TL;DR: roulette was OP as hell, is currently unplayable, and at the end is my proposed layout based off of 3000 rolls that I recorded by hand

Hey guys, so today when I was grinding in the casino I decided to record all the bets I placed, as well as a few hundred that I witnessed but did not place myself. The results were

total trials: 3003
total black: 1809 (~60.2%)
total red: 1194 (~39.8%)

Expected outcomes (keep in mind this was with 4 red tiles and 8 black tiles, so pre-nerf):
Black expected value: (1809/3003) * (2/1 payout) = 1.205
Red Expected value: (1194/3003) * (4/1 payout) = 1.590

This was how me and many others were able to "game" the casino: for each bet on red we profited a half coin gain in the long run. For a stable economy, this couldn't be allowed to persist and why I myself lobbied for a nerf. However, these results do show that not every pressure plate had an equal chance of being landed on. Since at the time each of the 4 middle plates were red and the 8 corner plates were black, the chance of landing on each of the plates are (assuming each middle plate and each corner plate have the same chance of being landed on):

corner plates: (1809/3003) * (1/8) = 7.53%
center plates: (1194/3003) * (1/4) = 9.94%

I am not sure whether the admins are tracking this type of data, although I would be interested in more accurate data with a larger sample size.

Now, on the current (post-nerf) table, the admins have switched out 2 of the 4 red plates and 3 of the 8 black plates in favor of green tiles where the player loses no matter what they bet on. When i calculated the expected returns for the game now, i got:
Black expected value: (1809/3003) * (2/1 payout) * (5/8 adjustment) = 0.753
Red Expected value: (1194/3003) * (4/1 payout) * (2/4 adjustment) = 0.795
Since both values are less than 1, a player can expect to lose coins in the long run (and quite quickly, i might add). If these are the odds, then I see no reason to ever play roulette. I don't know what further balancing changes the admins have for us (if this was a temporary fix to stop the exploiters or not), but Ideally these numbers would be much closer to 1 to entice players to actually play the game.

Therefore for my own entertainment I decided to redesign the roulette table to make it closer to even. This means that if we keep the same bet payouts (black pays 2 to 1 and red pays 4 to 1), then black would ideally get rolled 50% of the time, and red would get rolled 25% of the time in a game where neither the players nor the casino has an advantage (rather purely luck-based). Consider the following symmetric table layout:
__R_B_G__
B________B
G________R
B________B
__R_B_G__
Under such a layout, the payouts would be:
Black expected value:[ (1809/3003) *(4/8 corner plates) + (1194/3003) * (2/4 center plates) ]*(2/1 payout) = 1.000
Red expected value:[ (1809/3003) *(2/8 corner plates) + (1194/3003) * (1/4 center plates) ]*(4/1 payout) = 1.000
Using my data, this would be a perfect layout to make betting on both red and black a viable, fair strategy akin to flipping a coin. Also if there is a mechanical problem with adjacent corner plates (I notice sometimes the guardian presses down both at once), the following adjustment could be made, sacrificing some symmetry for practicality:
__R_B_B__
R________B
G________R
B________G
__B_B_G__
Which is my final suggestion for an unbiased roulette table.

TL;DR: roulette was OP as hell, is currently unplayable, and at the end is my proposed layout based off of 3000 rolls that I recorded by hand

If you made it this far, thanks so much for reading. I spent a considerable amount of time collecting data for this post today while grinding the casino for 8-10 hours, and made this post in the hopes that there will be enough incentive for me to play roulette again for fun in the future.

This is some very interesting data, it will certainly be taken into account when staff do some more balancing tweaks in the coming days.
Thanks for supplying it.

If the roulette is biased against players then no one will want to play. It seems to me it should be slightly in the players favour. And if some one is mad enough to play it for hours then good luck to them.

It was so loaded that it was devaluing the crafty coin so I guess somewhere in between would be nice. Roughly so that you get the same amount of wealth you would as if you had been mining.

