Bust Bonus side bet

**k_c** · 06-06-2022, 09:27 AM

Probability of blackjack w/up card ace = .3496
Probability of blackjack w/up card ten = .0874

Code:

Dealer probabilities - 6 decks dealer stands on soft 17....
Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Specific removals (1 - 10): {0,0,0,0,0,0,0,0,0,0}
Subgroup removals: None
Running count (before up card is dealt): 10   Cards remaining: 104

Up card    17      18      19      20      21      BJ     BUST
   1     0.1731  0.1871  0.1880  0.1912  0.0728          0.1879
   2     0.1288  0.1221  0.1267  0.1230  0.1198          0.3795
   3     0.1221  0.1196  0.1155  0.1199  0.1165          0.4065
   4     0.1205  0.1086  0.1117  0.1093  0.1133          0.4366
   5     0.1125  0.1119  0.1081  0.1007  0.1015          0.4653
   6     0.1714  0.0951  0.0969  0.0930  0.0909          0.4528
   7     0.4002  0.1369  0.0683  0.0705  0.0666          0.2574
   8     0.1209  0.3903  0.1295  0.0609  0.0631          0.2353
   9     0.1131  0.1027  0.3846  0.1232  0.0546          0.2218
  10     0.1164  0.1138  0.1153  0.4029  0.0320          0.2196

Overall  0.1483  0.1409  0.1377  0.2069  0.0691          0.2970

Press u or U to display unconditional values, any other key to exit


Dealer probabilities - 6 decks dealer hits soft 17....
Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Specific removals (1 - 10): {0,0,0,0,0,0,0,0,0,0}
Subgroup removals: None
Running count (before up card is dealt): 10   Cards remaining: 104

Up card    17      18      19      20      21      BJ     BUST
   1     0.0822  0.2026  0.2021  0.2055  0.0872          0.2204
   2     0.1200  0.1237  0.1280  0.1244  0.1212          0.3827
   3     0.1149  0.1208  0.1166  0.1209  0.1176          0.4092
   4     0.1128  0.1100  0.1128  0.1105  0.1144          0.4395
   5     0.1083  0.1126  0.1087  0.1014  0.1022          0.4669
   6     0.1174  0.1044  0.1053  0.1015  0.0995          0.4719
   7     0.4002  0.1369  0.0683  0.0705  0.0666          0.2574
   8     0.1209  0.3903  0.1295  0.0609  0.0631          0.2353
   9     0.1131  0.1027  0.3846  0.1232  0.0546          0.2218
  10     0.1164  0.1138  0.1153  0.4029  0.0320          0.2196

Overall  0.1370  0.1429  0.1395  0.2087  0.0708          0.3011

Press u or U to display unconditional values, any other key to exit

k_c

**aceside** · 06-06-2022, 09:50 AM

On my second thought, I prefer to treating the remaining 104-card deck as an infinite deck with your calculated probability numbers. We probably donot need to consider the dynamic variation of each card probability for now. I am actually thinking to extend this calculation to excess and deficit aces in the remaining 104 cards.

**21forme** · 06-06-2022, 12:50 PM

Originally Posted by aceside

On my second thought, I prefer to treating the remaining 104-card deck as an infinite deck with your calculated probability numbers. We probably donot need to consider the dynamic variation of each card probability for now. I am actually thinking to extend this calculation to excess and deficit aces in the remaining 104 cards.

Breaking news - the wheel has already been invented.

Why do you make everything more complex than it needs to be (making errors in the process)?

**aceside** · 06-06-2022, 01:47 PM

Originally Posted by 21forme

Breaking news - the wheel has already been invented.

Why do you make everything more complex than it needs to be (making errors in the process)?

There is no one wheel to fit in all wagons. That's why I keep digging into this. K_C has done a great work!

**aceside** · 06-06-2022, 02:04 PM

Originally Posted by k_c

Probability of blackjack w/up card ace = .3496
Probability of blackjack w/up card ten = .0874

We probably do not need these two numbers to calculate the dealer bust rate. When the dealer shows an Ace up card, there are still 104 cards at the RC=+10 remaining in the shoe. This means:

The probability of a dealer blackjack with up card ace = 0.34628, as you calculated.
The probability of a dealer blackjack with up card ten = 0.08657, as you calculated.

