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A mathematical discussion of pong. Mlayth: PLEASE READ!

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prusch Joined: 08.22.2006 Age: 30 Total Games: 145 W/L %: 77.24 Avg CD: 1.70 Full Stats	Posted: Aug 6th 2007, 11:37 pm Post subject: A mathematical discussion of pong. Mlayth: PLEASE READ! Well done Austin... I love the web interface (I need to learn php is all I can say about that).
jjm5750 Joined: 01.01.1991 Age: 39 Total Games: 82 W/L %: 52.44 Avg CD: -0.10 Full Stats	Posted: Aug 7th 2007, 01:35 am Post subject: A mathematical discussion of pong. Mlayth: PLEASE READ! Good job skinny!
thelegend Joined: 08.29.2006 Total Games: 0 W/L %: 0 Avg CD: 0 Full Stats	Posted: Aug 7th 2007, 03:18 am Post subject: A mathematical discussion of pong. Mlayth: PLEASE READ! I've got the attention span of an autistic kid at chucky cheese, so I didn't read all of it. So I'll just say good job anyways.. lol. Where's the reply, Foster?
austin Joined: 01.01.1991 Age: 32 Total Games: 122 W/L %: 77.87 Avg CD: 1.85 Full Stats	Posted: Aug 7th 2007, 05:26 am Post subject: A mathematical discussion of pong. Mlayth: PLEASE READ! skinny I've already got the simplistic version done, which is 1-on-1 pong, and the results are interesting: I see a small drop with the inclusion of a single rollback, and then the win pct does come back for unlimited rollbacks. I will try and extend this to regular pong, and let you know how it turns out... For 1-on-1 pong you only need one stat: Austin's win percentage is 100%.
prusch Joined: 08.22.2006 Age: 30 Total Games: 145 W/L %: 77.24 Avg CD: 1.70 Full Stats	Posted: Aug 7th 2007, 07:19 am Post subject: A mathematical discussion of pong. Mlayth: PLEASE READ! Austin - A couple of things... For the start of the game, when a team only has one shot - I like how you took the better of two players. I noticed that the end of the game is a little funny. I saw one game where the team apparently kept shooting at the last cup (0 remaining... get balls back, hit, -1 remaining, hit, -2 remaining) It might make things screwy when it comes to OT. Well done though. I obviously enjoy seeing the play-by-play when the results are printed out.
mlayth Joined: 01.01.1991 Total Games: 0 W/L %: 0 Avg CD: 0 Full Stats	Posted: Aug 7th 2007, 07:23 am Post subject: A mathematical discussion of pong. Mlayth: PLEASE READ! Well, I am out of state this weekend and I'll need to get back to this when I can read over it more fully and post an appropriate response. I'll try to keep an open mind then consider any mistakes I have made, as with all other people I am only human and have made mistakes, and will continue to make mistakes. That being said, consider I do have some forums with over 15,000+ posts that have nothing to do with beer pong, so try not make out my low post count here as if I am some kind of insane fanatic. Also I did feel like I was attacked a little bit here personally (aside from the ideas that I have suggested), but I am the same time I am very interested in learning more about the game and how these rules change the dynamic. My apologies if I have come off with an ego, sometimes I post quickly and do not sit down and prepare great essays such as skinny does. I am, however, just proposing ideas that I have thought of and have the right to be wrong as much as any other member of this board. If I am wrong - great, then correctly me and allow me to grow as a person. Which perhaps you may have done here, as I was saying before I should be home sometime tomorrow back in maryland and I will have time and paper..etc to go over this. I really do seem to have struck some nerves with the people at bpong, but consider that we really are all on the same side and I have respect for all of you.
prusch Joined: 08.22.2006 Age: 30 Total Games: 145 W/L %: 77.24 Avg CD: 1.70 Full Stats	Posted: Aug 7th 2007, 08:26 am Post subject: A mathematical discussion of pong. Mlayth: PLEASE READ! I was playing around some more with what Austin put together, and I wanted to see if I could dig anything up regarding the findings that skinny first posted. I thought some statistics would maybe help out. Setup: 10 cups Shooting percentage of both players for Team A: 60% Shooting percentage of both players for Team A: 50% Bring It Back Rule: (used all four) Rebuttal Rule: None (mimic the first day of WS play) Last Cup Rule: None Rebuttal Double-ups: None OT: None Games: 1000 I ran the tool 30 separate times, and recorded the number of wins out of 1000 for the team that shoots 60%. I re-did that test for each bring-it-back rule. I then calculated a mean/st. dev. so that the numbers could tell a little more truth, just to make sure they're not lying No bring-it-backs: 726 +/- 13.7 (One Sigma Range- 712-740) One ball: 723 +/- 13.7 (One Sigma Range- 709-736) 2 balls: 714 +/- 17.2 (One Sigma Range- 697-732) Unlimited Doublebacks: 713 +/- 9.55 (One Sigma Range- 703-722) The numbers still support the idea that unlimited doublebacks do not help ensure the better team wins, but rather that the added volatility only gives a weaker team a better chance. As far as distinguishing what the deviations mean, my statistics education would tell me that the difference is negligible between case one and two, and between 3 and 4. I do not have an explanation for the low deviation for case #4. Seeing as that would seemingly be the most volatile case, one would expect the deviation to be highest. I'd like to do this for other combinations of shooting percentages, but was just thinking a quick code change can make that possible. Or... someone can tear apart what I did as wrong... which I definitely can say might happen after I broke something out after not having used it for 6 years.