Thanks mate we're collecting all the data we can posts like this are helpful.

I thank you for the analysis, it means alot that someone would take the time to sinserly calculate the odds.

Its true, at the begining it was way over powered, and thats my fault. I forgot human nature is to abuse a situation. And yes, its true that my edit of the green tiles broke off the winning, but then what casino really lets the people win XD

Jest aside, i feel that your calcualtions, while sound, are missing a crucial variable- the guardian.

And that throws in a randomness that seems uncalculatably miniscule, but is vital to your overall answers. My algebra is a little rusty unfortuantly, but i think it would look something like..

Black expected value: (1809/3003) * (2/1 payout) * (5/8 adjustment)= 0.753^G
Red Expected value: (1194/3003) * (4/1 payout) * (2/4 adjustment) = 0.795^G

With G being the unknown calculable of the guardian, lets give it a variable based on possible directions, 8 initial directions against 12 possible plates, .6 on the scale seems fair that it would hit a plate without changing direction-

So
Black expected value: (1809/3003) * (2/1 payout) * (5/8 adjustment) = 0.753^.6 =1.3
Red Expected value: (1194/3003) * (4/1 payout) * (2/4 adjustment) = 0.795^.6=1.4

Now, we know you looked through 3003 bets, but we have no focus group-

So we tested it today, using your data, and a little tweak to the output being 3 and 5

On our first set of focus rounds, our test resulted in a gain
On the 2nd set of focus round thougj, our subject lost pretty much everything.

It is my belief that the unpredictablity of the roulette is still game- its a gamble. Like with every casino, you wont win everytime. Hell, you might lose everything while yhe guy behind you wins it all- and remember, we randomized the locarions of the green squares, so who knows.. if you dont like the table, try the next one ;)

Let me know what you think, if my math is wrong, or whatever :)

I considered doing a similar version of the Random Walk calculation, but without in-depth knowledge of the mathematics/programming behind the floundering of guardians decided to go with my purely empirical approach. Since I took nothing into account other than the final position of the guardian, it simply doesn't make sense to apply the type of adjustment factor you're proposing. I do, however defer to your opinion on the expected outcomes of the casino, although in my humble opinion the roulette table will be unplayable unless it falls within approximately .9 to 1.05 expected values ranges

@cepheid in my humble opinion the roulette table will be unplayable unless it falls within approximately .9 to 1.05 expected values ranges

Honey, what casino has the perfect win to lose ratio? In fact, you lose more at a regular casino than win. In my "humble" opinion, it's plenty playable.

I'm a big blackjack fan IRL, and blackjack has a pretty standard house edge of ~0.6% assuming perfect play, and therefore has an expected value of .994 .
With the adjustments Baron tested (3:1 and 5:1 payout), black now has an EV of 1.129 and red and EV of .994 which would be close to the ranges I'm suggesting. With those odds, betting on black would yield 1 craftycoin on average every 100 seconds with the information I have, but are much more reasonable than either the original or nerfed states

@Blackened_Dawn Honey, what casino has the perfect win to lose ratio? In fact, you lose more at a regular casino than win. In my "humble" opinion, it's plenty playable.

Here's the thing, this isn't a real casino. If I'm going to lose more than I win, and if I win I won't gain much anyways, then there's no point to play it at all. If you want people to actually play it, since this has turned like 90% of the players off, I'd recommend doing what Cepheid has suggested. Otherwise the main player base probably will barely ever go back there.

@OtherGreenGamer Here's the thing, this isn't a real casino. If I'm going to lose more than I win, and if I win I won't gain much anyways, then there's no point to play it at all. If you want people to actually play it, since this has turned like 90% of the players off, I'd recommend doing what Cepheid has suggested. Otherwise the main player base probably will barely ever go back there.

I second this
Since this is not a real casino a "house win" doesn't matter at all (only meaning a loss of crafty coins) and just adusting the values to make it as random as possible, would be more luck based, and maybe more enjoyable.

Why math