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Deconstructing Fable II Pub Game Keystone, mathematical odds calculated [updated]


If you're like me, then you were excited about the pre-order bonus (or just plain buy-for-ten-dollars) XBLA game Fable II: Pub Games. For me, it was a no-brainer, because I liked Fable just fine, and I absolutely love playing roulette when I hit up Vegas, so while Fortune's Tower looked fine and Spinnerbox seemed to be a glorified slot machine, all I really wanted out of the package was Keystone.

But then, if you're still with me, you've probably already heard about the glitch in Fortune's Tower that lets you amass ridiculous amounts of money (and place first in every tournament), and you probably have had enough experience with Spinnerbox to realize that pressing the A button over and over again is mildly amusing, though ultimately does nothing but slowly increase your gold (at least, it seems as though the odds are in your favor, especially in the later boxes). But Keystone, wow, this is actually pretty difficult to make money in. So what to do?

Well, I did a little bit of math, and calculated the odds for each of the inside bets. I don't have the game in front of me right now, so I can't compare them to the odds the game gives you, but keep in mind that the later tables with higher stakes give you better odds, so it's always to your advantage to play those tables. Also to note is that I can't really calculate the odds of "arch bets," because there are a ridiculous number of ways that a single game can go, and multiple ways that a particular arch bet can be won. So without further ado, the mathematical odds for the inside bets on Keystone.

I had some more time on my hands, so I went and looked at the payout odds given by the first Keystone board. Below are not only the mathematical odds, but then the payout odds, and for each one, I also calculated expected return, so you can see exactly which bets are best. Again, these additional calculations are only valid for the first board, but the mathematical odds (listed first) are absolute.

Bet - Math Odds - Payout Odds (1st board) - Expected Return (1st board)
3 - 215:1 - 190:1 - 88.4%
4 - 71:1 - 65:1 - 91.7%
5 - 35:1 - 31:1 - 88.9%
6 - 20.6:1 - 18:1 - 88.0%
7 - 13.4:1 - 12:1 - 90.3%
8 - ~9.3:1 - 8:1 - 87.5%
9 - 7.64:1 - 6:1 - 81.0%
10 - 7:1 - 6:1 - 87.5%
11 - 7:1 - 6:1 - 87.5%
12 - 7.64:1 - 6:1 - 81.0%
13 - ~9.3:1 - 8:1 - 87.5%
14 - 13.4:1 - 12:1 - 90.3%
15 - 20.6:1 - 18:1 - 88.0%
16 - 35:1 - 31:1 - 88.9%
17 - 71:1 - 65:1 - 91.7%
18 - 215:1 - 190:1 - 88.4%
4-9 - 1.7:1 - 1:1 - 74.1%
Keystone - 3:1 - 2:1 - 75.0%
12-17 - 1.7:1 - 1:1 - 74.1%
Black - 1.7:1 - 1:1 - 74.1%
Red - 1.7:1 - 1:1 - 74.1%
Even - 1.7:1 - 1:1 - 74.1%
Odd - 1.7:1 - 1:1 - 74.1%
Pair - ~2.27:1 - 1:1 - 61.1%
Run - 8:1 - 7:1 - 88.9%
Trips - 35:1 - 31:1 - 88.9%
2-2-2 - 215:1 - 190:1 - 88.4%
3-3-3 - 215:1 - 190:1 - 88.4%
4-4-4 - 215:1 - 190:1 - 88.4%
5-5-5 - 215:1 - 190:1 - 88.4%

So then, analyzing the new calculations, you can see that the best bets you can make are generally on single numbers, with four, seven, fourteen, and seventeen being the best. Just about all of the "safe" bets are actually the worst; despite their higher probability of occurrence, their payout is significantly lower than it should be. The absolute worst bet on the board is the "Pair" bet, with the best of the "safe" bets being the "Run" bet.

I was actually a bit surprised to see these results. Despite not having this data in front of me, I have been winning more than losing, so either I haven't been playing a statistically significant number of games yet and I've just been lucky so far, OR the random number generator that is determining the dice rolls is not as random as we've been lead to believe. Of course, I still haven't calculated expected value for the later boards, so it could just be that some of those bets are actually set up to make the player money (i.e. >100% in the last column).[/UPDATE]

There, now that you have that, what do you do? Well, you want to check the payout odds that the table features, and you ideally want to bet on only the bets that have equal or higher payout odds (left trigger in the game) than mathematical odds (what I calculated above). One particular thing that I noted when calculating this is that the "Trips" bet has the same probability of winning as a 5 or a 16, so whichever among those gives you better payout odds is the smarter bet to make. Again, I don't have the game in front of me, so I can't say for sure which is better, or whether they even differ at all.

So with that, happy gambling! And in case you are still having trouble with Keystone, my only other advice is to keep betting big on it, even if you're putting yourself into debt, because the more you bet, the more games you unlock, and the later games give you better payouts, so you'll eventually make the money back.
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About Darren Nakamuraone of us since 2:29 AM on 11.06.2006

Darren is a scientist during the day. He has been a Destructoid community member since 2006, joining the front page as a contributor in 2011.

While he enjoys shooters, RPGs, platformers, strategy, and rhythm games, he takes particular interest in independent games. He produced the Zero Cool Podcast for about four years, and he plays board games quite a bit when he can find willing companions.

FULL DISCLOSURE: Darren Nakamura knows several people in the video game industry, most of whom are Destructoid alumni. These include:

Anthony Burch, former writer for Gearbox Software
Ashly Burch, notable voice actor
Nick Chester, publicist for Harmonix Music Systems
Chad Concelmo, writer for Golin Harris
Aaron Linde, writer for Gearbox Software
Jayson Napolitano, publicist for Scarlet Moon Productions
Brad Nicholson, former publicist for Uber Entertainment
Alex Ryan, publicist for Kalypso Media
Jim Sterling, notable voice actor

Darren backs a lot of Kickstarter campaigns! If you want to see what he has backed, you can go here. If he ever reviews a game that he backed, that will be explicitly disclosed in the review.

Darren invested in Psychonauts 2 on Fig.
Xbox LIVE:Dexter345
PSN ID:Dexter345
Steam ID:http://steamcommunity.com/profil
Mii code:1257 7687 3747 6405


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