Thread Rating:

LiberLai
LiberLai
  • Threads: 2
  • Posts: 3
Joined: Jul 9, 2012
July 9th, 2012 at 1:26:58 AM permalink
EXACT SCORE: The sum of the 20 numbered balls drawn is equal to 810.

and the odds is 108.

what is the edge?
LiberLai
LiberLai
  • Threads: 2
  • Posts: 3
Joined: Jul 9, 2012
August 3rd, 2012 at 1:16:55 AM permalink
I have wrote a simulation program myself.

The probability for EXACT SCORE is very closed to 0.44%.

So the edge is over 52%.
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
August 3rd, 2012 at 8:15:02 AM permalink
I agree with your simulation.
I heart Crystal Math.
pokerface
pokerface
  • Threads: 12
  • Posts: 514
Joined: May 9, 2010
August 3rd, 2012 at 8:19:44 AM permalink
seems the edge is comparable with other keno bets
winning streaks come and go, losing streak never ends.
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
August 3rd, 2012 at 8:36:47 AM permalink
I actually get closer to .43%, but who's counting when the edge is crazy like this.

Live keno is horrible.
I heart Crystal Math.
mustangsally
mustangsally
  • Threads: 25
  • Posts: 2463
Joined: Mar 29, 2011
August 3rd, 2012 at 9:15:22 AM permalink
Quote: LiberLai

EXACT SCORE: The sum of the 20 numbered balls drawn is equal to 810.

and the odds is 108.

what is the edge?

edit
Crystal Math and my BF are correct
Sally
I Heart Vi Hart
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
August 3rd, 2012 at 9:26:22 AM permalink
Quote: mustangsally

An exact calculation is very easy in Excel using a few different methods.

Using the binomial coefficients formula
link found here.
https://wizardofvegas.com/forum/questions-and-answers/math/9660-probability-of-fair-die-equaling-sum-of-20/2/#post143909
It is the sum of 10 calculations


This is the same as asking the prob of a sum of 810 rolling 20d80 dice (20 - 80 sided die, or one 80 sided die rolled 20 times)

I get 0.383395%

In Excel,
there may be a few rounding errors,
I would have to use a high precision program on my other computer for an exact value)
this looks very close ;)

115,292,150,460,685,000,000,000,000,000,000,000,000 / 442,024,848,215,333,000,000,000,000,000,000,000


One could also use the posted Wizard's method or even the generating function I showed in an earlier thread.
(I think, when I have more time, I will use the Wizards method and see if there are no rounding errors)

A HE formula like this one
=((((Payoff to 1)+1)*P)-1)*100

108 to 1 payoff (but you said the odds are 108, that should be a 107 to 1 payout)
shows a =((((108)+1)*0.383395%)-1)*100 = -58.20989698% edge

107 to 1 payoff (but you said the odds are 108, that should be a 107 to 1 payout)
shows a =((((107)+1)*0.383395%)-1)*100 = -58.59329242% edge

I agree, over 50% house edge
Hey just about all State Lotteries are this bad, but people do hit the Lottery, just not me yet.

Sally



Actually, in keno, 20 numbers are drawn from a pool of 80, so all of the numbers must be unique and it is not like rolling 20 80 sided dice, where the numbers can be repeated.
I heart Crystal Math.
mustangsally
mustangsally
  • Threads: 25
  • Posts: 2463
Joined: Mar 29, 2011
August 3rd, 2012 at 9:32:39 AM permalink
removed
silly
I Heart Vi Hart
mustangsally
mustangsally
  • Threads: 25
  • Posts: 2463
Joined: Mar 29, 2011
August 3rd, 2012 at 10:13:13 AM permalink
Quote: LiberLai

EXACT SCORE: The sum of the 20 numbered balls drawn is equal to 810.

and the odds is 108.

what is the edge?



http://static.mansion88.com/microsites/m88/Keno/kenoRules_en.html

I do not know much yet about Keno, looks to be a simple game.

The 810 total is used in other bets as shown in the linked page.
(my guess the 810 is the mode)

I am sure this is easy to calculate without a simulation as all Keno is basic math.
well, using the right formulas

Looks like a good "Ask the Wizard" question
I Heart Vi Hart
ThatDonGuy
ThatDonGuy
  • Threads: 122
  • Posts: 6673
Joined: Jun 22, 2011
August 3rd, 2012 at 10:57:51 AM permalink
Sounds more like a "brute force" problem, although you don't have to check every possible combination of 20 numbers out of 80.

If the smallest number > 31, the smallest sum >= 32 + 33 + ... + 51, which is 830.
Keyser
Keyser
  • Threads: 35
  • Posts: 2112
Joined: Apr 16, 2010
August 3rd, 2012 at 11:02:47 AM permalink
Basically Keno is like going to the horse track.
EvenBob
EvenBob
  • Threads: 442
  • Posts: 29507
Joined: Jul 18, 2010
August 3rd, 2012 at 11:04:34 AM permalink
Quote: Keyser

Basically Keno is like going to the horse track.



It smells the same? Is that what you mean?
"It's not called gambling if the math is on your side."
Keyser
Keyser
  • Threads: 35
  • Posts: 2112
Joined: Apr 16, 2010
August 3rd, 2012 at 11:07:34 AM permalink
Both are basically carnival games. The house edge is so high for both that nobody can hope to win in the long run.
mustangsally
mustangsally
  • Threads: 25
  • Posts: 2463
Joined: Mar 29, 2011
August 3rd, 2012 at 11:14:02 AM permalink
removed
silly
I Heart Vi Hart
heather
heather
  • Threads: 8
  • Posts: 437
Joined: Jun 12, 2011
August 3rd, 2012 at 1:41:49 PM permalink
Quote: Keyser

Both are basically carnival games. The house edge is so high for both that nobody can hope to win in the long run.