For the sake of this Bust Bonus side bet, can you use the above numbers to re-calculate the dealer bust rate after peeking?

Also, can you extend this calculation to the case of RC=+20?

With these two RC points, I will extrapolate to all other values because the dealer bust rate seems a linear function of TC.

**k_c** · 06-06-2022, 03:37 PM

Originally Posted by aceside

The probability of a dealer blackjack with up card ace = 0.34628, as you calculated.
The probability of a dealer blackjack with up card ten = 0.08657, as you calculated.

It may be helpful to you if you check your math with a simple example.

For a full single deck, probability of Ten = 16/52

If dealer is given up card of Ace, probability of blackjack = 16/51 not 16/52.

k_c

**aceside** · 06-07-2022, 06:26 AM

Originally Posted by k_c

It may be helpful to you if you check your math with a simple example.

For a full single deck, probability of Ten = 16/52

If dealer is given up card of Ace, probability of blackjack = 16/51 not 16/52.

k_c

I’ve kind of got what you are talking about. Earlier you and Cacarulo had this same discussion on this part but I didn’t pay very much attention, so I still don’t know how to calculate the situation when a specific card is given to the dealer up card.

If 208 cards are randomly dealt from a 6-deck shoe and the running count is +10, you’ve already calculated everything. I understand this part.

However, if 207 cards are dealt out and an Ace card is given to the dealer up card from a 6-deck shoe, and the running count is +10, I don’t know how to calculate this anymore.

Specifying a certain dealer’s up card will have an effect on the card probability in the remaining 104-card deck, and thus on the dealer bust rate too. I agree. Please calculate this at RC=+20. If possible, at RC=-20 too.

**k_c** · 06-07-2022, 08:11 AM

Originally Posted by aceside

I’ve kind of got what you are talking about. Earlier you and Cacarulo had this same discussion on this part but I didn’t pay very much attention, so I still don’t know how to calculate the situation when a specific card is given to the dealer up card.

If 208 cards are randomly dealt from a 6-deck shoe and the running count is +10, you’ve already calculated everything. I understand this part.

However, if 207 cards are dealt out and an Ace card is given to the dealer up card from a 6-deck shoe, and the running count is +10, I don’t know how to calculate this anymore.

Specifying a certain dealer’s up card will have an effect on the card probability in the remaining 104-card deck, and thus on the dealer bust rate too. I agree. Please calculate this at RC=+20. If possible, at RC=-20 too.

My running count input is before up card is dealt. If ace or ten is up card, running count needs to be reduced by 1 to account for up card. If 7,8,9 is up card, running count is unchanged. If 2,3,4,5,6 is up card, running count needs to be increased by 1 to account for up card.

Running count is 20 with 104 cards remaining before up card, dealer probs conditioned on no dealer blackjack

Code:

Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Specific removals (1 - 10): {0,0,0,0,0,0,0,0,0,0}
No subgroup (removals) are defined
Decks: 6 (possible input for cards remaining: 1 to 312)
Cards remaining before up card (current = 156, no input = no change): 104
Initial running count (full shoe): 0
Running count (before up card is dealt, no input defaults to 0): 20
Computing.....please wait.....

Number of subsets for above conditions: 37
Prob of running count 20 with above removals from 6 decks: 0.00129

p[1] 0.09640  p[2] 0.05794  p[3] 0.05794  p[4] 0.05794  p[5] 0.05794
p[6] 0.05794  p[7] 0.07611  p[8] 0.07611  p[9] 0.07611  p[10] 0.38559


Dealer probabilities - 6 decks dealer stands on soft 17....
Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Specific removals (1 - 10): {0,0,0,0,0,0,0,0,0,0}
Subgroup removals: None
Running count (before up card is dealt): 20   Cards remaining: 104

