1663:
1683:
207:
although some paytables pay for hitting a lesser number of spots. For example, it is not uncommon to see casinos paying $ 500 or even $ 1,000 for a “catch” of 0 out of 20 on a 20 spot ticket with a $ 5.00 wager. Payouts vary widely by casino. Most casinos allow paytable wagers of 1 through 20 numbers, but some limit the choice to only 1 through 10, 12 and 15 numbers, or "spots" as keno aficionados call the numbers selected.
1693:
29:
1673:
221:
Even though it is highly improbable to hit all 20 numbers on a 20 spot ticket, the same player would typically also get paid for hitting “catches” 0, 1, 2, 3, and 7 through 19 out of 20, often with the 17 through 19 catches paying the same as the solid 20 hit. Some of the other paying "catches" on a
206:
Keno payouts are based on how many numbers the player chooses and how many of those numbers are "hit", multiplied by the proportion of the player's original wager to the "base rate" of the paytable. Typically, the more numbers a player chooses and the more numbers hit, the greater the payout,
749:
84:
Each casino sets its own series of payouts, called "paytables". The player is paid based on how many numbers were chosen (either player selection, or the terminal picking the numbers), the number of matches out of those chosen, and the wager.
72:
Players wager by choosing numbers ranging from 1 through (usually) 80. After all players make their wagers, 20 numbers (some variants draw fewer numbers) are drawn at random, either with a ball machine similar to ones used for lotteries and
590:
92:" than other games, ranging from less than 4 percent to over 35 percent in online play, and 20-40% in in-person casinos. By way of comparison, the typical house edge for non-slot casino games is under 5%.
182:, from which the winning characters were selected. Eventually, Chinese immigrants introduced keno to the West when they sailed across the Pacific Ocean to work on construction of the
1052:"Chinese Gambling Games; Mysteries Of Fan Tan And Boc Hop Bu. Two Popular Games In The Chinese Quarters Of American Cities-- Superstitions Of The Players. Boc Hop Bu. Superstitions"
842:
622:
889:
791:
610:
479:
455:
435:
484:
145:
decided to grant a licence to lottery operators. According to some, results of keno games in great cities were sent to outlying villages and hamlets by
1051:
1535:
1540:
1545:
1176:
1080:
194:. There were also other, earlier games called Keno, but these were played in the same way as the game now known as "
183:
1696:
1501:
130:
to raise money to defend an ancient city, and its widespread popularity later helped raise funds to build the
1522:
1194:
405:
Probabilities change significantly based on the number of spots and numbers that are picked on each ticket.
153:, with the literal reading "white dove tickets" in Mandarin, but in Southern varieties of Chinese spoken in
1550:
1413:
1318:
414:
1133:
796:
744:{\displaystyle P(X=4)={{{6 \choose 4}{{80-6} \choose {20-4}}} \over {80 \choose 20}}\approx 0.02853791}
178:
1676:
1263:
222:
20 spot ticket or any other ticket with high "solid catch" odds are in reality very possible to hit:
123:
1418:
1355:
855:
757:
1727:
1599:
1573:
195:
78:
1105:
1371:
1169:
1568:
1430:
1386:
20:
1648:
1440:
1408:
1376:
1258:
88:
There are a wide variety of keno paytables depending on the casino, usually with a larger "
1682:
1313:
894:
To calculate "odds-to-1", divide the probability into 1.0 and subtract 1 from the result.
8:
1496:
1466:
1450:
1350:
131:
1722:
1587:
1530:
1517:
1491:
1486:
1481:
1471:
1445:
1435:
1425:
1345:
1308:
1286:
595:
464:
440:
420:
173:
127:
1666:
1476:
1403:
1398:
1391:
1381:
1268:
1162:
616:
To calculate the probability of hitting 4 spots on a 6-spot ticket, the formula is:
585:{\displaystyle ={{n \choose r}\times {{80-n} \choose {20-r}} \over {80 \choose 20}}}
1643:
1278:
1235:
122:"five each"), but by all accounts the game originated in China. Legend has it that
41:
945:
1213:
214:
of a player hitting all 20 numbers on a 20 spot ticket is approximately 1 in 3.5
141:
Chinese lottery is not documented before 1847, when the
Portuguese government of
107:
1717:
1612:
1303:
1068:
146:
1711:
1617:
1291:
1220:
1686:
970:
138:
to fund a public institution was not accepted before the late 19th century.
1622:
1298:
74:
1084:
1607:
910:
215:
211:
1007:
1638:
89:
982:
845:
162:
154:
1225:
1185:
166:
135:
101:
62:
28:
1230:
1208:
923:
66:
417:. For Keno, one calculates the probability of hitting exactly
47:
1134:"Hypergeometric Distribution: Uses, Calculator & Formula"
142:
111:
1154:
53:
186:
in the 19th century, where the name was
Westernized into
172:
The
Chinese played the game using sheets printed with
858:
800:
760:
625:
598:
487:
467:
443:
423:
50:
44:
883:
836:
785:
743:
604:
584:
473:
449:
429:
875:
862:
777:
764:
1709:
924:"Keno - Strategy and Odds by The Wizard of Odds"
157:simply meaning "pigeon tickets", and pronounced
69:, and also offered as a game in some lotteries.
165:(on which the Western spelling 'pak-ah-pu' / '
1170:
727:
714:
704:
675:
666:
653:
574:
561:
551:
522:
510:
497:
1121:(Third ed.). Duxbury Press. p. 42.
915:
65:-like gambling game often played at modern
1177:
1163:
408:
1119:Mathematical Statistics and Data Analysis
27:
921:
176:, often the first 80 characters of the
1710:
1158:
1046:
1044:
1030:
1028:
367:1 in 1,496,372,110.872 (0.00000007%)
134:. In modern China, the idea of using
1672:
1116:
149:, resulting in its Chinese name 白鸽票
1692:
971:Casino advantages for various games
399:1 in 3,535,316,142,212,173,800.000
13:
1041:
1025:
866:
768:
718:
679:
657:
565:
526:
501:
359:1 in 41,751,453.986 (0.00000240%)
218:(1 in 3,535,316,142,212,174,320).
14:
1739:
1131:
1036:Colour, confusion and concessions
848:. Spreadsheets have the function
837:{\displaystyle n! \over r!(n-r)!}
351:1 in 1,821,881.628 (0.00005489%)
1691:
1681:
1671:
1662:
1661:
926:. Wizard Of Odds Consulting, Inc
201:
198:", not the modern game of Keno.
40:
1125:
1110:
1099:
1083:. Gambling Info. Archived from
1073:
1034:Melanie Yap, Dianne Leong Man.
413:Keno probabilities come from a
391:1 in 2,946,096,785,176,811.500
343:1 in 118,084.920 (0.00084685%)
184:First transcontinental railroad
1062:
1000:
975:
964:
950:Kiowa Casino - Oklahoma Casino
938:
904:
827:
815:
641:
629:
335:1 in 10,968.701 (0.00911685%)
1:
1081:"Tutorial - How to play Keno"
897:
884:{\displaystyle {n \choose r}}
844:, where X! is notation for X
786:{\displaystyle {n \choose r}}
457:-spot ticket by the formula:
327:1 in 1,423.822 (0.07023351%)
126:invented the game during the
1184:
383:1 in 10,512,388,171,906.553
7:
415:hypergeometric distribution
319:1 in 253.801 (0.39401000%)
239:1 in 843.380 (0.11857057%)
118:"five winning numbers", L.
32:A set of keno betting slips
10:
1744:
311:1 in 61.420 (1.62814048%)
303:1 in 20.055 (4.98618021%)
295:1 in 8.826 (11.32954556%)
287:1 in 5.258 (19.01745147%)
279:1 in 4.287 (23.32807380%)
271:1 in 4.877 (20.50318987%)
263:1 in 8.009 (12.48637168%)
255:1 in 20.115 (4.97142576%)
247:1 in 86.446 (1.15678605%)
179:Thousand Character Classic
99:
95:
18:
1657:
1631:
1598:
1582:
1561:
1510:
1459:
1364:
1338:
1331:
1277:
1264:Mathematics of bookmaking
1251:
1244:
1201:
1192:
946:"What is the House Edge?"
849:
375:1 in 90,624,035,964.712
409:Probability calculation
79:random number generator
1117:Rice, John A. (2007).
922:Shackleford, Michael.
885:
838:
787:
745:
606:
586:
475:
451:
431:
33:
1106:Probabilities in keno
886:
839:
788:
746:
607:
587:
476:
452:
432:
31:
21:Keno (disambiguation)
1649:Video game addiction
1259:Gambling mathematics
1195:Gambling terminology
856:
797:
758:
623:
596:
485:
465:
441:
421:
106:The word "keno" has
19:For other uses, see
1138:statisticsbyjim.com
132:Great Wall of China
1309:Due Column betting
1287:Advantage gambling
1058:. 5 February 1888.
1056:The New York Times
881:
807:
783:
741:
602:
582:
471:
447:
427:
174:Chinese characters
128:Chu-Han Contention
34:
1705:
1704:
1594:
1593:
1327:
1326:
1314:Labouchère system
1269:Poker probability
873:
834:
793:is calculated as
775:
733:
725:
702:
664:
605:{\displaystyle n}
580:
572:
549:
508:
474:{\displaystyle r}
450:{\displaystyle n}
430:{\displaystyle r}
403:
402:
1735:
1695:
1694:
1685:
1675:
1674:
1665:
1664:
1644:Problem gambling
1336:
1335:
1249:
1248:
1236:Riverboat casino
1179:
1172:
1165:
1156:
1155:
1149:
1148:
1146:
1144:
1129:
1123:
1122:
1114:
1108:
1103:
1097:
1096:
1094:
1092:
1077:
1071:
1066:
1060:
1059:
1048:
1039:
1032:
1023:
1022:
1020:
1018:
1004:
998:
997:
995:
993:
979:
973:
968:
962:
961:
959:
957:
952:. 2 January 2020
942:
936:
935:
933:
931:
919:
913:
911:Online Keno odds
908:
890:
888:
887:
882:
880:
879:
878:
865:
851:
843:
841:
840:
835:
833:
799:
792:
790:
789:
784:
782:
781:
780:
767:
750:
748:
747:
742:
734:
732:
731:
730:
717:
710:
709:
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707:
701:
690:
678:
671:
670:
669:
656:
648:
611:
609:
608:
603:
591:
589:
588:
583:
581:
579:
578:
577:
564:
557:
556:
555:
554:
548:
537:
525:
515:
514:
513:
500:
492:
480:
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472:
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436:
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428:
225:
224:
60:
59:
56:
55:
52:
49:
46:
1743:
1742:
1738:
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1734:
1733:
1732:
1708:
1707:
1706:
1701:
1653:
1627:
1590:
1578:
1557:
1551:Atlantic Canada
1506:
1455:
1360:
1323:
1273:
1240:
1197:
1188:
1183:
1153:
1152:
1142:
1140:
1130:
1126:
1115:
1111:
1104:
1100:
1090:
1088:
1079:
1078:
1074:
1067:
1063:
1050:
1049:
1042:
1033:
1026:
1016:
1014:
1006:
1005:
1001:
991:
989:
981:
980:
976:
969:
965:
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953:
944:
943:
939:
929:
927:
920:
916:
909:
905:
900:
874:
861:
860:
859:
857:
854:
853:
808:
798:
795:
794:
776:
763:
762:
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711:
703:
691:
680:
674:
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650:
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647:
624:
621:
620:
597:
594:
593:
573:
560:
559:
558:
550:
538:
527:
521:
520:
519:
509:
496:
495:
494:
493:
491:
486:
483:
482:
466:
463:
462:
442:
439:
438:
422:
419:
418:
411:
204:
147:carrier pigeons
104:
98:
43:
39:
24:
17:
12:
11:
5:
1741:
1731:
1730:
1728:Gambling games
1725:
1720:
1703:
1702:
1700:
1699:
1689:
1679:
1669:
1658:
1655:
1654:
1652:
1651:
1646:
1641:
1635:
1633:
1629:
1628:
1626:
1625:
1620:
1615:
1613:Game of chance
1610:
1604:
1602:
1596:
1595:
1592:
1591:
1586:
1584:
1580:
1579:
1577:
1576:
1571:
1565:
1563:
1559:
1558:
1556:
1555:
1554:
1553:
1548:
1546:Western Canada
1543:
1538:
1533:
1525:
1520:
1514:
1512:
1508:
1507:
1505:
1504:
1502:United Kingdom
1499:
1494:
1489:
1484:
1479:
1474:
1469:
1463:
1461:
1457:
1456:
1454:
1453:
1448:
1443:
1438:
1433:
1428:
1423:
1422:
1421:
1411:
1406:
1401:
1396:
1395:
1394:
1389:
1379:
1374:
1368:
1366:
1362:
1361:
1359:
1358:
1353:
1348:
1342:
1340:
1333:
1329:
1328:
1325:
1324:
1322:
1321:
1316:
1311:
1306:
1304:Asian handicap
1301:
1296:
1295:
1294:
1283:
1281:
1275:
1274:
1272:
1271:
1266:
1261:
1255:
1253:
1246:
1242:
1241:
1239:
1238:
1233:
1228:
1223:
1218:
1217:
1216:
1205:
1203:
1199:
1198:
1193:
1190:
1189:
1182:
1181:
1174:
1167:
1159:
1151:
1150:
1124:
1109:
1098:
1072:
1061:
1040:
1024:
999:
987:kenoonline.org
983:"Keno History"
974:
963:
937:
914:
902:
901:
899:
896:
877:
872:
869:
864:
852:to calculate
832:
829:
826:
823:
820:
817:
814:
811:
806:
803:
779:
774:
771:
766:
752:
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729:
724:
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689:
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634:
631:
628:
614:
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601:
576:
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568:
563:
553:
547:
544:
541:
536:
533:
530:
524:
518:
512:
507:
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446:
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410:
407:
401:
400:
397:
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392:
389:
385:
384:
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377:
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373:
369:
368:
365:
361:
360:
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353:
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333:
329:
328:
325:
321:
320:
317:
313:
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309:
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281:
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273:
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257:
256:
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249:
248:
245:
241:
240:
237:
233:
232:
229:
203:
200:
169:' was based).
97:
94:
16:Game of chance
15:
9:
6:
4:
3:
2:
1740:
1729:
1726:
1724:
1721:
1719:
1716:
1715:
1713:
1698:
1690:
1688:
1684:
1680:
1678:
1670:
1668:
1660:
1659:
1656:
1650:
1647:
1645:
1642:
1640:
1637:
1636:
1634:
1630:
1624:
1621:
1619:
1618:Game of skill
1616:
1614:
1611:
1609:
1606:
1605:
1603:
1601:
1597:
1589:
1585:
1583:South America
1581:
1575:
1572:
1570:
1567:
1566:
1564:
1560:
1552:
1549:
1547:
1544:
1542:
1539:
1537:
1534:
1532:
1529:
1528:
1526:
1524:
1523:United States
1521:
1519:
1516:
1515:
1513:
1511:North America
1509:
1503:
1500:
1498:
1495:
1493:
1490:
1488:
1485:
1483:
1480:
1478:
1475:
1473:
1470:
1468:
1465:
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1462:
1458:
1452:
1449:
1447:
1444:
1442:
1439:
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1429:
1427:
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1417:
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1410:
1407:
1405:
1402:
1400:
1397:
1393:
1390:
1388:
1385:
1384:
1383:
1380:
1378:
1375:
1373:
1370:
1369:
1367:
1363:
1357:
1354:
1352:
1349:
1347:
1344:
1343:
1341:
1337:
1334:
1330:
1320:
1317:
1315:
1312:
1310:
1307:
1305:
1302:
1300:
1297:
1293:
1292:Card counting
1290:
1289:
1288:
1285:
1284:
1282:
1280:
1276:
1270:
1267:
1265:
1262:
1260:
1257:
1256:
1254:
1250:
1247:
1243:
1237:
1234:
1232:
1229:
1227:
1224:
1222:
1221:Online casino
1219:
1215:
1212:
1211:
1210:
1207:
1206:
1204:
1200:
1196:
1191:
1187:
1180:
1175:
1173:
1168:
1166:
1161:
1160:
1157:
1139:
1135:
1128:
1120:
1113:
1107:
1102:
1087:on 6 May 2021
1086:
1082:
1076:
1070:
1065:
1057:
1053:
1047:
1045:
1038:, pp.240-241.
1037:
1031:
1029:
1013:
1009:
1003:
988:
984:
978:
972:
967:
951:
947:
941:
925:
918:
912:
907:
903:
895:
892:
870:
867:
847:
830:
824:
821:
818:
812:
809:
804:
801:
772:
769:
738:
735:
722:
719:
698:
695:
692:
687:
684:
681:
661:
658:
644:
638:
635:
632:
626:
619:
618:
617:
612:-spot ticket.
599:
569:
566:
545:
542:
539:
534:
531:
528:
516:
505:
502:
488:
468:
460:
459:
458:
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386:
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379:
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219:
217:
213:
208:
202:Probabilities
199:
197:
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185:
181:
180:
175:
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168:
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160:
159:baak-gaap-piu
156:
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1252:Mathematics
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850:COMBIN(n,r)
216:quintillion
212:probability
124:Zhang Liang
114:roots (Fr.
1712:Categories
1687:Wiktionary
1639:Gaming law
1372:Bangladesh
1319:Martingale
1279:Strategies
1012:Wiktionary
898:References
739:0.02853791
461:P(hitting
188:boc hop bu
151:báigē piào
100:See also:
90:house edge
1723:Lotteries
1569:Australia
1431:Singapore
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1332:By region
1017:22 August
846:factorial
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1677:Commons
1562:Oceania
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1245:Science
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592:for an
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67:casinos
63:lottery
1632:Issues
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992:9 June
754:where
108:French
1718:Bingo
1600:Games
1477:Italy
1404:Japan
1399:India
1392:Macau
1382:China
196:Bingo
143:Macao
120:quini
116:quine
112:Latin
75:bingo
61:is a
1365:Asia
1214:List
1145:2023
1093:2011
1019:2022
1008:"白鴿"
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