There is no house edge at the racetrack. The track takes a takeout (like a rake in Poker), and all the bettors bet against one another (parimutuel betting, like a cardroom). The takeout is what eats your lunch.
Keyser
Keyser
  • Threads: 35
  • Posts: 2112
Joined: Apr 16, 2010
August 3rd, 2012 at 3:42:04 PM permalink
The track hold is so high that you simply can't win in the long run. That's why there are not any professionals winning at the track. The only way to win at the track is to exploit some kind of rebate process.
In short, horse racing is a suckers bet. Virtually every casino game has much better odds.
qeqeqe
qeqeqe
  • Threads: 0
  • Posts: 3
Joined: May 22, 2013
May 22nd, 2013 at 1:22:50 AM permalink
yes,that'right.

But,let's back to the question

what is Keno 810's house edge? how to calculate it?
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
May 22nd, 2013 at 8:50:02 AM permalink
Quote: qeqeqe

yes,that'right.

But,let's back to the question

what is Keno 810's house edge? how to calculate it?



A simulation is good enough for this game and I don't think there is any need to calculate it.

A perfect score occurs about 0.43% of the time. If it pays 108 to 1, the return is about 46.5% with a house edge of 53.5%.
I heart Crystal Math.
Buzzard
Buzzard
  • Threads: 90
  • Posts: 6814
Joined: Oct 28, 2012
May 22nd, 2013 at 10:30:45 AM permalink
Quote: mustangsally

edit
Crystal Math and my BF are correct
Sally




So I and Crystal Math are correct once again ?
Shed not for her the bitter tear Nor give the heart to vain regret Tis but the casket that lies here, The gem that filled it Sparkles yet
qeqeqe
qeqeqe
  • Threads: 0
  • Posts: 3
Joined: May 22, 2013
May 25th, 2013 at 2:04:41 AM permalink
yes.A simulation is good. But i am just very very confused. If we want to calculate it what is the formula for it?
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
May 25th, 2013 at 5:59:36 AM permalink
Quote: qeqeqe

yes.A simulation is good. But i am just very very confused. If we want to calculate it what is the formula for it?



There is no easy solution that I know of. Sometimes, even in gaming, a simulation is the best we can do.
I heart Crystal Math.
qeqeqe
qeqeqe
  • Threads: 0
  • Posts: 3
Joined: May 22, 2013
May 27th, 2013 at 4:07:00 AM permalink
thank you Crystal Math.
mustangsally
mustangsally
  • Threads: 25
  • Posts: 2463
Joined: Mar 29, 2011
January 19th, 2018 at 9:36:33 AM permalink
Quote: qeqeqe

yes.A simulation is good. But i am just very very confused. If we want to calculate it what is the formula for it?

using full version Wolfram Alpha or Mathematica
it should be this for sum=810

A/B (simple part)

where:
A = Coefficient[Product[1 + x*y^i, {i, 1, 80}],x^20 y^810]
B = C(80,20)

x^20 y^810 means
x^20 is drawing 20 distinct values without replacement
y^810 is the sum

that number before x^20 y^810 (say 15 x^20 y^810)
would be 15 ways for draw 20 and sum=810

of course it is probably closer to
15,201,859,411,512,400 x^20 y^810
just guessing (as I do not have full versions of WA or M
and R does not really support this. maybe there is a package for it)

found this (for more reading)
How many ways are there to get a specific sum

ok
had some time to kill off before hitting the mall
Sally
I Heart Vi Hart
mustangsally
mustangsally
  • Threads: 25
  • Posts: 2463
Joined: Mar 29, 2011
June 4th, 2018 at 10:03:02 PM permalink
Quote: qeqeqe

yes.A simulation is good. But i am just very very confused. If we want to calculate it what is the formula for it?

in Mathematica in above post

or in Pari Gp (free)
prod(i=1, 80, 1 + x*y^i);

I used GP (took split second to calculate and print to a file)
answer (find x^20 = 20 draws without replacement and y= the sum)
exactly
15542763534960598 / 3535316142212174320 [ from C(80,20) ]
about = 0.0043964281862597251250724239977180641876

