if 6 decks only play half deck
- Thread starter beyondbj
- Start date
21gunsalute
Well-Known Member
What a waste. More time will be spent shuffling than playing.
If you're talking about a 50% penetration and a house edge of 0.08%, then yes;if they let you get away with a 50-1 spread you will beat this game quite nicely. With a house edge of 0.08%, and 1/2 deck dealt (8% penetration),a 50-1 spread would probably still mathematically beat the game, but the win rate would be extremely tiny and not worth your time, unless of course an expectation of something like 20 cents an hour is right up your alley.
jack.jackson
Well-Known Member
You could start raising as soon as the RC turned slightly positive. Also i imagine the number of players could be the deciding factor. For instance, you could spread to 7 hands on the last round if the RC count were positive. Id say it would break you even anyway along with a couple borderline indices.beyondbj said:
Last edited:
kewljason
Well-Known Member
Well, I am not so sure this is unbeatable. I am on the wrong location to run a sim right now, but I think It could be beaten pretty easily. With a regular game with a house edge of .50 you need a big spread because the player will only have an advantage a small percentage of hands and you need to bet big to overcome all those other hands that the house has an advantage. With a house edge of only .08, as soon as the running count goes positive, even +1 or +2, the advantage is going to swing from the house to the player. So the player will have an advantage a much higher percentage of time. Maybe like 40% of hands. So If you bet higher on those hands the game would be a winner. Probably as little as a 1-3 spread would make it a winner. May not be worthwhile. But I would think 1-10 and definately 1-50 could make it worthwhile. The problems of course would be huge variance which would require a huge BR and too much down time making for too few actual hands. Again, I would like to see a sim though. 
After running a few sims I found that a TC+1 or higher was achieved only 3.65% of the time with TC 0 @ ~60.3% and TC-1 @~33.8% of the time.beyondbj said:
The bet spread is tc0=1x1u, tc1=2x25u
If you know the Zender story then you know through exploitable means this game is beatable. If your war chest is full of other special weapons then you have the means to beat this game. If your straight counting then pure luck needs to be on your side the day you take this game on. I stopped the sim short due to the pitiful results.
Here's the best result I came up with. 0.5/6d, das, s17, rsa4, rs4, 3:2bj.
One note, your HE should be +0.08% otherwise as (-0.08) the player would always have the advantage, correct?
BJC
Attachments
Last edited:
chessplayer
Well-Known Member
I do not think this is reliable .>=+1 achieved mere 3.65 % but -1 at 33.8 %. The frequency of +1 should be about equal to the frequency of -1.
bjcount said:
These are the mathematically computed probabilities of all possible HiLo running counts after seeing 1 to 24 cards dealt from 6 decks. I wanted to post through 26 cards but there is a limit to number of characters permitted in post. I'll post probabilites for 25 and 26 cards in a second post.chessplayer said:
Code:
cards = 1
RC = -1 prob = 0.384615
RC = 0 prob = 0.230769
RC = 1 prob = 0.384615
cards = 2
RC = -2 prob = 0.147168
RC = -1 prob = 0.178086
RC = 0 prob = 0.349493
RC = 1 prob = 0.178086
RC = 2 prob = 0.147168
cards = 3
RC = -3 prob = 0.0560188
RC = -2 prob = 0.102543
RC = -1 prob = 0.232086
RC = 0 prob = 0.218705
RC = 1 prob = 0.232086
RC = 2 prob = 0.102543
RC = 3 prob = 0.0560188
cards = 4
RC = -4 prob = 0.021211
RC = -3 prob = 0.0522117
RC = -2 prob = 0.134143
RC = -1 prob = 0.17777
RC = 0 prob = 0.22933
RC = 1 prob = 0.17777
RC = 2 prob = 0.134143
RC = 3 prob = 0.0522117
RC = 4 prob = 0.021211
cards = 5
RC = -5 prob = 0.00798855
RC = -4 prob = 0.0247921
RC = -3 prob = 0.0714096
RC = -2 prob = 0.119561
RC = -1 prob = 0.181026
RC = 0 prob = 0.190445
RC = 1 prob = 0.181026
RC = 2 prob = 0.119561
RC = 3 prob = 0.0714096
RC = 4 prob = 0.0247921
RC = 5 prob = 0.00798855
cards = 6
RC = -6 prob = 0.00299246
RC = -5 prob = 0.0112412
RC = -4 prob = 0.0359364
RC = -3 prob = 0.0718659
RC = -2 prob = 0.124636
RC = -1 prob = 0.161514
RC = 0 prob = 0.183628
RC = 1 prob = 0.161514
RC = 2 prob = 0.124636
RC = 3 prob = 0.0718659
RC = 4 prob = 0.0359364
RC = 5 prob = 0.0112412
RC = 6 prob = 0.00299246
cards = 7
RC = -7 prob = 0.00111484
RC = -6 prob = 0.00492875
RC = -5 prob = 0.0173435
RC = -4 prob = 0.0400396
RC = -3 prob = 0.078134
RC = -2 prob = 0.11868
RC = -1 prob = 0.156156
RC = 0 prob = 0.167206
RC = 1 prob = 0.156156
RC = 2 prob = 0.11868
RC = 3 prob = 0.078134
RC = 4 prob = 0.0400396
RC = 5 prob = 0.0173435
RC = 6 prob = 0.00492875
RC = 7 prob = 0.00111484
cards = 8
RC = -8 prob = 0.000413038
RC = -7 prob = 0.0021054
RC = -6 prob = 0.00809839
RC = -5 prob = 0.0211005
RC = -4 prob = 0.0457079
RC = -3 prob = 0.0789894
RC = -2 prob = 0.117592
RC = -1 prob = 0.146414
RC = 0 prob = 0.159158
RC = 1 prob = 0.146414
RC = 2 prob = 0.117592
RC = 3 prob = 0.0789894
RC = 4 prob = 0.0457079
RC = 5 prob = 0.0211005
RC = 6 prob = 0.00809839
RC = 7 prob = 0.0021054
RC = 8 prob = 0.000413038
cards = 9
RC = -9 prob = 0.000152172
RC = -8 prob = 0.000880422
RC = -7 prob = 0.00368011
RC = -6 prob = 0.01065
RC = -5 prob = 0.0253388
RC = -4 prob = 0.0488486
RC = -3 prob = 0.0809402
RC = -2 prob = 0.114001
RC = -1 prob = 0.140585
RC = 0 prob = 0.149849
RC = 1 prob = 0.140585
RC = 2 prob = 0.114001
RC = 3 prob = 0.0809402
RC = 4 prob = 0.0488486
RC = 5 prob = 0.0253388
RC = 6 prob = 0.01065
RC = 7 prob = 0.00368011
RC = 8 prob = 0.000880422
RC = 9 prob = 0.000152172
cards = 10
RC = -10 prob = 5.57461e-005
RC = -9 prob = 0.000361596
RC = -8 prob = 0.00163418
RC = -7 prob = 0.0051908
RC = -6 prob = 0.0134497
RC = -5 prob = 0.0285242
RC = -4 prob = 0.0519574
RC = -3 prob = 0.0812742
RC = -2 prob = 0.111666
RC = -1 prob = 0.134305
RC = 0 prob = 0.143162
RC = 1 prob = 0.134305
RC = 2 prob = 0.111666
RC = 3 prob = 0.0812742
RC = 4 prob = 0.0519574
RC = 5 prob = 0.0285242
RC = 6 prob = 0.0134497
RC = 7 prob = 0.0051908
RC = 8 prob = 0.00163418
RC = 9 prob = 0.000361596
RC = 10 prob = 5.57461e-005
cards = 11
RC = -11 prob = 2.03049e-005
RC = -10 prob = 0.000146195
RC = -9 prob = 0.000711219
RC = -8 prob = 0.00245716
RC = -7 prob = 0.00688535
RC = -6 prob = 0.0158986
RC = -5 prob = 0.03153
RC = -4 prob = 0.0540631
RC = -3 prob = 0.0816613
RC = -2 prob = 0.108871
RC = -1 prob = 0.129361
RC = 0 prob = 0.136791
RC = 1 prob = 0.129361
RC = 2 prob = 0.108871
RC = 3 prob = 0.0816613
RC = 4 prob = 0.0540631
RC = 5 prob = 0.03153
RC = 6 prob = 0.0158986
RC = 7 prob = 0.00688535
RC = 8 prob = 0.00245716
RC = 9 prob = 0.000711219
RC = 10 prob = 0.000146195
RC = 11 prob = 2.03049e-005
cards = 12
RC = -12 prob = 7.35293e-006
RC = -11 prob = 5.82837e-005
RC = -10 prob = 0.000304047
RC = -9 prob = 0.00113435
RC = -8 prob = 0.00341771
RC = -7 prob = 0.00852362
RC = -6 prob = 0.018263
RC = -5 prob = 0.0339898
RC = -4 prob = 0.0558692
RC = -3 prob = 0.0815155
RC = -2 prob = 0.106474
RC = -1 prob = 0.124697
RC = 0 prob = 0.131493
RC = 1 prob = 0.124697
RC = 2 prob = 0.106474
RC = 3 prob = 0.0815155
RC = 4 prob = 0.0558692
RC = 5 prob = 0.0339898
RC = 6 prob = 0.018263
RC = 7 prob = 0.00852362
RC = 8 prob = 0.00341771
RC = 9 prob = 0.00113435
RC = 10 prob = 0.000304047
RC = 11 prob = 5.82837e-005
RC = 12 prob = 7.35293e-006
cards = 13
RC = -13 prob = 2.64705e-006
RC = -12 prob = 2.29411e-005
RC = -11 prob = 0.000127895
RC = -10 prob = 0.000512282
RC = -9 prob = 0.00165149
RC = -8 prob = 0.0044203
RC = -7 prob = 0.0101684
RC = -6 prob = 0.0203849
RC = -5 prob = 0.0361696
RC = -4 prob = 0.0571996
RC = -3 prob = 0.0812695
RC = -2 prob = 0.104083
RC = -1 prob = 0.120649
RC = 0 prob = 0.126676
RC = 1 prob = 0.120649
RC = 2 prob = 0.104083
RC = 3 prob = 0.0812695
RC = 4 prob = 0.0571996
RC = 5 prob = 0.0361696
RC = 6 prob = 0.0203849
RC = 7 prob = 0.0101684
RC = 8 prob = 0.0044203
RC = 9 prob = 0.00165149
RC = 10 prob = 0.000512282
RC = 11 prob = 0.000127895
RC = 12 prob = 2.29411e-005
RC = 13 prob = 2.64705e-006
cards = 14
RC = -14 prob = 9.47273e-007
RC = -13 prob = 8.92385e-006
RC = -12 prob = 5.3006e-005
RC = -11 prob = 0.000226856
RC = -10 prob = 0.00077927
RC = -9 prob = 0.00222686
RC = -8 prob = 0.00547125
RC = -7 prob = 0.0117425
RC = -6 prob = 0.0223451
RC = -5 prob = 0.0380133
RC = -4 prob = 0.0582669
RC = -3 prob = 0.0808237
RC = -2 prob = 0.101884
RC = -1 prob = 0.11694
RC = 0 prob = 0.122436
RC = 1 prob = 0.11694
RC = 2 prob = 0.101884
RC = 3 prob = 0.0808237
RC = 4 prob = 0.0582669
RC = 5 prob = 0.0380133
RC = 6 prob = 0.0223451
RC = 7 prob = 0.0117425
RC = 8 prob = 0.00547125
RC = 9 prob = 0.00222686
RC = 10 prob = 0.00077927
RC = 11 prob = 0.000226856
RC = 12 prob = 5.3006e-005
