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On April 24 2013 12:09 h3r1n6 wrote:Show nested quote +On April 24 2013 12:05 Sufficiency wrote:Oh man. I am doing some research on creating an algorithm that will allow me to find a way to get to 0 RP (thus "beating" the game) with the minimal amount of RP purchases... and it seems more difficult than I originally envisioned. + Show Spoiler +And it seems very interesting! http://en.wikipedia.org/wiki/Knapsack_problem
Yep.
First of all, I am pretty sure I can get rid of the inequality by adding slacking variables so my problem becomes a Knapsack problem (needs to be checked). Assuming that works out, then there is the problem that algorithm given above is only for 0-1 Knapsack, so I probably need to study the code more carefully and see if I can adapt and make it into 0-N Knapsack where N is some reasonably big number (I don't care for unbounded because there is a limit to the number of items I can purchase).
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On April 24 2013 12:05 Sufficiency wrote:Oh man. I am doing some research on creating an algorithm that will allow me to find a way to get to 0 RP (thus "beating" the game) with the minimal amount of RP purchases... and it seems more difficult than I originally envisioned. + Show Spoiler +And it seems very interesting!
From 0 or a variable starting point?
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Oh wait, I'm really tired, didn't realize that there aren't values and weights. Unless you want to prioritize what you buy.
There aren't that many different prices in the store (20ish?, 40 tops when counting boosts and sales), so you can just compile a list of combinations for rp numbers, store them and compare if one of them fits a specific value you have. It's the brute force method, but it'll be very easy to code and be still fast.
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On April 24 2013 12:24 Gahlo wrote:Show nested quote +On April 24 2013 12:05 Sufficiency wrote:Oh man. I am doing some research on creating an algorithm that will allow me to find a way to get to 0 RP (thus "beating" the game) with the minimal amount of RP purchases... and it seems more difficult than I originally envisioned. + Show Spoiler +And it seems very interesting! From 0 or a variable starting point?
From a variable starting point would be ideal.
On April 24 2013 12:25 h3r1n6 wrote:
Oh wait, I'm really tired, didn't realize that there aren't values and weights. Unless you want to prioritize what you buy.
There aren't that many different prices in the store (20ish?, 40 tops when counting boosts and sales), so you can just compile a list of combinations for rp numbers, store them and compare if one of them fits a specific value you have. It's the brute force method, but it'll be very easy to code and be still fast.
I agree, and that's one of the approaches I am considering.
First I will set an arbitrary bound of the money I am willing to spend, say, 200 dollars. With it, I can produce (I believe) less than 100 different amounts of RP for my account. But ultimately I still need to be able to check whether or not a particular amount of RP can become 0 by purchasing in-game contents (i.e. detecting the existence of non-negative solutions for a multivariate linear diophantine equation).
Ideally, if there is a quick way to solve these diophantine equations, they can be done on the fly. Otherwise, I guess I can brute-force it then tabulate these values.
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It sounds actually very similar to snakes and ladders which I thought was a ridiculously difficult algorithm. You've got purchases of RP (ladders) and expenditures of RP(snakes) and there are so many scenarios to consider on every step. The difference though is that it doesn't really matter which order you do the purchases of RP or expenditures.
My advice is to draw out all the scenarios by hand of a simplified problem and see if the amount of work needed to solve the problem by hand increases with time. If the problem is harder than that I give up.
Gahlo has a good point, if you are starting at 0RP then the problem can probably be solved by hand 
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OK so after thinking about it during a washroom break I think I will just make a chart of RP amounts that can go to 0 with in-game purchases, save that chart, then take a look to see if I can get to any of the values in the chart by buying more RP. It's pretty much entirely brute force, but it's simple to implement and what I was thinking about diophantine equations and Knapsack are just making things way too complicated.