here be the results

example: 3*y^1407
3 ways to get the sum=1407 (and sum=213)
 (y^1410 + y^1409 + 2*y^1408 + 3*y^1407 + 5*y^1406 + 7*y^1405 + 11*y^1404 + 15*y^1403 + 22*y^1402 + 30*y^1401 + 42*y^1400 + 56*y^1399 + 77*y^1398 + 101*y^1397 + 135*y^1396 + 176*y^1395 + 231*y^1394 + 297*y^1393 + 385*y^1392 + 490*y^1391 + 627*y^1390 + 791*y^1389 + 1000*y^1388 + 1251*y^1387 + 1568*y^1386 + 1946*y^1385 + 2417*y^1384 + 2980*y^1383 + 3673*y^1382 + 4498*y^1381 + 5507*y^1380 + 6703*y^1379 + 8154*y^1378 + 9871*y^1377 + 11937*y^1376 + 14375*y^1375 + 17293*y^1374 + 20722*y^1373 + 24803*y^1372 + 29588*y^1371 + 35251*y^1370 + 41869*y^1369 + 49668*y^1368 + 58754*y^1367 + 69414*y^1366 + 81801*y^1365 + 96271*y^1364 + 113039*y^1363 + 132559*y^1362 + 155112*y^1361 + 181274*y^1360 + 211428*y^1359 + 246288*y^1358 + 286364*y^1357 + 332557*y^1356 + 385528*y^1355 + 446405*y^1354 + 516054*y^1353 + 595872*y^1352 + 686983*y^1351 + 791131*y^1350 + 909741*y^1349 + 1044984*y^1348 + 1198689*y^1347 + 1373524*y^1346 + 1571812*y^1345 + 1796855*y^1344 + 2051569*y^1343 + 2340024*y^1342 + 2665885*y^1341 + 3034135*y^1340 + 3449359*y^1339 + 3917670*y^1338 + 4444748*y^1337 + 5038070*y^1336 + 5704686*y^1335 + 6453684*y^1334 + 7293767*y^1333 + 8236001*y^1332 + 9291060*y^1331 + 10472375*y^1330 + 11793028*y^1329 + 13269250*y^1328 + 14917024*y^1327 + 16755957*y^1326 + 18805464*y^1325 + 21089176*y^1324 + 23630664*y^1323 + 26458297*y^1322 + 29600587*y^1321 + 33091578*y^1320 + 36965620*y^1319 + 41263462*y^1318 + 46026431*y^1317 + 51303148*y^1316 + 57143201*y^1315 + 63604540*y^1314 + 70746444*y^1313 + 78637842*y^1312 + 87349501*y^1311 + 96963169*y^1310 + 107563103*y^1309 + 119246146*y^1308 + 132112328*y^1307 + 146276124*y^1306 + 161856093*y^1305 + 178987225*y^1304 + 197809729*y^1303 + 218482569*y^1302 + 241171101*y^1301 + 266062168*y^1300 + 293350487*y^1299 + 323255164*y^1298 + 356005000*y^1297 + 391856581*y^1296 + 431078138*y^1295 + 473969587*y^1294 + 520844871*y^1293 + 572053851*y^1292 + 627963266*y^1291 + 688980643*y^1290 + 755533468*y^1289 + 828095629*y^1288 + 907164667*y^1287 + 993290571*y^1286 + 1087051347*y^1285 + 1189084411*y^1284 + 1300059954*y^1283 + 1420715489*y^1282 + 1551826889*y^1281 + 1694245990*y^1280 + 1848869496*y^1279 + 2016679881*y^1278 + 2198711618*y^1277 + 2396096082*y^1276 + 2610024936*y^1275 + 2841798846*y^1274 + 3092788314*y^1273 + 3364486581*y^1272 + 3658467191*y^1271 + 3976441876*y^1270 + 4320214692*y^1269 + 4691744778*y^1268 + 5093097335*y^1267 + 5526511602*y^1266 + 5994347965*y^1265 + 6499162145*y^1264 + 7043648186*y^1263 + 7630718671*y^1262 + 8263443950*y^1261 + 8945138936*y^1260 + 9679297643*y^1259 + 10469687646*y^1258 + 11320279729*y^1257 + 12235349889*y^1256 + 13219404469*y^1255 + 14277290236*y^1254 + 15414114032*y^1253 + 16635362300*y^1252 + 17946814901*y^1251 + 19354673930*y^1250 + 20865472184*y^1249 + 22486212019*y^1248 + 24224267278*y^1247 + 26087533643*y^1246 + 28084323773*y^1245 + 30223529082*y^1244 + 32514508546*y^1243 + 34967262684*y^1242 + 37592314751*y^1241 + 40400898786*y^1240 + 43404832757*y^1239 + 46616720518*y^1238 + 50049817550*y^1237 + 53718247833*y^1236 + 57636860670*y^1235 + 61821464449*y^1234 + 66288674187*y^1233 + 71056162189*y^1232 + 76142496873*y^1231 + 81567411419*y^1230 + 87351632249*y^1229 + 93517168095*y^1228 + 100087127594*y^1227 + 107086028628*y^1226 + 114539605867*y^1225 + 122475141756*y^1224 + 130921262045*y^1223 + 139908291043*y^1222 + 149468034620*y^1221 + 159634159836*y^1220 + 170441966142*y^1219 + 181928790813*y^1218 + 194133766301*y^1217 + 207098254570*y^1216 + 220865589927*y^1215 + 235481542190*y^1214 + 250994045973*y^1213 + 267453694512*y^1212 + 284913452879*y^1211 + 303429185857*y^1210 + 323059354425*y^1209 + 343865577844*y^1208 + 365912314318*y^1207 + 389267459099*y^1206 + 414002006749*y^1205 + 440190689221*y^1204 + 467911618783*y^1203 + 497246966079*y^1202 + 528282584833*y^1201 + 561108732221*y^1200 + 595819672189*y^1199 + 632514442353*y^1198 + 671296435063*y^1197 + 712274211009*y^1196 + 755561059108*y^1195 + 801275859118*y^1194 + 849542617012*y^1193 + 900491381529*y^1192 + 954257753733*y^1191 + 1010983857544*y^1190 + 1070817824773*y^1189 + 1133914822434*y^1188 + 1200436509276*y^1187 + 1270552124993*y^1186 + 1344437917067*y^1185 + 1422278292091*y^1184 + 1504265214046*y^1183 + 1590599420536*y^1182 + 1681489788194*y^1181 + 1777154619819*y^1180 + 1877820975168*y^1179 + 1983726028916*y^1178 + 2095116368246*y^1177 + 2212249424868*y^1176 + 2335392734382*y^1175 + 2464825448513*y^1174 + 2600837554495*y^1173 + 2743731467669*y^1172 + 2893821211946*y^1171 + 3051434096031*y^1170 + 3216909849508*y^1169 + 3390602389686*y^1168 + 3572878910940*y^1167 + 3764121741811*y^1166 + 3964727389027*y^1165 + 4175108488550*y^1164 + 4395692797816*y^1163 + 4626925247931*y^1162 + 4869266881582*y^1161 + 5123197006289*y^1160 + 5389212078927*y^1159 + 5667827963566*y^1158 + 5959578755669*y^1157 + 6265019152487*y^1156 + 6584723213704*y^1155 + 6919286843610*y^1154 + 7269326489361*y^1153 + 7635481738958*y^1152 + 8018413948848*y^1151 + 8418808965914*y^1150 + 8837375680898*y^1149 + 9274848873719*y^1148 + 9731987693363*y^1147 + 10209578630140*y^1146 + 10708433913262*y^1145 + 11229394619008*y^1144 + 11773328981483*y^1143 + 12341135635235*y^1142 + 12933741839899*y^1141 + 13552106861442*y^1140 + 14197220100303*y^1139 + 14870104620270*y^1138 + 