RC = 13 prob = 8.92385e-006
RC = 14 prob = 9.47273e-007
cards = 15
RC = -15 prob = 3.3695e-007
RC = -14 prob = 3.43307e-006
RC = -13 prob = 2.16679e-005
RC = -12 prob = 9.86894e-005
RC = -11 prob = 0.000359932
RC = -10 prob = 0.00109341
RC = -9 prob = 0.0028567
RC = -8 prob = 0.0065309
RC = -7 prob = 0.0132576
RC = -6 prob = 0.0241151
RC = -5 prob = 0.0396142
RC = -4 prob = 0.0590687
RC = -3 prob = 0.0802984
RC = -2 prob = 0.0997839
RC = -1 prob = 0.1136
RC = 0 prob = 0.118595
RC = 1 prob = 0.1136
RC = 2 prob = 0.0997839
RC = 3 prob = 0.0802984
RC = 4 prob = 0.0590687
RC = 5 prob = 0.0396142
RC = 6 prob = 0.0241151
RC = 7 prob = 0.0132576
RC = 8 prob = 0.0065309
RC = 9 prob = 0.0028567
RC = 10 prob = 0.00109341
RC = 11 prob = 0.000359932
RC = 12 prob = 9.86894e-005
RC = 13 prob = 2.16679e-005
RC = 14 prob = 3.43307e-006
RC = 15 prob = 3.3695e-007
cards = 16
RC = -16 prob = 1.19124e-007
RC = -15 prob = 1.30696e-006
RC = -14 prob = 8.74386e-006
RC = -13 prob = 4.22381e-005
RC = -12 prob = 0.000163047
RC = -11 prob = 0.000524626
RC = -10 prob = 0.00145213
RC = -9 prob = 0.00352149
RC = -8 prob = 0.00759185
RC = -7 prob = 0.0146919
RC = -6 prob = 0.0257254
RC = -5 prob = 0.0409848
RC = -4 prob = 0.0596822
RC = -3 prob = 0.0796907
RC = -2 prob = 0.0978156
RC = -1 prob = 0.110539
RC = 0 prob = 0.115129
RC = 1 prob = 0.110539
RC = 2 prob = 0.0978156
RC = 3 prob = 0.0796907
RC = 4 prob = 0.0596822
RC = 5 prob = 0.0409848
RC = 6 prob = 0.0257254
RC = 7 prob = 0.0146919
RC = 8 prob = 0.00759185
RC = 9 prob = 0.00352149
RC = 10 prob = 0.00145213
RC = 11 prob = 0.000524626
RC = 12 prob = 0.000163047
RC = 13 prob = 4.22381e-005
RC = 14 prob = 8.74386e-006
RC = 15 prob = 1.30696e-006
RC = 16 prob = 1.19124e-007
cards = 17
RC = -17 prob = 4.18542e-008
RC = -16 prob = 4.92592e-007
RC = -15 prob = 3.48568e-006
RC = -14 prob = 1.78059e-005
RC = -13 prob = 7.25513e-005
RC = -12 prob = 0.000246494
RC = -11 prob = 0.000720507
RC = -10 prob = 0.00184686
RC = -9 prob = 0.00421251
RC = -8 prob = 0.00863706
RC = -7 prob = 0.0160478
RC = -6 prob = 0.0271808
RC = -5 prob = 0.0421676
RC = -4 prob = 0.0601315
RC = -3 prob = 0.0790399
RC = -2 prob = 0.0959537
RC = -1 prob = 0.107737
RC = 0 prob = 0.111967
RC = 1 prob = 0.107737
RC = 2 prob = 0.0959537
RC = 3 prob = 0.0790399
RC = 4 prob = 0.0601315
RC = 5 prob = 0.0421676
RC = 6 prob = 0.0271808
RC = 7 prob = 0.0160478
RC = 8 prob = 0.00863706
RC = 9 prob = 0.00421251
RC = 10 prob = 0.00184686
RC = 11 prob = 0.000720507
RC = 12 prob = 0.000246494
RC = 13 prob = 7.25513e-005
RC = 14 prob = 1.78059e-005
RC = 15 prob = 3.48568e-006
RC = 16 prob = 4.92592e-007
RC = 17 prob = 4.18542e-008
cards = 18
RC = -18 prob = 1.46135e-008
RC = -17 prob = 1.83875e-007
RC = -16 prob = 1.37346e-006
RC = -15 prob = 7.40057e-006
RC = -14 prob = 3.17523e-005
RC = -13 prob = 0.000113603
RC = -12 prob = 0.000349696
RC = -11 prob = 0.000944575
RC = -10 prob = 0.00227208
RC = -9 prob = 0.00491823