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On April 24 2013 12:47 Sufficiency wrote:
OK so after thinking about it during a washroom break I think I will just make a chart of RP amounts that can go to 0 with in-game purchases, save that chart, then take a look to see if I can get to any of the values in the chart by buying more RP. It's pretty much entirely brute force, but it's simple to implement and what I was thinking about diophantine equations and Knapsack are just making things way too complicated.
My favorite: 650($5)*3 = 1950 = 975*2
Once I got to zero, I'm always there, =]
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On April 24 2013 12:51 Gahlo wrote:Show nested quote +On April 24 2013 12:47 Sufficiency wrote:
OK so after thinking about it during a washroom break I think I will just make a chart of RP amounts that can go to 0 with in-game purchases, save that chart, then take a look to see if I can get to any of the values in the chart by buying more RP. It's pretty much entirely brute force, but it's simple to implement and what I was thinking about diophantine equations and Knapsack are just making things way too complicated. My favorite: 650($5)*3 = 1950 = 975*2 Once I got to zero, I'm always there, =]
"We have lowered the price of one of the legendary skins you own. To compensate, have 470 RP back"
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On April 24 2013 12:57 thenexusp wrote:Show nested quote +On April 24 2013 12:51 Gahlo wrote:On April 24 2013 12:47 Sufficiency wrote:
OK so after thinking about it during a washroom break I think I will just make a chart of RP amounts that can go to 0 with in-game purchases, save that chart, then take a look to see if I can get to any of the values in the chart by buying more RP. It's pretty much entirely brute force, but it's simple to implement and what I was thinking about diophantine equations and Knapsack are just making things way too complicated. My favorite: 650($5)*3 = 1950 = 975*2 Once I got to zero, I'm always there, =] "We have lowered the price of one of the legendary skins you own. To compensate, have 470 RP back"
Speaking of which, when will the RP changes take place?
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On April 24 2013 12:57 thenexusp wrote:Show nested quote +On April 24 2013 12:51 Gahlo wrote:On April 24 2013 12:47 Sufficiency wrote:
OK so after thinking about it during a washroom break I think I will just make a chart of RP amounts that can go to 0 with in-game purchases, save that chart, then take a look to see if I can get to any of the values in the chart by buying more RP. It's pretty much entirely brute force, but it's simple to implement and what I was thinking about diophantine equations and Knapsack are just making things way too complicated. My favorite: 650($5)*3 = 1950 = 975*2 Once I got to zero, I'm always there, =] "We have lowered the price of one of the legendary skins you own. To compensate, have 470 RP back"
Jokes on them, they'd have to lower the price of PFE.
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On April 24 2013 12:59 Sufficiency wrote:Show nested quote +On April 24 2013 12:57 thenexusp wrote:On April 24 2013 12:51 Gahlo wrote:On April 24 2013 12:47 Sufficiency wrote:
OK so after thinking about it during a washroom break I think I will just make a chart of RP amounts that can go to 0 with in-game purchases, save that chart, then take a look to see if I can get to any of the values in the chart by buying more RP. It's pretty much entirely brute force, but it's simple to implement and what I was thinking about diophantine equations and Knapsack are just making things way too complicated. My favorite: 650($5)*3 = 1950 = 975*2 Once I got to zero, I'm always there, =] "We have lowered the price of one of the legendary skins you own. To compensate, have 470 RP back" Speaking of which, when will the RP changes take place?
April 25th
http://euw.leagueoflegends.com/board/showthread.php?p=11168003#post11168003
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On April 24 2013 12:47 Sufficiency wrote:
OK so after thinking about it during a washroom break I think I will just make a chart of RP amounts that can go to 0 with in-game purchases, save that chart
That chart is harder than you think:
http://mathworld.wolfram.com/FrobeniusNumber.html
Edit: On second thought, its only hard if you want to find an elegant upper bound. You can brute force out the chart with basic linear combination iteration up to some reasonable/arbitrary upper bound of input RP values.
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You may also want to consider the dollar to RP ratios of each purchase level in order to also get the most RP for your money? Gahlo's example made me think of this, $5 RP purchases are pretty inefficient from a cost perspective.