Up card    17      18      19      20      21      BJ     BUST
   1     0.1588  0.1843  0.1878  0.1924  0.0692          0.2075
   2     0.1173  0.1101  0.1227  0.1221  0.1202          0.4076
   3     0.1104  0.1077  0.1053  0.1177  0.1175          0.4413
   4     0.1095  0.0964  0.1014  0.1009  0.1130          0.4788
   5     0.1043  0.1003  0.0979  0.0913  0.0942          0.5121
   6     0.1787  0.0838  0.0864  0.0838  0.0833          0.4841
   7     0.4317  0.1370  0.0589  0.0620  0.0594          0.2510
   8     0.1125  0.4213  0.1311  0.0530  0.0562          0.2259
   9     0.1059  0.0939  0.4168  0.1261  0.0480          0.2092
  10     0.1104  0.1065  0.1084  0.4446  0.0261          0.2040

Overall  0.1440  0.1367  0.1348  0.2317  0.0607          0.2920


Dealer probabilities - 6 decks dealer hits soft 17....
Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Specific removals (1 - 10): {0,0,0,0,0,0,0,0,0,0}
Subgroup removals: None
Running count (before up card is dealt): 20   Cards remaining: 104

Up card    17      18      19      20      21      BJ     BUST
   1     0.0808  0.1990  0.1987  0.2035  0.0804          0.2375
   2     0.1094  0.1116  0.1237  0.1233  0.1213          0.4108
   3     0.1040  0.1089  0.1063  0.1185  0.1185          0.4439
   4     0.1025  0.0977  0.1023  0.1020  0.1139          0.4816
   5     0.0993  0.1012  0.0986  0.0920  0.0949          0.5140
   6     0.1221  0.0946  0.0944  0.0920  0.0915          0.5055
   7     0.4317  0.1370  0.0589  0.0620  0.0594          0.2510
   8     0.1125  0.4213  0.1311  0.0530  0.0562          0.2259
   9     0.1059  0.0939  0.4168  0.1261  0.0480          0.2092
  10     0.1104  0.1065  0.1084  0.4446  0.0261          0.2040

Overall  0.1338  0.1386  0.1363  0.2331  0.0622          0.2959

k_c

**aceside** · 06-10-2022, 07:23 AM

Originally Posted by k_c

My running count input is before up card is dealt. If ace or ten is up card, running count needs to be reduced by 1 to account for up card. If 7,8,9 is up card, running count is unchanged. If 2,3,4,5,6 is up card, running count needs to be increased by 1 to account for up card.

Running count is 20 with 104 cards remaining before up card, dealer probs conditioned on no dealer blackjack

Hi k_c,
I made a graph to summarize your results at these two points, TC=~+5 and TC=~+10, but realized I probably stretched too much especially at negative TCs, so I deleted it. At negative TCs, the dealer bust rate should become nonlinear. Can you also help do the same calculation at TC=-10 and TC=0?

**k_c** · 06-10-2022, 05:51 PM

Originally Posted by aceside

Hi k_c,
I made a graph to summarize your results at these two points, TC=~+5 and TC=~+10, but realized I probably stretched too much especially at negative TCs, so I deleted it. At negative TCs, the dealer bust rate should become nonlinear. Can you also help do the same calculation at TC=-10 and TC=0?

After dealer has checked for blackjack, dealer hits soft 17, RC = 0,-10,-20 before up card:

Code:

Dealer probabilities - 6 decks dealer hits soft 17....
Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Specific removals (1 - 10): {0,0,0,0,0,0,0,0,0,0}
Subgroup removals: None
Running count (before up card is dealt): 0   Cards remaining: 104

Up card    17      18      19      20      21      BJ     BUST
   1     0.0823  0.2061  0.2066  0.2082  0.0942          0.2025
   2     0.1299  0.1348  0.1323  0.1257  0.1209          0.3564
   3     0.1250  0.1319  0.1259  0.1230  0.1168          0.3774
   4     0.1225  0.1215  0.1223  0.1178  0.1145          0.4014
   5     0.1175  0.1233  0.1179  0.1096  0.1079          0.4238
   6     0.1155  0.1141  0.1154  0.1099  0.1062          0.4389
   7     0.3703  0.1382  0.0780  0.0788  0.0734          0.2613
   8     0.1298  0.3610  0.1290  0.0689  0.0696          0.2417
   9     0.1210  0.1121  0.3539  0.1211  0.0610          0.2309
  10     0.1225  0.1217  0.1226  0.3637  0.0385          0.2310

