Improved truly fair Rail Baron rules
do...@cornell.uucp
After looking at my previous posting, I decided that my scheme for railroad
pricing was sound, but that the Northeast rails needed a little fixing.
So, I went back and made changes to Portland, Boston, and New York in the
weights they give to the rails they connect to. I gave half of Portland's
weight to the B&M, and a quarter each to the PA and NYC. I split Boston
four equal ways, to the B&M, NYNH&H, PA, and NYC. Finally, I split New
York equally between the NYC and the PA. The reasons are that Portland and
Boston are effectively locked by the PA and NYC in addition to the B&M and
NYNH&H, and the NYNH&H doesn't really ever help you get to New York. So,
posted below are the resulting prices as a result of this fix. I also ran
the algorithm for the Seattle rules, with and without the fix.
Original Seattle
fix no fix fix no fix
56,000 47,000 48,000 42,000 PA - Pennsylvania
40,000 31,000 34,000 28,000 NYC - New York Central
39,000 39,000 34,000 34,000 AT&SF - Atchison, Topeka, & Santa Fe
38,000 38,000 36,000 36,000 SP - Southern Pacific
30,000 30,000 31,000 31,000 UP - Union Pacific
26,000 26,000 18,000 18,000 B&O - Baltimore & Ohio
23,000 23,000 20,000 20,000 SAL - Seaboard Air Line
23,000 23,000 30,000 30,000 L&N - Louisville & Nashville
19,000 19,000 25,000 25,000 CRI&P - Chicago, Rock Island, & Pacific
19,000 19,000 19,000 19,000 C&O - Chesapeake & Ohio
16,000 16,000 20,000 20,000 NP - Northern Pacific
15,000 15,000 18,000 18,000 WP - Western Pacific
15,000 15,000 17,000 17,000 SOU - Southern
15,000 15,000 17,000 17,000 CMSTP&P - Chicago, Milwaukee, St. Paul, & Pac.
15,000 15,000 16,000 16,000 CB&Q - Chicago, Burlington, & Quincy
15,000 15,000 22,000 22,000 C&NW - Chicago & NorthWestern
14,000 14,000 18,000 18,000 GN - Great Northern
13,000 13,000 11,000 11,000 ACL - Atlantic Coast Line
12,000 12,000 13,000 13,000 SLSF - St. Louis - San Fransisco
12,000 12,000 14,000 14,000 MP - Missouri Pacific
10,000 10,000 14,000 14,000 N&W - Norfolk & Western
10,000 16,000 6,000 12,000 B&M - Boston & Maine
9,000 9,000 6,000 6,000 T&P - Texas & Pacific
8,000 8,000 9,000 9,000 IC - Illinois Central
8,000 8,000 8,000 8,000 GM&O - Gulf, Mobile, & Ohio
7,000 7,000 7,000 7,000 D&RGW - Denver & Rio Grande Western
4,000 14,000 1,000 8,000 NYNH&H - New York, New Haven, & Hartford
3,000 3,000 2,000 2,000 RF&P - Richmond, Fredericksburg, & Potomac
I believe that the prices with the fix are much more reasonable.
Just for fun, I printed out the probabilities of going to each city under
the original and the Seattle rules. Here are some highlights:
(Numbers are the percent chance of going to the city)
Top 10
Original Seattle
4.05 New York 2.70 New York
3.94 Los Angeles 2.55 Portland, Ore.
3.40 Chicago 2.51 Oklahoma City
2.89 Philadelphia 2.51 Kansas City
2.89 Boston 2.33 Indianapolis
2.78 Seattle 2.33 Detroit
2.78 Kansas City 2.31 Philadelphia
2.62 Portland, Ore. 2.31 Memphis
2.60 Baltimore 2.12 Spokane
2.60 Atlanta 2.12 Salt Lake City
Bottom 10
Original Seattle
0.69 Tucumcari 0.77 Dallas
0.69 Reno 0.77 Chattanooga
0.69 Little Rock 0.64 Billings
0.69 Charleston 0.58 St. Paul
0.62 Pocatello 0.58 Shreveport
0.62 Casper 0.39 Tampa
0.52 Shreveport 0.39 El Paso
0.52 Chattanooga 0.39 Charleston
0.52 Charlotte 0.39 Birmingham
0.46 Fargo 0.39 Albany
Other
Original Seattle
2.31 San Fransisco 1.35 San Fransisco
2.08 Oakland 1.54 Oakland
1.74 Miami 1.35 Miami
1.16 Portland, Me. 1.54 Portland, Me.
Where the top 10 went/came from
Original Seattle
1.23 Oklahoma City 1.93 Los Angeles
1.06 Indianapolis 1.91 Seattle
2.33 Detroit 1.70 Chicago
1.22 Memphis 1.35 Atlanta
0.77 Spokane 1.16 Boston
1.39 Salt Lake City 0.96 Baltimore
In conclusion, I think I will use the original rules for destinations,
and the new railroad prices with the fix. This is because the rail price
changes seem more effective than the probability changes (shown by the
relatively small price changes in railroads under probability changes).
