doug@cornell.UUCP (12/04/85)
From: doug (Douglas Campbell)
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}wrd@tekigm2.UUCP (Bill Dippert) (12/04/85)
> From: doug (Douglas Campbell) > > 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... > ......etc......... > > 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 > 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
srt@ucla-cs.UUCP (12/06/85)
In article <1324@cornell.UUCP> doug@cornell.UUCP writes: > 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) srt@UCLA-LOCUS.ARPA (soon) srt@LOCUS.UCLA.EDU UUCP: ...!{cepu,ihnp4,trwspp,ucbvax}!ucla-cs!srt FISHNET: ...!{flounder,crappie,flipper}!srt@fishnet-relay.arpa
doug@cornell.UUCP (12/09/85)
From: doug (Douglas Campbell) > From: wrd@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). Doug Campbell doug@cornell.{UUCP|ARPA}
wrd@tekigm2.UUCP (Bill Dippert) (12/10/85)
> From: doug (Douglas Campbell) > > From: wrd@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--
franka@mmintl.UUCP (Frank Adams) (12/16/85)
In article <307@tekigm2.UUCP> wrd@tekigm2.UUCP (Bill Dippert) writes: >> 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 >[etc] 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