15571815175325*y^1137 + 16303441884554*y^1136 + 17066108157849*y^1135 + 17860974520443*y^1134 + 18689236426307*y^1133 + 19552128242181*y^1132 + 20450920942555*y^1131 + 21386926250737*y^1130 + 22361494215565*y^1129 + 23376017513498*y^1128 + 24431928894154*y^1127 + 25530705653070*y^1126 + 26673866939713*y^1125 + 27862978398196*y^1124 + 29099649337087*y^1123 + 30385537541434*y^1122 + 31722346290416*y^1121 + 33111829351342*y^1120 + 34555787837266*y^1119 + 36056075379039*y^1118 + 37614594822327*y^1117 + 39233303581272*y^1116 + 40914210159126*y^1115 + 42659379693854*y^1114 + 44470930294083*y^1113 + 46351038772509*y^1112 + 48301936795528*y^1111 + 50325916807381*y^1110 + 52425327976532*y^1109 + 54602582321801*y^1108 + 56860150445667*y^1107 + 59200567856702*y^1106 + 61626430488492*y^1105 + 64140401221500*y^1104 + 66745205168528*y^1103 + 69443636407019*y^1102 + 72238553020681*y^1101 + 75132884036461*y^1100 + 78129624219915*y^1099 + 81231841219122*y^1098 + 84442670093739*y^1097 + 87765320677722*y^1096 + 91203071830294*y^1095 + 94759279010024*y^1094 + 98437368245632*y^1093 + 102240843924128*y^1092 + 106173282459017*y^1091 + 110238340304328*y^1090 + 114439747308027*y^1089 + 118781314944316*y^1088 + 123266929349329*y^1087 + 127900559773363*y^1086 + 132686251275763*y^1085 + 137628133409981*y^1084 + 142730412563985*y^1083 + 147997380868998*y^1082 + 153433408182971*y^1081 + 159042951225485*y^1080 + 164830545178892*y^1079 + 170800813062207*y^1078 + 176958456936318*y^1077 + 183308267507535*y^1076 + 189855114934011*y^1075 + 196603958660512*y^1074 + 203559837800120*y^1073 + 210727881214639*y^1072 + 218113297456569*y^1071 + 225721385084601*y^1070 + 233557522163930*y^1069 + 241627176819381*y^1068 + 249935896266269*y^1067 + 258489317615563*y^1066 + 267293156421037*y^1065 + 276353217726061*y^1064 + 285675384124940*y^1063 + 295265627053394*y^1062 + 305129994336046*y^1061 + 315274621737283*y^1060 + 325705719979621*y^1059 + 336429586543371*y^1058 + 347452592155562*y^1057 + 358781192841696*y^1056 + 370421915855964*y^1055 + 382381372002154*y^1054 + 394666240991089*y^1053 + 407283284019903*y^1052 + 420239328556562*y^1051 + 433541281180913*y^1050 + 447196111767398*y^1049 + 461210866607609*y^1048 + 475592651976889*y^1047 + 490348647526558*y^1046 + 505486089237058*y^1045 + 521012283085036*y^1044 + 536934587353256*y^1043 + 553260426593322*y^1042 + 569997273279789*y^1041 + 587152662058258*y^1040 + 604734170747184*y^1039 + 622749434876858*y^1038 + 641206128010489*y^1037 + 660111976597920*y^1036 + 679474739604064*y^1035 + 699302223666421*y^1034 + 719602262037791*y^1033 + 740382730055707*y^1032 + 761651523370470*y^1031 + 783416573752126*y^1030 + 805685826594439*y^1029 + 828467257050350*y^1028 + 851768846820577*y^1027 + 875598600626154*y^1026 + 899964522255079*y^1025 + 924874631401209*y^1024 + 950336938960611*y^1023 + 976359464227661*y^1022 + 1002950209453776*y^1021 + 1030117177412699*y^1020 + 1057868345195045*y^1019 + 1086211682173956*y^1018 + 1115155123030642*y^1017 + 1144706586113291*y^1016 + 1174873945708909*y^1015 + 1205665050808215*y^1014 + 1237087696599984*y^1013 + 1269149643677458*y^1012 + 1301858588751637*y^1011 + 1335222184292444*y^1010 + 1369248008480895*y^1009 + 1403943585301204*y^1008 + 1439316353708705*y^1007 + 1475373688210195*y^1006 + 1512122867248405*y^1005 + 1549571094266055*y^1004 + 1587725465329523*y^1003 + 1626592990693830*y^1002 + 1666180561645293*y^1001 + 1706494972609528*y^1000 + 1747542887215360*y^999 + 1789330860941288*y^998 + 1831865306428571*y^997 + 1875152516686548*y^996 + 1919198629635734*y^995 + 1964009651915660*y^994 + 2009591422664545*y^993 + 2055949637927477*y^992 + 2103089813703016*y^991 + 2151017310973098*y^990 + 2199737298000372*y^989 + 2249254776027773*y^988 + 2299574540834782*y^987 + 2350701209103646*y^986 + 2402639179270463*y^985 + 2455392658582214*y^984 + 2508965623226933*y^983 + 2563361846130743*y^982 + 2618584856379097*y^981 + 2674637967752948*y^980 + 2731524237478957*y^979 + 2789246495528881*y^978 + 2847807302685929*y^977 + 2907208980659856*y^976 + 2967453569482805*y^975 + 3028542858437463*y^974 + 3090478342825046*y^973 + 3153261255732853*y^972 + 3216892524160984*y^971 + 3281372801682291*y^970 + 3346702423944313*y^969 + 3412881442219846*y^968 + 3479909578328192*y^967 + 3547786259101073*y^966 + 3616510570712255*y^965 + 3686081294113980*y^964 + 3756496858791478*y^963 + 3827755379165355*y^962 + 3899854607818599*y^961 + 3972791972891010*y^960 + 4046564530766019*y^959 + 4121169004511073*y^958 + 4196601736043217*y^957 + 4272858725610066*y^956 + 4349935583482269*y^955 + 4427827570497986*y^954 + 4506529549270567*y^953 + 4586036025851501*y^952 + 4666341100470600*y^951 + 4747438510307985*y^950 + 4829321579817147*y^949 + 4911983264628415*y^948 + 4995416101440403*y^947 + 5079612253106599*y^946 + 5164563458113973*y^945 + 5250261076840903*y^944 + 5336696040671980*y^943 + 5423858899445150*y^942 + 5511739770187560*y^941 + 5600328385803359*y^940 + 5689614043446161*y^939 + 5779585654429600*y^938 + 5870231692286645*y^937 + 5961540243918360*y^936 + 6053498957320960*y^935 + 6146095094019128*y^934 + 6239315476476153*y^933 + 6333146541790366*y^932 + 6427574288835366*y^931 + 6522584333229145*y^930 + 6618161854183309*y^929 + 6714291650789160*y^928 + 6810958088586958*y^927 + 6908145157139459*y^926 + 7005836416368480*y^925 + 7104015055421622*y^924 + 7202663838749386*y^923 + 7301765166303075*y^922 + 7401301019361722*y^921 + 7501253022027266*y^920 + 7601602386843987*y^919 + 7702329977589080*y^918 + 7803416254655222*y^917 + 7904841339170873*y^916 + 8006584958150181*y^915 + 8108626509899889*y^914 + 8210945008978195*y^913 + 8313519152881939*y^912 + 8416327266778085*y^911 + 8519347371498567*y^910 + 8622557128046053*y^909 + 8725933906847840*y^908 + 8829454732072484*y^907 + 8933096352127635*y^906 + 9036835183748460*y^905 + 9140647383762528*y^904 + 9244508792945678*y^903 + 9348395008996007*y^902 + 9452281330191897*y^901 + 9556142829555643*y^900 + 9659954298267308*y^899 + 9763690321033408*y^898 + 9867325219249981*y^897 + 9970833127512512*y^896 + 10074187936558122*y^895 + 10177363370888455*y^894 + 10280332931441733*y^893 + 10383069974340297*y^892 + 10485547653279647*y^891 + 10587738999328217*y^890 + 10689616863061737*y^889 + 10791153995382729*y^888 + 10892322989344543*y^887 + 10993096361994634*y^886 + 11093446495874170*y^885 + 11193345721807668*y^884 + 11292766260101878*y^883 + 11391680304241666*y^882 + 11490059961730183*y^881 + 11587877338692722*y^880 + 11685104480338701*y^879 + 11781713456388257*y^878 + 11877676301179640*y^877 + 11972965099875122*y^876 + 12067551928151070*y^875 + 12161408939178544*y^874 + 12254508302876326*y^873 + 12346822293578054*y^872 + 12438323228868060*y^871 + 12528983557886059*y^870 + 12618775799682379*y^869 + 12707672632154594*y^868 + 12795646829899064*y^867 + 12882671353685064*y^866 + 12968719287824486*y^865 + 13053763930133222*y^864 + 13137778728752338*y^863 + 13220737372587114*y^862 + 13302613727557896*y^861 + 13383381927422176*y^860 + 13463016309475063*y^859 + 13541491505700427*y^858 + 13618782377856223*y^857 + 13694864108945970*y^856 + 13769712137666260*y^855 + 13843302250100143*y^854 + 13915610513550433*y^853 + 13986613368402674*y^852 + 14056287561278035*y^851 + 14124610237055954*y^850 + 14191558871327486*y^849 + 14257111362481292*y^848 + 14321245963481667*y^847 + 14383941373963924*y^846 + 14445176671275633*y^845 + 14504931402574878*y^844 + 14563185515116493*y^843 + 14619919448256126*y^842 + 14675114063011110*y^841 + 14728750733921081*y^840 + 14780811277822859*y^839 + 14831278045561927*y^838 + 14880133849969280*y^837 + 14927362057331041*y^836 + 14972946514599961*y^835 + 15016871640574771*y^834 + 15059122352292240*y^833 + 15099684155916740*y^832 + 15138543072303315*y^831 + 15175685727506919*y^830 + 15211099277556439*y^829 + 15244771498541818*y^828 + 15276690710548182*y^827 + 15306845867323822*y^826 + 15335226479373283*y^825 + 15361822703122288*y^824 + 15386625263213894*y^823 + 15409625541131887*y^822 + 15430815496656959*y^821 + 15450187755959996*y^820 + 15467735532221058*y^819 + 15483452713112335*y^818 + 15497333780632956*y^817 + 15509373897951036*y^816 + 15519568828416239*y^815 + 15527915021776296*y^814 + 15534409532379142*y^813 + 15539050104692302*y^812 + 15541835090752144*y^811 + 15542763534960598*y^810 + 15541835090752144*y^809 + 15539050104692302*y^808 + 15534409532379142*y^807 + 15527915021776296*y^806 + 15519568828416239*y^805 + 15509373897951036*y^804 + 15497333780632956*y^803 + 15483452713112335*y^802 + 15467735532221058*y^801 + 15450187755959996*y^800 + 15430815496656959*y^799 + 15409625541131887*y^798 + 15386625263213894*y^797 + 15361822703122288*y^796 + 15335226479373283*y^795 + 15306845867323822*y^794 + 15276690710548182*y^793 + 15244771498541818*y^792 + 15211099277556439*y^791 + 15175685727506919*y^790 + 15138543072303315*y^789 + 15099684155916740*y^788 + 15059122352292240*y^787 + 15016871640574771*y^786 + 14972946514599961*y^785 + 14927362057331041*y^784 + 14880133849969280*y^783 + 14831278045561927*y^782 + 14780811277822859*y^781 + 14728750733921081*y^780 + 14675114063011110*y^779 + 14619919448256126*y^778 + 14563185515116493*y^777 + 14504931402574878*y^776 + 14445176671275633*y^775 + 14383941373963924*y^774 + 14321245963481667*y^773 + 14257111362481292*y^772 + 14191558871327486*y^771 + 14124610237055954*y^770 + 14056287561278035*y^769 + 13986613368402674*y^768 + 13915610513550433*y^767 + 13843302250100143*y^766 + 13769712137666260*y^765 + 13694864108945970*y^764 + 13618782377856223*y^763 + 13541491505700427*y^762 + 13463016309475063*y^761 + 13383381927422176*y^760 + 13302613727557896*y^759 + 13220737372587114*y^758 + 13137778728752338*y^757 + 13053763930133222*y^756 + 12968719287824486*y^755 + 12882671353685064*y^754 + 12795646829899064*y^753 + 12707672632154594*y^752 + 12618775799682379*y^751 + 12528983557886059*y^750 + 12438323228868060*y^749 + 12346822293578054*y^748 + 12254508302876326*y^747 + 12161408939178544*y^746 + 12067551928151070*y^745 + 11972965099875122*y^744 + 11877676301179640*y^743 + 11781713456388257*y^742 + 11685104480338701*y^741 + 11587877338692722*y^740 + 11490059961730183*y^739 + 11391680304241666*y^738 + 11292766260101878*y^737 + 11193345721807668*y^736 + 11093446495874170*y^735 + 10993096361994634*y^734 + 10892322989344543*y^733 + 10791153995382729*y^732 + 10689616863061737*y^731 + 10587738999328217*y^730 + 10485547653279647*y^729 + 10383069974340297*y^728 + 10280332931441733*y^727 + 10177363370888455*y^726 + 10074187936558122*y^725 + 9970833127512512*y^724 + 9867325219249981*y^723 + 9763690321033408*y^722 + 9659954298267308*y^721 + 9556142829555643*y^720 + 9452281330191897*y^719 + 9348395008996007*y^718 + 9244508792945678*y^717 + 9140647383762528*y^716 + 9036835183748460*y^715 + 8933096352127635*y^714 + 8829454732072484*y^713 + 8725933906847840*y^712 + 8622557128046053*y^711 + 8519347371498567*y^710 + 8416327266778085*y^709 + 8313519152881939*y^708 + 8210945008978195*y^707 + 8108626509899889*y^706 + 8006584958150181*y^705 + 7904841339170873*y^704 + 7803416254655222*y^703 + 7702329977589080*y^702 + 7601602386843987*y^701 + 7501253022027266*y^700 + 7401301019361722*y^699 + 7301765166303075*y^698 + 7202663838749386*y^697 + 7104015055421622*y^696 + 7005836416368480*y^695 + 6908145157139459*y^694 + 6810958088586958*y^693 + 6714291650789160*y^692 + 6618161854183309*y^691 + 6522584333229145*y^690 + 6427574288835366*y^689 + 6333146541790366*y^688 + 6239315476476153*y^687 + 6146095094019128*y^686 + 6053498957320960*y^685 + 5961540243918360*y^684 + 5870231692286645*y^683 + 5779585654429600*y^682 + 5689614043446161*y^681 + 5600328385803359*y^680 + 5511739770187560*y^679 + 5423858899445150*y^678 + 5336696040671980*y^677 + 5250261076840903*y^676 + 5164563458113973*y^675 + 5079612253106599*y^674 + 4995416101440403*y^673 + 4911983264628415*y^672 + 4829321579817147*y^671 + 4747438510307985*y^670 + 4666341100470600*y^669 + 4586036025851501*y^668 + 4506529549270567*y^667 + 4427827570497986*y^666 + 4349935583482269*y^665 + 4272858725610066*y^664 + 4196601736043217*y^663 + 4121169004511073*y^662 + 4046564530766019*y^661 + 3972791972891010*y^660 + 3899854607818599*y^659 + 3827755379165355*y^658 + 3756496858791478*y^657 + 3686081294113980*y^656 + 3616510570712255*y^655 + 3547786259101073*y^654 + 3479909578328192*y^653 + 3412881442219846*y^652 + 3346702423944313*y^651 + 3281372801682291*y^650 + 3216892524160984*y^649 + 3153261255732853*y^648 + 3090478342825046*y^647 + 3028542858437463*y^646 + 2967453569482805*y^645 + 2907208980659856*y^644 + 2847807302685929*y^643 + 2789246495528881*y^642 + 2731524237478957*y^641 + 2674637967752948*y^640 + 2618584856379097*y^639 + 2563361846130743*y^638 + 2508965623226933*y^637 + 2455392658582214*y^636 + 2402639179270463*y^635 + 2350701209103646*y^634 + 2299574540834782*y^633 + 2249254776027773*y^632 + 2199737298000372*y^631 + 2151017310973098*y^630 + 2103089813703016*y^629 + 2055949637927477*y^628 + 2009591422664545*y^627 + 1964009651915660*y^626 + 1919198629635734*y^625 + 1875152516686548*y^624 + 1831865306428571*y^623 + 1789330860941288*y^622 + 1747542887215360*y^621 + 1706494972609528*y^620 + 1666180561645293*y^619 + 1626592990693830*y^618 + 1587725465329523*y^617 + 1549571094266055*y^616 + 1512122867248405*y^615 + 1475373688210195*y^614 + 1439316353708705*y^613 + 1403943585301204*y^612 + 1369248008480895*y^611 + 1335222184292444*y^610 + 1301858588751637*y^609 + 1269149643677458*y^608 + 1237087696599984*y^607 + 1205665050808215*y^606 + 1174873945708909*y^605 + 1144706586113291*y^604 + 1115155123030642*y^603 + 1086211682173956*y^602 + 1057868345195045*y^601 + 1030117177412699*y^600 + 1002950209453776*y^599 + 976359464227661*y^598 + 950336938960611*y^597 + 924874631401209*y^596 + 899964522255079*y^595 + 875598600626154*y^594 + 851768846820577*y^593 + 828467257050350*y^592 + 805685826594439*y^591 + 783416573752126*y^590 + 761651523370470*y^589 + 740382730055707*y^588 + 719602262037791*y^587 + 699302223666421*y^586 + 679474739604064*y^585 + 660111976597920*y^584 + 641206128010489*y^583 + 622749434876858*y^582 + 604734170747184*y^581 + 587152662058258*y^580 + 569997273279789*y^579 + 553260426593322*y^578 + 536934587353256*y^577 + 521012283085036*y^576 + 505486089237058*y^575 + 490348647526558*y^574 + 475592651976889*y^573 + 461210866607609*y^572 + 447196111767398*y^571 + 433541281180913*y^570 + 420239328556562*y^569 + 407283284019903*y^568 + 394666240991089*y^567 + 382381372002154*y^566 + 370421915855964*y^565 + 358781192841696*y^564 + 347452592155562*y^563 + 336429586543371*y^562 + 325705719979621*y^561 + 315274621737283*y^560 + 305129994336046*y^559 + 295265627053394*y^558 + 285675384124940*y^557 + 276353217726061*y^556 + 267293156421037*y^555 + 258489317615563*y^554 + 249935896266269*y^553 + 241627176819381*y^552 + 233557522163930*y^551 + 225721385084601*y^550 + 218113297456569*y^549 + 210727881214639*y^548 + 203559837800120*y^547 + 196603958660512*y^546 + 189855114934011*y^545 + 183308267507535*y^544 + 176958456936318*y^543 + 170800813062207*y^542 + 164830545178892*y^541 + 159042951225485*y^540 + 153433408182971*y^539 + 147997380868998*y^538 + 142730412563985*y^537 + 137628133409981*y^536 + 132686251275763*y^535 + 127900559773363*y^534 + 123266929349329*y^533 + 118781314944316*y^532 + 114439747308027*y^531 + 110238340304328*y^530 + 106173282459017*y^529 + 102240843924128*y^528 + 98437368245632*y^527 + 94759279010024*y^526 + 91203071830294*y^525 + 87765320677722*y^524 + 84442670093739*y^523 + 81231841219122*y^522 + 78129624219915*y^521 + 75132884036461*y^520 + 72238553020681*y^519 + 69443636407019*y^518 + 66745205168528*y^517 + 64140401221500*y^516 + 61626430488492*y^515 + 59200567856702*y^514 + 56860150445667*y^513 + 54602582321801*y^512 + 52425327976532*y^511 + 50325916807381*y^510 + 48301936795528*y^509 + 46351038772509*y^508 + 44470930294083*y^507 + 42659379693854*y^506 + 40914210159126*y^505 + 39233303581272*y^504 + 37614594822327*y^503 + 36056075379039*y^502 + 34555787837266*y^501 + 33111829351342*y^500 + 31722346290416*y^499 + 