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On April 24 2013 13:34 YouGotNothin wrote:
You may also want to consider the dollar to RP ratios of each purchase level in order to also get the most RP for your money? Gahlo's example made me think of this, $5 RP purchases are pretty inefficient from a cost perspective.
Yeah. For me, sitting there at 0 or 975 is much nicer than having the 80 "bonus" RP from a $10/$5 setup. Then again, I also rage about the CDR mastery in offense not being a nice 5% by doing 1.25/point.
I view it as fast food drinks. I could get X more for 30 cents, and it makes economic sense to do so, but I don't want it.
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On April 24 2013 13:18 xes wrote:Show nested quote +On April 24 2013 12:47 Sufficiency wrote:
OK so after thinking about it during a washroom break I think I will just make a chart of RP amounts that can go to 0 with in-game purchases, save that chart That chart is harder than you think: http://mathworld.wolfram.com/FrobeniusNumber.htmlEdit: On second thought, its only hard if you want to find an elegant upper bound. You can brute force out the chart with basic linear combination iteration up to some reasonable/arbitrary upper bound of input RP values.
Yes, that's the plan - brute force linear combinations... starting from the smallest values.
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On April 24 2013 13:37 Gahlo wrote:Show nested quote +On April 24 2013 13:34 YouGotNothin wrote:
You may also want to consider the dollar to RP ratios of each purchase level in order to also get the most RP for your money? Gahlo's example made me think of this, $5 RP purchases are pretty inefficient from a cost perspective. Yeah. For me, sitting there at 0 or 975 is much nicer than having the 80 "bonus" RP from a $10/$5 setup. Then again, I also rage about the CDR mastery in offense not being a nice 5% by doing 1.25/point. I view it as fast food drinks. I could get X more for 30 cents, and it makes economic sense to do so, but I don't want it.
In another economic sense (a game-theoretic one) you actually get weakly less for "bonus" RP because it comes in meaningless amounts (unless you're buying $100 of RP at once).
Gaining 300 bonus RP is basically gaining 0 RP because you have to spend more money to actually be able to spend it on anything.
So if you can solidly say that your lifetime desire for RP purchases will be under some ceiling where the bonus chunks don't add up enough then you should actually purchase RP in the smallest pieces possible for optimal income/consumption smoothing.
Edit:
I will add that unless this is your final purchase of RP ever to rebalance to 0 that you're actually playing into the game rather than beating it.
The value-added system is basically a tax put on your money to spend it which you can rephrase as a increased cost to the purchases you're making.
If having a leftover inclines you to spend more money to even it out than you would've if you had just been billed the taxed amount upfront, then you are basically playing right into the sales idea of value-added systems.
i.e. unless you wanted to spend $20 anyways, you're basically spending $20 to avoid spending $15.83 which is a net loss
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PBE ARAM Elo tooo high.
![[image loading]](http://i.imgur.com/yr6QYt1.png)
It's seriously super fun and I can't wait for it to go live.
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Korea (South)11232 Posts
Shy is now no.1 for toplane korean all-stars team
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United States23455 Posts
Top - (1) MakNooN (35.5%) / (1) shy (35.5%) / (3) Reapered (9.8%)
Jungle - (1) inSec (49.1%) / (2) CloudTemplar (23.3%) / (3) Watch (9.7%)
Mid - (1) Ambition (42.5%) / (2) RapidStar (23.2%) / (3) Faker (15.7%)
ADC - (1) Pray (40.3%) / (2) Locodoco (30.5%) / (3) imp (11.5%)
Sup - (1) MadLife (81%) / (2) Cain (7.6%) / (3) PoohManDu (3%)
Coach - (1) Reach (Najin) (51.4%) / Im Hyun-suk (MVP) (20%)
Updated on: (April 24) / Voting ends on: (April 24)
cya, maknoon
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maknoon v shy 1v1 lets go~
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EPT
