1 - m1) = (n2 - m2) you go second
if (n1, m1) is where (n1 - m1) ≠ (n2 - m2) you go first

So the strategy is to be in a spot where you're not in the first situation, but I don't know if this would be the solution they're looking for especially if the cutoff to find it is 20 seconds like >>16409885 said.

140 midwit here,
The question is beyond flawed.
Which player do we want to win?
Who goes first?
Does m=n?

I don't know the answer,I get confused just thinking of it.
But It's fine.

>>16416308
Youre a moron. No other person ITT has had a problem understanding the statement.

>>16415220
>The game is simple enough to be beat
Well then let's play. The starting position is (20,13). Do you wanna start or should I start?

>>16416493
You start

>>16416804
Ok
(8,13)

>>16416813
(3,8)

>>16416836
(3,5)

>>16416836
Not so easy now huh

>>16416853
(1,2)

>>16416813
(8,10)

>>16416870
Illegal move. Reread the rules. You took a different number of coins from each pile.

>>16416879
(3,5)

>>16416886
My bad, I don't take any

>>16416899
Read the rules. You must take at least 1 coin.

>>16416901
why?
that doesn't make sense

>>16416930
Because otherwise you could stall the game like you are trying to do right now, moron.

>>16416930
lol rekt

>>16416484
The question is poorly stated and thus refuse to answer it on principle. Should I instead throw out a list of conditionals or stake my victory on who goes first? The question states it's two people playing, but that's not us. Why would I throw out victory strategies when there is so much information left unknown. "Two armies with x military strength and y military strength are going to fight. How do you ensure victory?"

>>16417021
The question is for a given starting position (n,m) do you want to go first or second, and what is the winning strategy based on that position, given that you have chosen whether to go first or second.
now stop pussying out

hey got any more of these? it's amazing how confidently incorrect some people in this thread are

>>16409078
I can't figure out how to abstract it, but the winning strategy is to leave your opponent with two coins in one pile and one coin in another. If starting and m = n, you win. If m = n+1, and it's not 2,1 you win (because you can take n-1 from each pile).

>>16417322
you have the right idea, but there are losing positions other than (2,1) which follow from (2,1) being a losing position

>>16409078
We assume you go first.
We also assume m < n because otherwise the problem is trivial.
We name piles A and B as (#_A, #_B) = (m, n)
> So let's try to break it into first principles
We identify that a player who starts their turn with (1,2) will lose - this is trivial to prove. Similarly we can prove that for starting their turn with (3,y) where y=[1,2,3,4] a player has a winning strategy. Similarly starting with (3,5) is defeat.
We recognise that in the case that the start of your turn finds you at (3,X) you cannot under any circumstance remove a coin from pile A.
> It seems there is a pattern here
Actually, we do. We can prove that for any n if a player starts with (n-1,n) they have a winning strategy whereas if it is (n-2, n) they do not and the other party has. This is trivial. A player starting with (n-1, n) can remove n-2 coins from both piles and produce a (1,2). A player starting with (n-2,n) can produce an (n-2,n-1) == (n-1,n) or increase the difference by k where (n-k, n). It is worth mentioning that removing from any pile will produce these results because n represents the number in the highest pile. A player starting with an (n-k, n) can reduce the largest pile by k-2 such that in the end of their round we have (n-k, n-k-2) or (n-2, n). That process ad infinitum will produce a (1,3) at the end of their second to last round, which is a losing pair.
> So?
So the winning strategy is - assuming the first player doesn't have a (n-2,n) start - to either produce a (n-k, n-k-2)/ (n-2, n) and follow the strategy or, in case of a (n-1,n) follow the strategy.

>>16409885
Pretty cool. I managed to solve this and formulate (poorly) in ~10 min so there's that.Usually I'm better when I can discuss about problems with people. I tend to solve them faster.

>t. CSfag with MSc in ML

>>16417409
Youre wrong. Lets play. Start with (8,10). If I start, according to you I will lose (if you play well).
I make it into (6,10). Your turn.

>>16417434
This is a winning strategy assuming you have the first turn.