30385537541434*y^498 + 29099649337087*y^497 + 27862978398196*y^496 + 26673866939713*y^495 + 25530705653070*y^494 + 24431928894154*y^493 + 23376017513498*y^492 + 22361494215565*y^491 + 21386926250737*y^490 + 20450920942555*y^489 + 19552128242181*y^488 + 18689236426307*y^487 + 17860974520443*y^486 + 17066108157849*y^485 + 16303441884554*y^484 + 15571815175325*y^483 + 14870104620270*y^482 + 14197220100303*y^481 + 13552106861442*y^480 + 12933741839899*y^479 + 12341135635235*y^478 + 11773328981483*y^477 + 11229394619008*y^476 + 10708433913262*y^475 + 10209578630140*y^474 + 9731987693363*y^473 + 9274848873719*y^472 + 8837375680898*y^471 + 8418808965914*y^470 + 8018413948848*y^469 + 7635481738958*y^468 + 7269326489361*y^467 + 6919286843610*y^466 + 6584723213704*y^465 + 6265019152487*y^464 + 5959578755669*y^463 + 5667827963566*y^462 + 5389212078927*y^461 + 5123197006289*y^460 + 4869266881582*y^459 + 4626925247931*y^458 + 4395692797816*y^457 + 4175108488550*y^456 + 3964727389027*y^455 + 3764121741811*y^454 + 3572878910940*y^453 + 3390602389686*y^452 + 3216909849508*y^451 + 3051434096031*y^450 + 2893821211946*y^449 + 2743731467669*y^448 + 2600837554495*y^447 + 2464825448513*y^446 + 2335392734382*y^445 + 2212249424868*y^444 + 2095116368246*y^443 + 1983726028916*y^442 + 1877820975168*y^441 + 1777154619819*y^440 + 1681489788194*y^439 + 1590599420536*y^438 + 1504265214046*y^437 + 1422278292091*y^436 + 1344437917067*y^435 + 1270552124993*y^434 + 1200436509276*y^433 + 1133914822434*y^432 + 1070817824773*y^431 + 1010983857544*y^430 + 954257753733*y^429 + 900491381529*y^428 + 849542617012*y^427 + 801275859118*y^426 + 755561059108*y^425 + 712274211009*y^424 + 671296435063*y^423 + 632514442353*y^422 + 595819672189*y^421 + 561108732221*y^420 + 528282584833*y^419 + 497246966079*y^418 + 467911618783*y^417 + 440190689221*y^416 + 414002006749*y^415 + 389267459099*y^414 + 365912314318*y^413 + 343865577844*y^412 + 323059354425*y^411 + 303429185857*y^410 + 284913452879*y^409 + 267453694512*y^408 + 250994045973*y^407 + 235481542190*y^406 + 220865589927*y^405 + 207098254570*y^404 + 194133766301*y^403 + 181928790813*y^402 + 170441966142*y^401 + 159634159836*y^400 + 149468034620*y^399 + 139908291043*y^398 + 130921262045*y^397 + 122475141756*y^396 + 114539605867*y^395 + 107086028628*y^394 + 100087127594*y^393 + 93517168095*y^392 + 87351632249*y^391 + 81567411419*y^390 + 76142496873*y^389 + 71056162189*y^388 + 66288674187*y^387 + 61821464449*y^386 + 57636860670*y^385 + 53718247833*y^384 + 50049817550*y^383 + 46616720518*y^382 + 43404832757*y^381 + 40400898786*y^380 + 37592314751*y^379 + 34967262684*y^378 + 32514508546*y^377 + 30223529082*y^376 + 28084323773*y^375 + 26087533643*y^374 + 24224267278*y^373 + 22486212019*y^372 + 20865472184*y^371 + 19354673930*y^370 + 17946814901*y^369 + 16635362300*y^368 + 15414114032*y^367 + 14277290236*y^366 + 13219404469*y^365 + 12235349889*y^364 + 11320279729*y^363 + 10469687646*y^362 + 9679297643*y^361 + 8945138936*y^360 + 8263443950*y^359 + 7630718671*y^358 + 7043648186*y^357 + 6499162145*y^356 + 5994347965*y^355 + 5526511602*y^354 + 5093097335*y^353 + 4691744778*y^352 + 4320214692*y^351 + 3976441876*y^350 + 3658467191*y^349 + 3364486581*y^348 + 3092788314*y^347 + 2841798846*y^346 + 2610024936*y^345 + 2396096082*y^344 + 2198711618*y^343 + 2016679881*y^342 + 1848869496*y^341 + 1694245990*y^340 + 1551826889*y^339 + 1420715489*y^338 + 1300059954*y^337 + 1189084411*y^336 + 1087051347*y^335 + 993290571*y^334 + 907164667*y^333 + 828095629*y^332 + 755533468*y^331 + 688980643*y^330 + 627963266*y^329 + 572053851*y^328 + 520844871*y^327 + 473969587*y^326 + 431078138*y^325 + 391856581*y^324 + 356005000*y^323 + 323255164*y^322 + 293350487*y^321 + 266062168*y^320 + 241171101*y^319 + 218482569*y^318 + 197809729*y^317 + 178987225*y^316 + 161856093*y^315 + 146276124*y^314 + 132112328*y^313 + 119246146*y^312 + 107563103*y^311 + 96963169*y^310 + 87349501*y^309 + 78637842*y^308 + 70746444*y^307 + 63604540*y^306 + 57143201*y^305 + 51303148*y^304 + 46026431*y^303 + 41263462*y^302 + 36965620*y^301 + 33091578*y^300 + 29600587*y^299 + 26458297*y^298 + 23630664*y^297 + 21089176*y^296 + 18805464*y^295 + 16755957*y^294 + 14917024*y^293 + 13269250*y^292 + 11793028*y^291 + 10472375*y^290 + 9291060*y^289 + 8236001*y^288 + 7293767*y^287 + 6453684*y^286 + 5704686*y^285 + 5038070*y^284 + 4444748*y^283 + 3917670*y^282 + 3449359*y^281 + 3034135*y^280 + 2665885*y^279 + 2340024*y^278 + 2051569*y^277 + 1796855*y^276 + 1571812*y^275 + 1373524*y^274 + 1198689*y^273 + 1044984*y^272 + 909741*y^271 + 791131*y^270 + 686983*y^269 + 595872*y^268 + 516054*y^267 + 446405*y^266 + 385528*y^265 + 332557*y^264 + 286364*y^263 + 246288*y^262 + 211428*y^261 + 181274*y^260 + 155112*y^259 + 132559*y^258 + 113039*y^257 + 96271*y^256 + 81801*y^255 + 69414*y^254 + 58754*y^253 + 49668*y^252 + 41869*y^251 + 35251*y^250 + 29588*y^249 + 24803*y^248 + 20722*y^247 + 17293*y^246 + 14375*y^245 + 11937*y^244 + 9871*y^243 + 8154*y^242 + 6703*y^241 + 5507*y^240 + 4498*y^239 + 3673*y^238 + 2980*y^237 + 2417*y^236 + 1946*y^235 + 1568*y^234 + 1251*y^233 + 1000*y^232 + 791*y^231 + 627*y^230 + 490*y^229 + 385*y^228 + 297*y^227 + 231*y^226 + 176*y^225 + 135*y^224 + 101*y^223 + 77*y^222 + 56*y^221 + 42*y^220 + 30*y^219 + 22*y^218 + 15*y^217 + 11*y^216 + 7*y^215 + 5*y^214 + 3*y^213 + 2*y^212 + y^211 + y^210)*x^20 

