Tie Condition Eliminated

The tie condition has been eliminated. A point is now awarded based on 9,999 coin flips, so that there is truly a 50/50 distribution as opposed to a 50.4/49.6 like there was before.

Of course, the statistics calculated before still apply in principle. At one point I ignored the tie condition, but in my last post, since I realized it's probability was 0.4%, I mentioned it. The adjusted value of a 0.01% affect is 0.8%.

I'm going to make stats up 'til this point (10:30 PM Tuesday, May 25th, 2010) be listed under the "Pre-Alpha" section of some upcoming statistics page, and the ones after that under the "Alpha" section.

For now, stats are piled into one, sorry newcomers, your job is 0.4% harder, but I think you can live up to it.

Also, at the top of my to-do list is make the matches won/lost and percent available on the stats page. That should be even greater of a deviation than the number of points won, although exactly how much I haven't calculated yet, but I will.

Enjoy Psychic Ball!

Measured Affect of Mind on Matter by PEAR

So, I've been looking for some mind-matter data to help me get a bearing of, "is Psychic Ball getting the expected results, is this a fun game mechanic," etc. and I found this to be right up my alley.

From http://www.princeton.edu/~pear/pdfs/correlations.pdf (top of page 7)

Consistent with the terminal values listed in Table 1, the average slopes of these two patterns of
achievement, in units of bits deviation per bit processed, are roughly 1.3 × 10–4 and –7.8 × 10–5
respectively.

What that's saying is that people were able to affect the random distribution by about +0.013% when trying to increase the number of events and -0.0078% when trying to decrease the number of events.

I ran the calculation for Psychic Ball, and if you can have a +0.01% affect on the number of 1s that come up in 10,000 calls of rand(0,1) in the PHP script (which Princeton's PEAR suggests that you can), then you increase your chance of winning a point from 50.4% to 51.2%. (The 50.4% is actually because there is roughly a 0.4% chance of splitting 5,000 to 5,000, and right now I'm giving red the tie. I know, not fair, I need to change it. Don't worry, all the data is dated, so I can mark it and distinguish it when I make a change.)

So, the summary is this: Princeton Engineering Anomalies Research (PEAR) shows that on average, people can affect the distribution of random events by more than +0.013%. So shoot for a points won percentage of 51.2% or higher against the computer. Once playing other players is implemented, it will be a whole new ball game.

Keep playing Psychic Ball at http://psychicballgame.com!

Psychic Ball Scores

So, I'll probably add this report to the a new page soon, but here's what we have so far:

Points Won	Points Lost	Percent	Games Played	User
269	230	0.5391	3	Guest
1919	1830	0.5119	22	Zanthir
271	238	0.5324	3	Rebi
52	70	0.4262	1	Test
102	93	0.5231	1	Melissa

Sorry, Jing. You're not on the report, because you haven't played any games. I'm going to hold off on any statistical analysis of the data so far, because, well, there is so little, and I expect so much more. It would be interesting, though, to see if it made a difference whether the points awarded are based on one random event, or 10,000. I could always make another mode of play to test that.

Tell me what you think of the data so far. I know there is so little, but I just wanna chat with someone. :)

Site Map Up

Please start at http://psychicballgame.com/Home.php. The four working pages are:

• Home
• Play
• Log In
• Sign Up

Actually there are two Play pages, one if you're not logged in, one if you are. You can link to two broken pages right now, Log Out, and Account. Your logged in status will remain for ten minutes as is.

Enjoy the updates!

Reverse Look Up Table for Psychic Powers

Below is a table that allows you to look up your calculated affect on the probability of each coin flip that goes into determing every point. Since ten thousand (10,000) coin flips go into every point (the little red/blue squares at the center), a small affect on the probability can have a large affect on your probability of winning a point.

For example, a 0.05% affect on your probability of winning a coin flip translates into a 3.98% increase in your probability of winning a point.