>>16417456
>We can prove that for any n if a player starts with (n-1,n) they have a winning strategy whereas if it is (n-2, n) they do not and the other party has.
Youre contradicting yourself. Anyway, lets play.
(12,19). Do you want to start or should I start?

>>16417434
Hey, I am >>16417409 not >>16417456. Let's go.
(6,8) your turn

>>16417502
(3,5)

>>16409078
My IQ is over 135 and I learnt long ago that wasting time of stupid logic puzzles like this is for midwits.

>>16417508
hey, that's nice you won. I have some issues with my edge conditions. Let me check it again.

>>16417512
Oh yeah? What then do you spend your precious time on instead?

>>16417079
A winning strategy implies the other person cannot win. There is no winning strategy as long as the opponent's victory is possible and at that point you might as well just play the game normally.

>>16417528
There is a winning strategy for every case as long as you are the one who decides whether to go first or second.

>>16417434
>CSfag here
btw this is reduntant. You can move immediatelly by making it into (3,5). Don't have time atm but the idea here is how to always make sure that an (n-k, n) is turned into an (n-2,n) or (n-1, n) in the right turn which both lead to (3,5) and (1,2) respectively. My assertion above was wrong. I am strongly confident the one starting has a winning strategy and will try to work out the details

>>16417512
bullshit

>>16409078
If the game starts with 2 equal piles, can I take both of them?
>>16415092
This was my first thought, but I'm unsure if my opponent would be allowed to take both coins, one from each pile.

>>16417612
I see. Wanna play again? (23,40). You can start or I can.
>>16417635
You can take the both piles, yes.

>>16410513
I am afraid you are doomed too.

>>16417668
I'll play with you if you want
I start
(23,14)

>>16417774
I was just asking him to play to verify if his strategy works.
You already seem to know how to play. Lets find out for sure.
(22,14)

>>16417794
(12,20)

>>16417799
Yup you definitely know how to play.
(11,20)

>>16417802
(11,18)

>>16417813
Youre doing all the right moves so theres no point playing anymore. You win.

>>16417794
Hey
>CSfag
Let's play with another pair. Pick it and I may start.

>>16417818
Yeah, that guy hasn't realised the full induction yet I think

>>16417824
(21,36)
Go (or ask me to start)

>>16417833
hm (21,34)

>>16417840
(19,32)

>>16417842
(19,31)

>>16417846
(10,23)

>>16417842
shouldn't you have changed it to (19,31)?

>>16417857
That move is not allowed.

>>16417854
(10,6)

>>16417854
>>16417846
Fuck I meant
(10,22)

>>16417867
Yup you definitely know how to play. All your moves were the right ones. Congratz you win.

>>16417877
>>16417873
Lets play again. (1000, 1500)

>>16417877
Thanks man :)
I haven't formalised the induction yet but I have the algorithm to produce it and which can be found as starting from (1,2) which "covers ground" == "any piles can be thrown here in that distance" for a distance of 1. Then you move to the numbers that has not been addressed 3 for a distance of 2 so (3,5). Then 4 for a distance of 3 so (4,7). Then 6 since 5 has already been part of a pair and you can throw the pile to a (3,5) state already, since you have 5 in a pair etc. etc.

I hope that the spoilers work bc it's been a while I've been to /lit/. Maybe not the highest IQ (I was too lazy to approach the induction from the start and tried to cut corners) but I try to make it up by not letting go. I doubt it's a very healthy approach though.

>>16417921
fuck is that a spoiler

>>16417926
the UX of 4ch is, in this case, misleading.

>>16417921
considering even wikipedia doesnt offer any good traditional formula, the x+1 distance to m for any new n not previously used in a losing position as a concept is what would work best to always win if you get to chose.

>>16417890
not that guy, but (1000,618)

>>16418013
Did you write a script?

>>16418018
maybe

>>16417974
>doesnt offer any good traditional formula
what are you on about, the article gives the formula that works

>>16418031
The algo is super simple anyway and the implementation should be simple as per >>16418028

>t. CSfag