The purpose of the post is to share with others how I **suspected**
when a slot game is "not random." Anyone can apply this technique
to vp, but that is not the thrust of the post.
The game is a slot machine called "Wheel of Fortune Triple Action"
http://www.igtonline.com/megajackpots/new_games/wof_video_slots.html
The key point is the following "You select from the two rows of
tiles at the bottom of the screen to reveal letters or a pointer in
the three puzzles." There are 20 tiles, of which 15 are consider
good and 5 are consider bad. The difference is that a bad tile
immediately ends the bonus round and limits the winning amount.
The math - this is called sampling without replacement because each
exposed tile does not get thrown back to the original pool, i.e. on
each succesive pick, the odds of getting a bad tile increases,
respectively. On average, a player should pick 2.5 good tiles.
Sometimes, you pick one good tile, sometimes, you pick 6 good tiles,
etc, but on average, **assuming the tiles are random**, you should
average 2.5 good tiles.
The first time I played this game, I was having fun picking tiles
(reminds of Jackpot Party) so I wasn't thinking about keeping
statistics. 3 weeks later, I decided to keep statistics and when I
replayed the game, I notice something was different. I hit a total
of 8 bonus rounds and the first 4 times I hit a bad tile on my
first try (i.e. busted out the first tile). In fact, I hit a bad
tile on the first attempt in 6 of the 8 bonus rounds. I hit 4 tiles
(i.e. 3 good tiles followed by a bad tile) once and 2 tiles once.
It soon became obvious the bonus round **could be** rigged.
I kept choosing the same tile (or same sequence of tiles) to control
for the game. The probability of me hitting a bad tile on the first
shot was 25% and that occurred 4 times in a row? Additionally, that
occurred 6 of 8 times? I went home and ran an excel spreadsheet
using the HYPGEOMDIST function, and here are the exact probabilites
(number of successful trials in a row out of the same number of
trials [i.e. picking good tiles in a row before a bad tile], and
associate probabilities) - note the sum of the success is 2.5,
which is the average number of tiles to be chosen:
1 0.7500000
2 0.5526316
3 0.3991228
4 0.2817337
5 0.1936920
6 0.1291280
7 0.0830108
8 0.0510836
9 0.0297988
10 0.0162539
11 0.0081269
12 0.0036120
13 0.0013545
14 0.0003870
15 0.0000645
Sum: 2.5000000
So how did I **suspect** the game wasn't random? I quit playing
and observe other players, who were also experiencing the same
problem of busting out on the first tile. The probability of busting
out on the first tile for 4 straight times is (1/4)^4 or 0.0039;
and, the probability of 6 of 8 trials busted out on the first tile
is 0.0038 (here, I used Binomdist function set to false). Do you see
the pattern?
For VP, given enough observations of hands played and winning hands
(i.e. quads, FH, FL, ST, and Trips), you can apply this technique
for vp, and the results should help support where a game is random
or not.
Lastly, you can never prove a game is random or not random with 100%
certainity, but you can make a very strong case.