RC = -8 prob = 0.00965974
RC = -7 prob = 0.0173215
RC = -6 prob = 0.0284984
RC = -5 prob = 0.0431843
RC = -4 prob = 0.0604525
RC = -3 prob = 0.0783558
RC = -2 prob = 0.0941981
RC = -1 prob = 0.105154
RC = 0 prob = 0.109074
RC = 1 prob = 0.105154
RC = 2 prob = 0.0941981
RC = 3 prob = 0.0783558
RC = 4 prob = 0.0604525
RC = 5 prob = 0.0431843
RC = 6 prob = 0.0284984
RC = 7 prob = 0.0173215
RC = 8 prob = 0.00965974
RC = 9 prob = 0.00491823
RC = 10 prob = 0.00227208
RC = 11 prob = 0.000944575
RC = 12 prob = 0.000349696
RC = 13 prob = 0.000113603
RC = 14 prob = 3.17523e-005
RC = 15 prob = 7.40057e-006
RC = 16 prob = 1.37346e-006
RC = 17 prob = 1.83875e-007
RC = 18 prob = 1.46135e-008
cards = 19
RC = -19 prob = 5.06999e-009
RC = -18 prob = 6.79976e-008
RC = -17 prob = 5.35178e-007
RC = -16 prob = 3.03494e-006
RC = -15 prob = 1.36824e-005
RC = -14 prob = 5.14296e-005
RC = -13 prob = 0.000166311
RC = -12 prob = 0.00047214
RC = -11 prob = 0.00119432
RC = -10 prob = 0.00272112
RC = -9 prob = 0.00563112
RC = -8 prob = 0.0106524
RC = -7 prob = 0.0185155
RC = -6 prob = 0.0296893
RC = -5 prob = 0.0440597
RC = -4 prob = 0.0606663
RC = -3 prob = 0.0776544
RC = -2 prob = 0.0925379
RC = -1 prob = 0.102765
RC = 0 prob = 0.106412
RC = 1 prob = 0.102765
RC = 2 prob = 0.0925379
RC = 3 prob = 0.0776544
RC = 4 prob = 0.0606663
RC = 5 prob = 0.0440597
RC = 6 prob = 0.0296893
RC = 7 prob = 0.0185155
RC = 8 prob = 0.0106524
RC = 9 prob = 0.00563112
RC = 10 prob = 0.00272112
RC = 11 prob = 0.00119432
RC = 12 prob = 0.00047214
RC = 13 prob = 0.000166311
RC = 14 prob = 5.14296e-005
RC = 15 prob = 1.36824e-005
RC = 16 prob = 3.03494e-006
RC = 17 prob = 5.35178e-007
RC = 18 prob = 6.79976e-008
RC = 19 prob = 5.06999e-009
cards = 20
RC = -20 prob = 1.74768e-009
RC = -19 prob = 2.49174e-008
RC = -18 prob = 2.06301e-007
RC = -17 prob = 1.22886e-006
RC = -16 prob = 5.81022e-006
RC = -15 prob = 2.2897e-005
RC = -14 prob = 7.7618e-005
RC = -13 prob = 0.000231053
RC = -12 prob = 0.000613139
RC = -11 prob = 0.00146652
RC = -10 prob = 0.0031886
RC = -9 prob = 0.00634406
RC = -8 prob = 0.0116113
RC = -7 prob = 0.0196317
RC = -6 prob = 0.0307662
RC = -5 prob = 0.0448121
RC = -4 prob = 0.0607932
RC = -3 prob = 0.0769435
RC = -2 prob = 0.0909675
RC = -1 prob = 0.100547
RC = 0 prob = 0.103953
RC = 1 prob = 0.100547
RC = 2 prob = 0.0909675
RC = 3 prob = 0.0769435
RC = 4 prob = 0.0607932
RC = 5 prob = 0.0448121
RC = 6 prob = 0.0307662
RC = 7 prob = 0.0196317
RC = 8 prob = 0.0116113
RC = 9 prob = 0.00634406
RC = 10 prob = 0.0031886
RC = 11 prob = 0.00146652
RC = 12 prob = 0.000613139
RC = 13 prob = 0.000231053
RC = 14 prob = 7.7618e-005
RC = 15 prob = 2.2897e-005
RC = 16 prob = 5.81022e-006
RC = 17 prob = 1.22886e-006
RC = 18 prob = 2.06301e-007
RC = 19 prob = 2.49174e-008
RC = 20 prob = 1.74768e-009
cards = 21
RC = -21 prob = 5.9852e-010
RC = -20 prob = 9.04962e-009
RC = -19 prob = 7.86988e-008
RC = -18 prob = 4.91542e-007
RC = -17 prob = 2.43325e-006