austin Joined: 01.01.1991 Age: 32 Total Games: 122 W/L %: 77.87 Avg CD: 1.85 Full Stats	Posted: Aug 7th 2007, 02:03 pm Post subject: A mathematical discussion of pong. Mlayth: PLEASE READ! Yeah, I allowed the end of the game to go into negative cups just because it doesn't make a difference in the long run and it also make the "two balls in the last cup" rule work a little easier. In one of my test games the one team got to like -7 cups but it really doesn't effect the outcome of the game. prusch Austin - A couple of things... For the start of the game, when a team only has one shot - I like how you took the better of two players. I noticed that the end of the game is a little funny. I saw one game where the team apparently kept shooting at the last cup (0 remaining... get balls back, hit, -1 remaining, hit, -2 remaining) It might make things screwy when it comes to OT. Well done though. I obviously enjoy seeing the play-by-play when the results are printed out.
skinny Joined: 01.01.1991 Age: 31 Total Games: 1 W/L %: 100 Avg CD: 1.00 Full Stats	Posted: Aug 7th 2007, 03:46 pm Post subject: A mathematical discussion of pong. Mlayth: PLEASE READ! mlayth: glad to see youre taking this in the right spirit. believe me, no personal attack was intended - just figured that i needed to argue with vigor on this one.... prusch: I actually just ran 30 trials of the unlimited scenario and I got a s.d. of 13.6. In theory, every game should be independent of every other game. Therefore, the probability distribution for 1000 games should be binomial, with n=1000 and p = the expected winning percentage for each game. In this case, say p=71%. Then the variance for 1000 trials should be np(1-p) = 1000.71(1-.71) =205.9, giving a s.d. of 14.3. As p gets closer to 50%, the s.d should go a little bit higher (max of 15.8 or so). In other words, all of the scenarios should have pretty much the same standard deviation on 1000 trials (with the only difference coming from the actual win pct)....I think that the standard deviation you observed was a bit of a fluke.... mLayth Well, I am out of state this weekend and I'll need to get back to this when I can read over it more fully and post an appropriate response. I'll try to keep an open mind then consider any mistakes I have made, as with all other people I am only human and have made mistakes, and will continue to make mistakes. That being said, consider I do have some forums with over 15,000+ posts that have nothing to do with beer pong, so try not make out my low post count here as if I am some kind of insane fanatic. Also I did feel like I was attacked a little bit here personally (aside from the ideas that I have suggested), but I am the same time I am very interested in learning more about the game and how these rules change the dynamic. My apologies if I have come off with an ego, sometimes I post quickly and do not sit down and prepare great essays such as skinny does. I am, however, just proposing ideas that I have thought of and have the right to be wrong as much as any other member of this board. If I am wrong - great, then correctly me and allow me to grow as a person. Which perhaps you may have done here, as I was saying before I should be home sometime tomorrow back in maryland and I will have time and paper..etc to go over this. I really do seem to have struck some nerves with the people at bpong, but consider that we really are all on the same side and I have respect for all of you.
mlayth Joined: 01.01.1991 Total Games: 0 W/L %: 0 Avg CD: 0 Full Stats	Posted: Aug 7th 2007, 04:44 pm Post subject: A mathematical discussion of pong. Mlayth: PLEASE READ! I'll break up this response into a couple of parts.. First: You don't need to put my name in a title for me to read a thread, I pretty much read everything here haha skinny He exhibits a great deal of confidence when posting, and generally assumes that his ability to understand the mathematical basis of pong is extremely strong (and better than everyone elses on here). On this board, and a couple of others, I give up my time to try to help people. Answer their questions about beer pong, and grow the sport and size of the community. I can see how my matter-of-fact posting style may come off as arrogant, but I do not see it that way. It's not so much a matter of intelligence, but a matter of time dedicated and research that other people may not have done. For example I am on here talking to you, and now in the future anyone who asks me questions may get a matter-of-fact answer out of me that is simply a paraphrase of what you have taught me. So because of my experience I try to borrow from that and help people where ever I can. skinny I have read many of the posts that Mlayth has made over the past. I am, in general, shocked with the conclusions that he comes up with, as he is, in my opinion, does not employ proper logic. I will take your shock at my shortcomings as a compliment, since I assume that you wouldn't exhibit shock toward the errors of every person you meet. skinny For some reason though, Mlayth has claimed that this means that having rollbacks benefits better players (he has repeated this about 10 million times). I have always been really, really annoyed by this argument, because it is completely abstracting many very important concepts in probability theory (some of which are basic concepts, some of which are not). These concepts are something you probably should have brought up earlier.. I've done a ton of calculus, lambda calc.. linear algebra, discrete math, algorithmic analysis..etc but only a single class on statistics. I don't think I'm perfect - but it's as you said before, most people on this board don't have that same kind of background. It's for that reason that I am stepping up to the plate, and trying to do my best to help contribute where my strengths may aid other peoples weaknesses. In turn their strengths can counterbalance my own shortcomings, and hopefully with all of us we can form a complete picture. If not for my meddling, I don't think some of these topics would have gone nearly as in depth, and we would not have come to as deep of an understanding of the game. So perhaps you can explain something to me. I know that the skill curve is mathematically solid, and judging by the tests preformed by austin and yourself it appears that better players are not given the kind of advantage one would be lead to believe. You've shown me the numbers.. but whats the reason. Why not?