Dealer stands on whatever

I wonder how efficient the dealer's rules are.

Everyone knows the dealer stands if and only if his total is "hard" and at least X, or his total is "soft" and at least Y. And everyone knows that X is always 17, and Y is always 17 or 18.

What if you chose other values? And what if you then determined an optimal basic strategy for them, and compared EVs? Does {X=17, Y=18} yield a worse EV for its corresponding BS than any other set of values and corresponding BS? In other words, is {X=17, Y=18} the best possible set of rules?

I'm guessing this is indeed the case, but I'd like to know if anyone has, perchance, bothered to investigate this. Since I don't own a copy, feel free to slap me across the face with the Griffin book if I'm asking a question he already answered.

Just wondering, for my own edification....

and I can give you standing/busting stats.

Dave

Try one deck. It should be the easiest to calculate. Why take more time than necessary just to satisfy my idle curiosity?

I'm not sure busting percentages are sufficient, though. Ideally, I would like to develop a basic (i.e. optimal) strategy based on the dealer's hitting and standing rules. For instance, I imagine that if the dealer stood on 16, you would double more hands, and you would hit more hands if the dealer showed 6. Then, figure out what the player's EV is with these rules and this strategy. Repeat for every combination of "dealer stands on hard X" and "dealer stands on soft Y." Determine whether or not hard 17 and soft 18 truly gives the player the lowest EV. I'm guessing it does, but, like I said, it's just an idle curiosity.

Then again, it might be that no other factor outweighs the effect of the dealer's bust percentage on the player's EV. In other words, as the dealer's bust percentage goes, so goes the player's EV, so all this calculation (which I didn't really expect anyone to actually perform) would just be verifying that. Or it might not.

I'm not sure busting percentages are sufficient, though. Ideally, I would like to develop a basic (i.e. optimal) strategy based on the dealer's hitting and standing rules.

Here's some data. Obviously, to improve the dealer's average standing total, you must increase soft or hard hitting rules, which means % bust goes up. Conversely, to decrease % bust, you decrease soft or hard hitting rules, which means average standing total goes down.
Entire BS expectation for the game must be considered to find optimal dealer play, which at the moment will be too much to calculate.

Stand Hard 17, H15 

upcard    2       3       4       5       6       7       8       9      10       A

bust:  0.3477  0.3706  0.4010  0.3992  0.4208  0.2599  0.2386  0.2334  0.2143  0.0777

16  :  0.0134  0.0127  0.0047  0.0784  0.0000  0.0000  0.0000  0.0000  0.0000  0.1018

17  :  0.1375  0.1289  0.1306  0.1112  0.1669  0.3723  0.1309  0.1219  0.1144  0.1154

18  :  0.1303  0.1296  0.1135  0.1130  0.1065  0.1386  0.3630  0.1039  0.1129  0.1177

19  :  0.1303  0.1223  0.1200  0.1063  0.1072  0.0773  0.1294  0.3574  0.1147  0.1160

20  :  0.1221  0.1216  0.1158  0.0942  0.1007  0.0789  0.0683  0.1223  0.3289  0.1181

21  :  0.1186  0.1143  0.1144  0.0977  0.0979  0.0730  0.0698  0.0611  0.0365  0.0396

BJ  :  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0784  0.3137



Stand Hard 17, H16 (S17) 

upcard   2        3       4      5       6       7        8      9       10      A

bust:  0.3530  0.3756  0.4028  0.4289  0.4208  0.2599  0.2386  0.2334  0.2143  0.1165

 17 :  0.1390  0.1303  0.1310  0.1197  0.1669  0.3723  0.1309  0.1219  0.1144  0.1261

 18 :  0.1318  0.1309  0.1142  0.1235  0.1065  0.1386  0.3630  0.1039  0.1129  0.1310

 19 :  0.1318  0.1238  0.1207  0.1169  0.1072  0.0773  0.1294  0.3574  0.1147  0.1295

 20 :  0.1239  0.1233  0.1163  0.1047  0.1007  0.0789  0.0683  0.1223  0.3289  0.1316

 21 :  0.1205  0.1160  0.1151  0.1063  0.0979  0.0730  0.0698  0.0611  0.0365  0.0516

 BJ :  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0784  0.3137



Stand Hard 17, H17

upcard   2       3       4       5       6       7       8       9      10       A

bust:  0.3563  0.3781  0.4058  0.4300  0.4378  0.2599  0.2386  0.2334  0.2143  0.1404

17  :  0.1298  0.1235  0.1228  0.1167  0.1161  0.3723  0.1309  0.1219  0.1144  0.0561

18  :  0.1331  0.1319  0.1154  0.1238  0.1138  0.1386  0.3630  0.1039  0.1129  0.1410

19  :  0.1332  0.1249  0.1219  0.1174  0.1161  0.0773  0.1294  0.3574  0.1147  0.1415

20  :  0.1256  0.1242  0.1178  0.1052  0.1096  0.0789  0.0683  0.1223  0.3289  0.1437