Here's how you use it. Look up your calculated % chance of winning a point on your stats page (does not exist yet), and match that as closely as possible to the number at the right, under P(Z > z) = P(Winning a Point). Then go to the left in the same row to find your correlating probability of winning a coin flip.

Enjoy!

n = Number of Trials	p = P(Winning a Coin Flip)	E[X] = np	STD[X] = sqrt(npq)	z = ( 5000 - E[X]/STD[X])	P(Z > z) = P(Winning a Point)
10000	0.5050	5050	49.8075	-1.0001	0.8413
10000	0.5045	5045	49.8080	-0.8000	0.8159
10000	0.5040	5040	49.8084	-0.8000	0.7881
10000	0.5035	5035	49.8088	-0.7000	0.7580
10000	0.5030	5030	49.8091	-0.6000	0.7257
10000	0.5025	5025	49.8094	-0.5000	0.6915
10000	0.5020	5020	49.8096	-0.4000	0.6554
10000	0.5015	5015	49.8098	-0.3000	0.6179
10000	0.5010	5010	49.8080	-0.2000	0.5793
10000	0.5005	5005	50.0000	-0.1000	0.5398
10000	0.5000	5000	50.0000	0.0000	5.0000
			*q = 1 - p

mysql> select * from games;
+--------+-------+--------+-----------+------------+-------+
| gameid | redid | blueid | redpoints | bluepoints | score |
+--------+-------+--------+-----------+------------+-------+
| 1 | 3 | 1 | 91 | 80 | 76 |
+--------+-------+--------+-----------+------------+-------+

The above means that game 1 was played by user 3 and user 1, and user 3 scored 91 points, and user 1 scored 80 points, and the last set was 7 to 6.

Translated this means the computer and I (blue and red, respectively) played the first game entered in the database, that I scored 91 points, and the computer scored 80 points, and that I won the last set 7 to 6.

This "last set" score at the end has been fixed to record a six digit code that is the set scores for all three sets (or four digit code if it was a two set match). I know, I may still need to explain how the game works, but that will come soon on an info page at psychicballgame.com. The score format is RBRBRB where the first two are the number of games in the first set for red and blue ... I digress. You don't need to know this anyways, because I'm going to parse it and turn it into pretty reports anyways.

So, please visit http://psychicball.com/LogIn.html and log in as "Guest" with password "password" to record some data for the user Guest. You will be playing against the user Computer, for now. You are Red, for score keeping purposes.

Please try to make red win. This will go a little way towards collecting useful data, as I am trying to show that by trying to make one side win, it affects the probability distribution of the random numbers generated. Again, I'm just using PHPs built in rand(0,1) function.

Enjoy, and look for a sign up page coming soon!

Demo Up

Please visit http://psychicballgame.com/ and demo the game. Remember, focus your psychic power on getting the color of your choice to appear.

I just redid the calculation for 10,000 random events for determining one point, as the game is being played now, and if you can affect the probability from 50% to 50.5%, your expected value is 5050, which means you expect to win every point, and your stadard deviation is almost exactly 50. This meas you should expect to win 84.13% of the points.

For any math nerds, this is: for the number of coin flips won out of 10,000, X, with the probability of a coin flip being 50.5%, the probability of winning a point in Psychic Ball is

P[X>5000]=P[Z>1]=.8413

based on the area under the curve of the normal curve looked up in the Z-table of any given statistics book.

So, at some point, once I get user sign up and log in pages up, and a version that records your game data, I will make a conversion chart that will let you look up your measured affect on the random events. In this example, a win rate of 84.13% of the points gets converted into winning 50.5% of the random events I refer to as coin flips (actually the function rand(0,1) in php, zero bein for blue, one being for red).

So, just to be clear, those are the three things that are in line to go up on http://psychicballgame.com/. Again, they are

• User Sign Up Page
  
• User Log in Page
  
• Psychic Ball with Database Records

Hope you enjoy it so far!