Doug Campbell
doug@cornell.{UUCP|ARPA}
Bill Dippert
>
> After looking at my previous posting, I decided that my scheme for railroad
> ......etc.........
Out of curiosity: how did you calculate the odds to get the cities? Did
you take into consideration the odds to get to the region first, then the
odds that once in that region you could roll that city? Or what?
When I did my calculations to get the differences of obtaining SE between
the original rules and the Seattle Rules, I did the following math:
Under the "Seattle Rules" reaching Southeast requires:
an odd 3
an odd 10
or an even 6
The odds of rolling an odd 3 are [(l/2)(1/6 + 1/6)];
the odds of rolling an odd 10 are {[1/2][(1/6 + 1/6)(1/6 + 1/6)]};
and finally the odds of rolling an even 6 are
{[1/2][(1/6 + 1/6)(1/6 + 1/6)(1/6 + 1/6)]}.
To get the odds of any of these to happen is the sum of these three
probabilities or reducing this down:
(1/6) + (1/18) + (1/54) = .24 or 24%
This compares to the 7% for the original rules. (Per another
posting, I did not check this out.)
All of the above based on the forumulas of probability as
expressed in an "Introduction to Modern Algebra" by Neal H.
McCoy. (And at least 20 years after receiving my B.S. in Math!)
Are you or is there anyone out there willing and knowledgeable to first
calculate the odds of reaching each region and second of reaching each
city within each region? -- for both the original and the Seattle rules?
Thanks,
--Bill--
tektronix!tekigm2!wrd
s...@ucla-cs.uucp
> Top 10
> Original Seattle
> 4.05 New York 2.70 New York
> 3.94 Los Angeles 2.55 Portland, Ore.
>
I got somewhat different results. If you count San Francisco and Oakland
as a single city, it is the most popular at 4.47%. Here are the odds for
everything as I calculated them (regular rules):
CITY PROBABILITIES FOR RAIL BARON
Odds for Regions
Plains .112
Southeast .126
North Central .154
Northeast .210
Southwest .168
South Central .126
Northwest .112
Odds by City
Northeast
South Central
New York .0412
Albany .0118 Memphis .0124
Boston .0294 Little Rock .0071
Buffalo .0176 New Orleans .0159
Portland .0118 Birmingham .0106
Washington .0235 Louisville .0124
Pittsburgh .0206 Shreveport .0053
Philly .0294 Dallas .0141
Baltimore .0265 San Antonio .0106
Houston .0159
Southeast Fort Worth .0106
Charlotte .0053 Plains
Chattanooga .0053
Atlanta .0265 Kansas City .0282
Richmond .0088 Denver .0188
Knoxville .0106 Pueblo .0078
Mobile .0106 Okl. City .0125
Norfolk .0125 St. Paul .0094
Charleston .0071 Minneapolis .0125
Miami .0176 Min-St.Pl .0209
JacksonVl .0106 Des Moines .0078
Tampa .0124 Omaha .0110
Fargo .0047
North Central Northwest
Cleveland .0216 Spokane .0078
Detroit .0237 Seattle .0282
Indianplis .0108 Rapid City .0078
Milwaukee .0173 Casper .0063
Chicago .0345 Billings .0078
Cincinnati .0151 Salt Lake .0141
Columbus .0108 Portland .0267
St. Louis .0194 Pocatello .0063
Butte .0078
Southwest
San Diego .0165
Reno .0071
Sacramento .0118
Las Vegas .0141
Phoenix .0188
El Paso .0094
Tucumcari .0071
Los Angeles .0400
Oakland .0212
San Fran .0235
Oak-San .0447
In Order
Oak-San .0447 Okl.-City .0125
New-York .0412 Norfolk .0125
Los-Angeles .0400 Tampa .0124
Chicago .0345 Memphis .0124
Boston .0294 Louisville .0124
Philly .0294 Albany .0118
Seattle .0282 Sacramento .0118
Kansas-City .0282 Portland .0118
Portland .0267 Omaha .0110
Baltimore .0265 Indianplis .0108
Atlanta .0265 Columbus .0108
Detroit .0237 San-Antonio .0106
San-Fran .0235 Mobile .0106
Washington .0235 Knoxville .0106
Cleveland .0216 JacksonVl .0106
Oakland .0212 Fort-Worth .0106
Min-St.Pl .0209 Birmingham .0106
Pittsburgh .0206 St.-Paul .0094
St.-Louis .0194 El-Paso .0094
Phoenix .0188 Richmond .0088
Denver .0188 Spokane .0078
Buffalo .0176 Rapid-City .0078
Miami .0176 Pueblo .0078
Milwaukee .0173 Des-Moines .0078
San-Diego .0165 Butte .0078
New-Orleans .0159 Billings .0078
Houston .0159 Tucumcari .0071
Cincinnati .0151 Reno .0071
Salt-Lake .0141 Little-Rock .0071
Las-Vegas .0141 Charleston .0071
Dallas .0141 Pocatello .0063
Minneapolis .0125 Casper .0063
Shreveport .0053
Chattanooga .0053
Charlotte .0053
Fargo .0047
Scott R. Turner
ARPA: (now) s...@UCLA-LOCUS.ARPA (soon) s...@LOCUS.UCLA.EDU
UUCP: ...!{cepu,ihnp4,trwspp,ucbvax}!ucla-cs!srt
FISHNET: ...!{flounder,crappie,flipper}!s...@fishnet-relay.arpa
do...@cornell.uucp
> From: w...@tekigm2.UUCP (Bill Dippert)
> > From: doug (Douglas Campbell)
> >
> > Just for fun, I printed out the probabilities of going to each city under
> > the original and the Seattle rules. Here are some highlights:
> >
> Out of curiosity: how did you calculate the odds to get the cities? Did
> you take into consideration the odds to get to the region first, then the
> odds that once in that region you could roll that city? Or what?