21  :  0.1220  0.1173  0.1163  0.1069  0.1067  0.0730  0.0698  0.0611  0.0365  0.0636

BJ  :  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0784  0.3137



Stand Hard 17, H18

upcard   2       3       4       5       6       7       8       9      10       A

bust:  0.3600  0.3814  0.4089  0.4328  0.4388  0.2765  0.2386  0.2334  0.2143  0.1660

17  :  0.1316  0.1252  0.1243  0.1181  0.1166  0.3812  0.1309  0.1219  0.1144  0.0695

18  :  0.1228  0.1226  0.1066  0.1157  0.1108  0.0879  0.3630  0.1039  0.1129  0.0649

19  :  0.1347  0.1263  0.1232  0.1187  0.1164  0.0847  0.1294  0.3574  0.1147  0.1523

20  :  0.1271  0.1258  0.1193  0.1064  0.1102  0.0877  0.0683  0.1223  0.3289  0.1568

21  :  0.1238  0.1187  0.1177  0.1083  0.1072  0.0819  0.0698  0.0611  0.0365  0.0768

BJ  :  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0784  0.3137



Stand Hard 17, H19

upcard   2       3       4       5       6       7       8       9      10       A

bust:  0.3639  0.3849  0.4114  0.4358  0.4416  0.2776  0.2562  0.2334  0.2143  0.1939

17  :  0.1336  0.1269  0.1256  0.1196  0.1181  0.3818  0.1382  0.1219  0.1144  0.0821

18  :  0.1248  0.1244  0.1079  0.1172  0.1123  0.0885  0.3722  0.1039  0.1129  0.0795

19  :  0.1235  0.1159  0.1156  0.1098  0.1083  0.0817  0.0789  0.3574  0.1147  0.0715

20  :  0.1288  0.1273  0.1204  0.1077  0.1114  0.0881  0.0758  0.1223  0.3289  0.1684

21  :  0.1254  0.1205  0.1190  0.1099  0.1084  0.0825  0.0787  0.0611  0.0365  0.0908

BJ  :  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0784  0.3137



Stand Hard 18, H16 (S17)

upcard   2       3       4       5       6       7       8       9       10       A

bust: 0.4410  0.4610  0.4872  0.5088  0.4823  0.5140  0.3286  0.3172  0.2930  0.1295

17  : 0.0143  0.0106  0.0127  0.0047  0.0784  0.0000  0.0000  0.0000  0.0000  0.1083

18  : 0.1416  0.1404  0.1235  0.1326  0.1130  0.1682  0.3733  0.1135  0.1219  0.1320

19  : 0.1391  0.1331  0.1299  0.1250  0.1139  0.1068  0.1396  0.3668  0.1235  0.1308

20  : 0.1337  0.1304  0.1247  0.1136  0.1075  0.1084  0.0785  0.1317  0.3378  0.1329

21  : 0.1303  0.1246  0.1220  0.1153  0.1047  0.1025  0.0800  0.0707  0.0454  0.0529

BJ  : 0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0784  0.3137



Stand Hard 18, H17

upcard   2       3       4       5       6       7       8       9      10       A

bust:  0.4481  0.4662  0.4935  0.5110  0.5185  0.5140  0.3286  0.3172  0.2930  0.1802

18  :  0.1433  0.1416  0.1250  0.1330  0.1221  0.1682  0.3733  0.1135  0.1219  0.1442

19  :  0.1407  0.1346  0.1314  0.1257  0.1251  0.1068  0.1396  0.3668  0.1235  0.1458

20  :  0.1358  0.1314  0.1266  0.1143  0.1187  0.1084  0.0785  0.1317  0.3378  0.1481

21  :  0.1321  0.1262  0.1235  0.1160  0.1157  0.1025  0.0800  0.0707  0.0454  0.0679

BJ  :  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0784  0.3137



Stand Hard 16, H16 (S17)

upcard   2       3       4       5       6       7       8       9      10       A

bust:  0.2754  0.3049  0.3299  0.3558  0.1969  0.1816  0.1765  0.1637  0.1506  0.0863

16  :  0.1222  0.1112  0.1147  0.1149  0.3713  0.1285  0.1016  0.1144  0.1047  0.0472

17  :  0.1294  0.1216  0.1220  0.1115  0.1374  0.3622  0.1229  0.1129  0.1062  0.1234

18  :  0.1246  0.1224  0.1061  0.1146  0.0771  0.1286  0.3551  0.0951  0.1048  0.1274

19  :  0.1223  0.1179  0.1118  0.1080  0.0778  0.0673  0.1216  0.3485  0.1065  0.1258

20  :  0.1152  0.1147  0.1096  0.0957  0.0712  0.0689  0.0603  0.1133  0.3207  0.1279

21  :  0.1109  0.1073  0.1061  0.0995  0.0683  0.0629  0.0619  0.0522  0.0282  0.0482

BJ  :  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0784