Overall  0.1406  0.1477  0.1430  0.1890  0.0789          0.3008


Dealer probabilities - 6 decks dealer hits soft 17....
Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Specific removals (1 - 10): {0,0,0,0,0,0,0,0,0,0}
Subgroup removals: None
Running count (before up card is dealt): -10   Cards remaining: 104

Up card    17      18      19      20      21      BJ     BUST
   1     0.0813  0.2098  0.2120  0.2116  0.1016          0.1838
   2     0.1392  0.1451  0.1366  0.1272  0.1204          0.3315
   3     0.1345  0.1422  0.1342  0.1250  0.1160          0.3480
   4     0.1318  0.1323  0.1309  0.1239  0.1143          0.3668
   5     0.1270  0.1335  0.1262  0.1167  0.1122          0.3845
   6     0.1163  0.1239  0.1247  0.1173  0.1115          0.4063
   7     0.3422  0.1408  0.0879  0.0868  0.0798          0.2625
   8     0.1394  0.3336  0.1296  0.0768  0.0756          0.2451
   9     0.1297  0.1223  0.3247  0.1199  0.0671          0.2364
  10     0.1288  0.1303  0.1305  0.3268  0.0453          0.2383

Overall  0.1447  0.1531  0.1467  0.1733  0.0863          0.2959


Dealer probabilities - 6 decks dealer hits soft 17....
Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Specific removals (1 - 10): {0,0,0,0,0,0,0,0,0,0}
Subgroup removals: None
Running count (before up card is dealt): -20   Cards remaining: 104

Up card    17      18      19      20      21      BJ     BUST
   1     0.0794  0.2135  0.2180  0.2154  0.1091          0.1647
   2     0.1481  0.1546  0.1409  0.1289  0.1197          0.3078
   3     0.1437  0.1519  0.1415  0.1270  0.1153          0.3206
   4     0.1407  0.1427  0.1387  0.1288  0.1139          0.3352
   5     0.1367  0.1432  0.1338  0.1227  0.1151          0.3485
   6     0.1200  0.1338  0.1332  0.1236  0.1154          0.3740
   7     0.3158  0.1448  0.0982  0.0947  0.0857          0.2608
   8     0.1498  0.3080  0.1313  0.0847  0.0811          0.2451
   9     0.1390  0.1333  0.2972  0.1195  0.0730          0.2380
  10     0.1352  0.1398  0.1388  0.2922  0.0527          0.2413

Overall  0.1495  0.1589  0.1505  0.1613  0.0930          0.2869

k_c

**aceside** · 06-11-2022, 07:16 AM

Originally Posted by k_c

After dealer has checked for blackjack, dealer hits soft 17, RC = 0,-10,-20 before up card:

k_c

I’ve graphed all your results together. They match perfectly to Dog Hand’s CVData simulation results. Great work! Thank you!

**aceside** · 06-11-2022, 07:31 PM

I am thinking to simplify all these calculations by using this one function. The probability of a dealer ace up card as a function of TC can be written as,

P_a=0.001966xTC + 0.07674.

The probability of each ten-valued card is the same as above. With this basic formula, we can calculate out several different player’s advantages at all TCs. Earlier, I used this formula to find out that the player’s insurance advantage at TC=+6.5 is about 8% of the total player advantage at that moment, but many people disagreed with me.

**DSchles** · 06-11-2022, 08:58 PM

Originally Posted by aceside

I am thinking to simplify all these calculations by using this one function. The probability of a dealer ace up card as a function of TC can be written as,

P_a=0.001966xTC + 0.07674.

The probability of each ten-valued card is the same as above. With this basic formula, we can calculate out several different player’s advantages at all TCs. Earlier, I used this formula to find out that the player’s insurance advantage at TC=+6.5 is about 8% of the total player advantage at that moment, but many people disagreed with me.

Insurance is a linear function. You have an even bet at +3 Hi-Lo in a 6-deck game. Each TC adds 2.3% to the insurance wager. For some reason, if you pick TC = +6.5, then your advantage is 3.5 x 2.3 = 8.05%. In other words, you're right.

Don