dank memes

Jaleb says

Giving us results from fp gives us zero valid information for whatever tl;dr you gave us.

It only suggests that there was a pattern for the small sample of ten rounds, and it wasn't a good measure of what the actual roles of the boxes would be either.

The 6700 Other trials seem to hold steadfast, though, and I'm collecting more data.

Giving us results from fp gives us zero valid information for whatever tl;dr you gave us.

uhuh yep, this makes sense.

Applying polish, or doubling down:

If we can see that there is a 50% chance of being on the left or right, we can also then narrow down the odds further by applying the curve expected for the law of averages on 50/50, if we treat the right as one side of a coin, we can bet on the opposite should a streak start to emerge on going right or left.

Maximum bets and the double 00 (null) were introduced to prevent the Martingale system from being profitable in the long run, however it did not actually prevent the Martingale system being effective.

This is because a person can wait around the tables to find streaks of heads or tails before they even start doubling down at all, otherwise capitalizing on the trials of other people whom have lost.

Other possible explanation:

http://www.thecalculatorsite.com/images/articles/20140409-dice-probabilities.jpg

After 7 Trials are done we can consider this a single instance where the odds of 1/7 have had their opportunity to appear as one pinball heading down the path 7 Times just as expected.
However if the pinball has the option to go down the path 8 Times, if it does go down that path the pinball has essentially rolled a double 7 out of two 7-sided dice throws.

Weight is biased towards the right:

http://i.gyazo.com/7ae641e95b14018366743503d9f09909.png

Weight bias towards left:

http://i.gyazo.com/af3d533a74f8afb85070c7736822fbfb.png

In both cases it is unlikely to find a Mafia in the middle of the boxes.

Total trials done by myself now exceeds 10,000. Trials done to falsify this theory appear to be 0. Tl;dr, I don't need your pity.

pity post

http://www.mathsisfun.com/data/quincunx.html

This tool can be used to demonstrate that.

http://gyazo.com/2ca32a1c56416c3af8efdb042acc8e94

0.50 Chance of heading left or right. Over 4,700+ Trials the pattern is demonstrated, the expected result is confirmed; more of the balls have landed on the positions of -1 and 1.

For a weight that is higher, it will tend towards the left or right respectively, however one should always apply a mirror and note that it was equally likely that it landed on the - or + equivalents, with little deviation at least, from these two paths.

Or to put this in even simpler terms. If you make a graph that records outcomes of trials that include chance, you will see that the landing positions for the majority of the events corresponds to their positions from zero.

A chance of 50/50 means that the the positions that someone lands on a graph is simply going to be concentrated in +1 and -1.

Whereas if someone had a 25% chance, they would land on numbers 3, 4 and 5 More often than any other number, due to the law of large numbers reflecting their weighted values.

However, the inverse is always true as well, meaning that they are just as likely to land on -3, -4, and -5.

However it becomes clear which of the two scenarios is most likely from the moment that the first event happens. If they're heading left, all probability tells us that they will keep heading left until they reach the positions they're expected to be in, from 0.

How this works:

A weighted chance of 1/7 Essentially just means that from the centre (0) you are more likely to take 7 Right or left turns, in this case right and left is just "up and down".

If there are two players that take right turns with the odds of 7 in that direction, on the seventh, they will simply fall into the only available box (2, or 6).

This means that if the Mafia is both on the bottom, the most likely positions of the power roles are 1, 2, and 5.

If you and your partner occupy top and bottom box, instead of being on the same side, assume that power roles are likely in the boxes 1 and 7.

This theory is falsifiable, under the condition that the weights do not result in the games showing that Mafia ends up in boxes 1 and 7 more often.

Any other observation would just suggest that they do.

http://i.imgur.com/fqdpmUz.png

Post-game recording of roles do not reflect actual positions of players in the boxes on the right side.

This just means that if anyone wants to see the pattern form in-game, they have to record the positions of each player at the start of the round and compare them to the post-game positions.

If there is no pattern and randomness is assumed, we will not see the bellcurve form. Over time, the distribution of roles would be perceived as a flat line.

The alternative is that a flat line does not form very commonly, suggesting a bellcurve that points towards Mafia being within the top and bottom boxes more often than other roles.