house edge should now be easy
back to eating
Sally
I Heart Vi Hart
Ace2
Ace2
  • Threads: 32
  • Posts: 2706
Joined: Oct 2, 2017
June 5th, 2018 at 1:13:49 PM permalink
If you pick one number the expected value is 40.5 and the standard deviation σ is 23.0922....

For 20 numbers the standard deviation is 20^.5 * σ * (60 / 79 ) ^.5 = 90.

So the expected value is 810 +/- 90. The probability mass function for the value 810 is 0.00443.
Last edited by: Ace2 on Jun 5, 2018
It’s all about making that GTA
Ace2
Ace2
  • Threads: 32
  • Posts: 2706
Joined: Oct 2, 2017
June 5th, 2018 at 2:44:04 PM permalink
There is another solution using the formula for the probability of a result being equal to expectations...which is 1 / (variance * N * 2 * pi) ^ .5

So:

1 / (σ * (60 / 79 * 20 * 2 * pi)^.5) = 0.00443.
Last edited by: Ace2 on Jun 5, 2018
It’s all about making that GTA
mustangsally
mustangsally
  • Threads: 25
  • Posts: 2463
Joined: Mar 29, 2011
June 5th, 2018 at 4:09:54 PM permalink
Quote: mustangsally

here be the results

I thought I would add this to a webpage so anyone can view or inspect.
I never have seen this info (keno 80 draw 20 sums) published as exact results.
Can't say that anymore

I am certain I am NOT the 1st to do this.

https://sites.google.com/view/krapstuff/keno

approximations in Excel are close enough for me

Sally
I Heart Vi Hart
  • Jump to: