[Buzz]

[ QUOTE ]
Average low limit live game with 20 people seeing the flop.

Which AAxx hands have enough of an equity edge to raise out of the blinds for value? I'm assuming suitedness matters a lot here...

[/ QUOTE ]Hi Niediam - You tell me where to draw the line.

Following are simulated win totals for 211 double ace hands.
d means double suited
s means two cards in same suit including an ace
s- means two cards in same suit not including an ace
s”’ means three cards in same suit
n means rainbow (four different suits)

For all s hands shown, the ace is the same suit as the lowest card (but it would not make much difference if the ace were the same suit as the middle card).

Results are all for 10,000 runs against eight non-folding random hands. (In other words, a different random hand was simulated as dealt to each of eight different table positions 10,000 times).

The first column is the hand,
the second column is high only win sub-total,
the third column is low only win sub-total,
the fourth column is scoop sub-total,
the fifth column is total of second, third and fourth columns.

For the second and third columns each solo win is counted as 0.5, each a two way tie is counted as 0.25, each three way tie is counted as 1/6, and each four way tie is counted as 0.125. All values are rounded off to the nearest whole number. In the case of exact halves, the numbers are rounded to the nearest even number.

If the simulations were re-run, it is expected that the totals would change somewhat, but not substantially. 1,111 is average for a nine handed 10,000 run simulation.

In a real game, obviously all eight opponents who are dealt hands will not continue to the showdown. How many opponents do continue to the showdown depends on the actual hands dealt, the flop cards, the turn card, the river card, the betting, and how the opponents interact. If the simulations were run against a different number of opponents, the relative order would change somewhat. If the simulations were run against different groups or mixtures of opponent tendencies, the relative order would change even more.

Note that the worst starting hand on this list, AA89n, would not be the worst hand on a one-on-one list of the same hands. Also note that if you raise before the flop against Chester Milktoast with AA89n, you have a better chance of stealing the pot, or winning after the flop with a continuation bet than if you raise before the flop with an even better hand against Bulldog Doubter.

You tell me where to draw the line.

AA23d.....361+1520+1325=3206
AA24d.....405+1364+1279=3048
AA23s.....314+1599+1016=2929
AA34d.....424+1189+1290=2903
AA25d.....441+1225+1198=2864
AA22d.....516+1164+1131=2811
AA23s”’.....271+1601+920=2792
AA24s.....454+1385+916=2755
AA35d.....487+1063+1175=2725
AA33d.....574+964+1167=2705
AA2Kd.....574+1034+1065=2673
AA26d.....473+1117+1081=2671
AA24s”’.....325+1506+838=2669
AA23s-.....240+1675+736=2651
AA2Jd.....556+1032+1053=2641
AA2Qd.....555+1026+1056=2637
AA2Td.....573+1027+1033=2633
AA23n.....253+1685+686=2624
AA34s.....372+1317+931=2620
AA25s.....364+1340+912=2616
AA22s.....485+1232+853=2570
AA27d.....499+1023+1038=2560
AA36d.....504+947+1103=2554
AA3Qd.....594+860+1077=2531
AA3Jd.....608+873+1046=2527
AA29d.....544+1032+944=2520
AA45d.....510+872+1125=2507
AA3Td.....556+885+1044=2485
AA44d.....600+742+1142=2484
AA25s”’.....346+1292+845=2483
AA28d.....515+930+1033=2478
AA3Kd.....592+876+1008=2476
AA24s-.....291+1500+683=2474
AA35s.....415+1153+872=2440
AA46d.....585+762+1068=2415
AA33s.....492+1031+888=2411
AA2Ts.....458+1069+883=2410
AA2Qs.....440+1125+843=2408
AA37d.....555+838+1013=2406
AA2Js.....461+1097+844=2402
AA2Ks.....466+1091+844=2401
AA39d.....537+843+1002=2382
AA24n.....191+1548+641=2380
AA26s.....394+1180+785=2359
AA4Kd.....610+670+1045=2325
AA25s-.....318+1365+626=2309
AA34s-.....335+1306+667=2308
AA38d.....524+797+975=2296
AA25n.....316+1392+583=2291
AA34n.....316+1334+640=2290
AA45s.....422+969+898=2289
AA4Td.....599+689+992=2280
AA36s.....419+1008+843=2270
AA4Jd.....604+684+980=2268
AA3Ts.....495+928+843=2266
AA29s.....381+1106+770=2257
AA4Qd.....604+687+960=2251
AA22n.....422+1317+498=2237
AA3Ks.....475+925+828=2228
AA3Qs.....465+901+857=2223
AA27s.....409+1033+762=2204
AA47d.....582+673+949=2204
AA3Js.....463+921+818=2202
AA55d.....641+508+1037=2186
AA44s.....522+811+845=2178
AA45s”’.....420+927+811=2158
AA28s.....422+993+736=2151
AA48d.....567+646+928=2141
AA49d.....572+684+882=2138
AA35s-.....342+1138+654=2134
AA39s.....454+938+716=2108
AA35n.....325+1175+600=2100
AA38s.....433+836+812=2081
AA37s.....427+870+774=2071
AA4Ks.....498+713+856=2067
AA2Kn.....376+1156+534=2066
AA46s.....447+818+801=2066
AA33n.....456+1069+539=2064
AA2Jn.....382+1137+542=2061
AA2Qn.....382+1169+504=2055
AA26n.....307+1231+508=2046
AA2Tn.....371+1147+508=2026
AA4Ts.....487+719+802=2008
AA4Js.....489+731+782=2002
AA66d.....666+305+1013=1984
AAKKd.....794+0+1186=1980
AA45s-.....371+959+644=1974
AA4Qs.....493+726+741=1960
AA29n.....360+1172+416=1948
AA3Kn.....383+993+568=1944
AA55s.....561+567+812=1940
AA3Jn.....405+1001+533=1939
AA3Tn.....408+991+525=1924
AAQQd.....784+0+1137=1921
AA45n.....340+981+599=1920
AAJJd.....807+0+1113=1920
AA27n.....349+1125+445=1919
AA47s.....486+709+713=1908
AA36n.....335+1055+510=1900
AA5Js.....516+531+743=1889
AA3Qn.....401+960+527=1888
AA49s.....456+725+688=1869
AA57s.....508+530+718=1856
AA28n.....342+1047+450=1839
AA48s.....468+677+681=1826
AA44n.....455+808+561=1824
AA5Ts.....521+531+769=1821
AATTd.....800+0+1019=1819
AA5Ks.....532+534+744=1810
AA68d.....639+309+854=1802
AA6Kd.....643+304+851=1798
AA37n.....354+959+467=1780
AA46n.....371+866+538=1775
AA39n.....348+954+453=1755
AAKKs.....656+0+1091=1747
AA4Tn.....395+809+528=1732
AA38n.....356+901+450=1707
AA77d.....760+103+844=1707
AA4Qn.....394+750+560=1704
AATJd.....809+0+884=1693
AA4Kn.....391+763+522=1676
AATQd.....782+0+893=1675
AATKd.....771+0+904=1675
AAJKd.....781+0+893=1674
AA66s.....559+352+759=1670
AAQQs.....660+0+1008=1668
AAQKd.....738+0+922=1660
AA4Jn.....382+751+523=1656
AA88d.....765+8+879=1652
AAJQd.....762+0+894=1636
AA99d.....765+0+868=1633
AA47n.....384+731+517=1632
AA55n.....449+582+579=1610
AATTs.....672+0+931=1603
AAJJs.....646+0+956=1602
AA49n.....365+776+457=1598
AA78d.....677+95+820=1592
AA48n.....376+715+498=1589
AA56n.....397+655+531=1583
AA9Jd.....814+0+747=1561
AA67s.....550+339+669=1558
AA79d.....697+92+758=1547
AA5Tn.....403+559+569=1531
AA6Ks.....501+316+696=1513
AA89d.....754+10+746=1510
AA5Qn.....385+544+572=1501
AA5Kn.....386+577+536=1499
AA5Jn.....388+547+548=1483
AA68s.....540+309+631=1480
AA69s.....526+324+610=1460
AA68s”’.....482+319+638=1439
AAKKn.....506+0+932=1438
AA77s.....609+108+721=1437
AAJKs.....610+0+827=1437
AA7Ts.....603+102+726=1431
AAQQn.....481+0+945=1426
AA57n.....412+534+478=1424
AATJs.....662+0+757=1419
AATQs.....615+0+803=1418
AA58n.....390+539+488=1417
AAQKs.....616+0+800=1416
AA99s.....575+0+827=1402
AA8Ts.....636+16+740=1392
AA59n.....386+550+441=1377
AAJQs.....617+0+758=1375
AAJJn.....503+0+868=1371
AA66n.....470+383+508=1361
AA88s.....630+13+708=1351
AA7Qs.....519+101+728=1348
AA7Ks.....496+104+736=1336
AATKs.....587+0+736=1323
AA68s-.....418+339+559=1316
AATTn.....530+0+773=1303
AA7Js.....503+103+684=1290
AA9Ts.....649+0+634=1283
AA79s.....560+113+606=1279
AA6Kn.....408+350+516=1274
AA6Jn.....379+359+522=1260
AA78s.....545+108+599=1252
AA6Tn.....401+349+493=1243
AA89s.....623+15+601=1239
AA6Qn.....401+355+477=1233
AA67n.....409+354+456=1219
AA68n.....418+329+469=1216
AA99n.....439+0+762=1201
AA77n.....494+115+541=1150
AA89s”’.....585+13+543=1141
AA69n.....394+337+404=1135
AATJn.....503+0+621=1124
AAJQn.....476+0+647=1123
AAJKn.....464+0+658=1122
AATQn.....454+0+650=1104
AA7Tn.....438+115+539=1092
AAQKn.....442+0+627=1069
AATKn.....459+0+609=1068
AA9Tn.....508+0+548=1056
AA88n.....512+14+528=1054
AA8Jn.....458+13+569=1040
AA8Tn.....484+15+535=1034
AA7Qn.....388+124+516=1028
AA89s-.....487+19+512=1018
AA7Kn.....393+109+508=1010
AA7Jn.....398+105+502=1005
AA79n.....427+115+455=997
AA78n.....441+113+429=983
AA9Jn.....463+0+512=975
AA9Kn.....399+0+557=956
AA8Qn.....408+11+532=951
AA9Qn.....430+0+520=950
AA8Kn.....407+15+524=946
AA89n.....451+14+455=920

Buzz