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.