There are 72 combinations possible for each region/city roll. (72 = 6x6x2
for the 2 six-sided and the even/odd roll). The number of combinations that
result in the following values with 2 dice are listed below:
Result Ways
------ ----
2 1
3 2
4 3
5 4
6 5
7 6
8 5
9 4
10 3
11 2
12 1
So, the probability of rolling, say, an even 5 is 4/72. Adding up the
probabilities for each case gives the total probability.
The city probabilities were computed by multiplying the city's probability
within the region by the region's probability. Thus, they should be
correct global probabilities (barring typos in my data).
Bill Dippert
> > From: w...@tekigm2.UUCP (Bill Dippert)
> > > From: doug (Douglas Campbell)
> > >
> > > Just for fun, I printed out the probabilities of going to each city under
> > > the original and the Seattle rules. Here are some highlights:
> > >
> > Out of curiosity: how did you calculate the odds to get the cities? Did
> > you take into consideration the odds to get to the region first, then the
> > odds that once in that region you could roll that city? Or what?
>
> There are 72 combinations possible for each region/city roll. (72 = 6x6x2
> for the 2 six-sided and the even/odd roll). The number of combinations that
> result in the following values with 2 dice are listed below:
*****WRONG! YOU ARE CALCULATING PERMUTATIONS AND NOT COMBINATIONS. FOR
DETERMINING THE ODDS OF REACHING A REGION YOU NEED THE COMBINATIONS OF THE
DICE NOT THE PERMUTATIONS.*****
>
"Permutations" "Combinations"
Result Ways Result Ways
------ ---- ------ ----
2 1 2 1
3 2 3 1
4 3 4 2
5 4 5 2
6 5 6 3
7 6 7 3
8 5 8 3
9 4 9 2
10 3 10 2
11 2 11 1
12 1 12 1
--- ---
36 21
Regardless, no matter which way you calculate it, the NE bias goes away with
the Seattle Rules and you have a better chance at reaching more cities.
Using Seattle Rules, we have never had the problem of "trying to reach
a bad city" on the first roll. (Quoting or misquoting an earlier posting.)
I agree with the posters that changing the $ value of the railroads does
not make much sense, the prices are relative to the real rr value apparently.
But as stated, regardless of rules used, in the long run the rr cost does
not matter. Which you buy considering the destination chart does.
However, I think that the basic game (either rules) is probably the best
railroad game on the market. The only other game that is comparable is
the old "Dispatcher" game (also by A-H) but it had a rather bads bias also
-- one player always had the advantage over the other. It was only a two
person game and I do not remember which player had the advantage. I realize
that this is the wrong group to discuss this, but does anyone have any opinions
on the various railroad computer games now on the market? (It would be nice
to have net.railroad.games!!)
--Bill--
Frank Adams
>> There are 72 combinations possible for each region/city roll. (72 = 6x6x2
>> for the 2 six-sided and the even/odd roll). The number of combinations that
>
>> result in the following values with 2 dice are listed below:
>
>*****WRONG! YOU ARE CALCULATING PERMUTATIONS AND NOT COMBINATIONS. FOR
>DETERMINING THE ODDS OF REACHING A REGION YOU NEED THE COMBINATIONS OF THE
>DICE NOT THE PERMUTATIONS.*****
>>
> "Permutations" "Combinations"
> Result Ways Result Ways
> ------ ---- ------ ----
> 2 1 2 1
> 3 2 3 1
No, he was right and you are wrong. You are twice as likely to roll a
3 as a 2 on two dice. Suppose you were rolling the dice one at a time.
To roll a two, you have to roll a 1 on each die. The chance for each
die to be a 1 is (1/6), so the total chance is (1/6)(1/6) = (1/36). To
roll a 3 you can roll a 1 on the first die and a 2 on the second, or a 2
on the first and a 1 on the second. Each of these has a (1/36) chance, giving
a total chance of (2/36) or (1/18).
The odds aren't any different when both dice are rolled at the same time.
Frank Adams ihpn4!philabs!pwa-b!mmintl!franka
Multimate International 52 Oakland Ave North E. Hartford, CT 06108
Lucasfilm Games Division
Does anyone have variations on Rail Baron that do not concern
different destinations or payoffs? I heard a rumor once about some
similar game that involved specifying the actual cargo your train
was carrying.
Noah Falstein