RC = -16 prob = 1.00348e-005
RC = -15 prob = 3.55912e-005
RC = -14 prob = 0.000110869
RC = -13 prob = 0.000307977
RC = -12 prob = 0.000771519
RC = -11 prob = 0.00175816
RC = -10 prob = 0.00366939
RC = -9 prob = 0.00705182
RC = -8 prob = 0.0125333
RC = -7 prob = 0.0206738
RC = -6 prob = 0.0317397
RC = -5 prob = 0.0454583
RC = -4 prob = 0.0608482
RC = -3 prob = 0.0762307
RC = -2 prob = 0.0894795
RC = -1 prob = 0.0984812
RC = 0 prob = 0.101674
RC = 1 prob = 0.0984812
RC = 2 prob = 0.0894795
RC = 3 prob = 0.0762307
RC = 4 prob = 0.0608482
RC = 5 prob = 0.0454583
RC = 6 prob = 0.0317397
RC = 7 prob = 0.0206738
RC = 8 prob = 0.0125333
RC = 9 prob = 0.00705182
RC = 10 prob = 0.00366939
RC = 11 prob = 0.00175816
RC = 12 prob = 0.000771519
RC = 13 prob = 0.000307977
RC = 14 prob = 0.000110869
RC = 15 prob = 3.55912e-005
RC = 16 prob = 1.00348e-005
RC = 17 prob = 2.43325e-006
RC = 18 prob = 4.91542e-007
RC = 19 prob = 7.86988e-008
RC = 20 prob = 9.04962e-009
RC = 21 prob = 5.9852e-010
cards = 22
RC = -22 prob = 2.0362e-010
RC = -21 prob = 3.25792e-009
RC = -20 prob = 2.97177e-008
RC = -19 prob = 1.9432e-007
RC = -18 prob = 1.00557e-006
RC = -17 prob = 4.3328e-006
RC = -16 prob = 1.60513e-005
RC = -15 prob = 5.22288e-005
RC = -14 prob = 0.000151584
RC = -13 prob = 0.000396917
RC = -12 prob = 0.000945959
RC = -11 prob = 0.0020662
RC = -10 prob = 0.00415913
RC = -9 prob = 0.00775003
RC = -8 prob = 0.0134171
RC = -7 prob = 0.0216455
RC = -6 prob = 0.0326201
RC = -5 prob = 0.0460122
RC = -4 prob = 0.0608443
RC = -3 prob = 0.0755208
RC = -2 prob = 0.0880682
RC = -1 prob = 0.0965516
RC = 0 prob = 0.099553
RC = 1 prob = 0.0965516
RC = 2 prob = 0.0880682
RC = 3 prob = 0.0755208
RC = 4 prob = 0.0608443
RC = 5 prob = 0.0460122
RC = 6 prob = 0.0326201
RC = 7 prob = 0.0216455
RC = 8 prob = 0.0134171
RC = 9 prob = 0.00775003
RC = 10 prob = 0.00415913
RC = 11 prob = 0.0020662
RC = 12 prob = 0.000945959
RC = 13 prob = 0.000396917
RC = 14 prob = 0.000151584
RC = 15 prob = 5.22288e-005
RC = 16 prob = 1.60513e-005
RC = 17 prob = 4.3328e-006
RC = 18 prob = 1.00557e-006
RC = 19 prob = 1.9432e-007
RC = 20 prob = 2.97177e-008
RC = 21 prob = 3.25792e-009
RC = 22 prob = 2.0362e-010
cards = 23
RC = -23 prob = 6.88095e-011
RC = -22 prob = 1.16274e-009
RC = -21 prob = 1.11106e-008
RC = -20 prob = 7.59528e-008
RC = -19 prob = 4.10306e-007
RC = -18 prob = 1.8444e-006
RC = -17 prob = 7.12598e-006
RC = -16 prob = 2.41812e-005
RC = -15 prob = 7.32012e-005
RC = -14 prob = 0.000199986
RC = -13 prob = 0.000497512
RC = -12 prob = 0.00113497
RC = -11 prob = 0.00238778
RC = -10 prob = 0.00465399
RC = -9 prob = 0.00843541
RC = -8 prob = 0.0142621
RC = -7 prob = 0.0225508
RC = -6 prob = 0.0334164
RC = -5 prob = 0.0464857
RC = -4 prob = 0.0607917
RC = -3 prob = 0.0748178
RC = -2 prob = 0.0867278
RC = -1 prob = 0.0947442
RC = 0 prob = 0.0975741
RC = 1 prob = 0.0947442
RC = 2 prob = 0.0867278
RC = 3 prob = 0.0748178
RC = 4 prob = 0.0607917
RC = 5 prob = 0.0464857
RC = 6 prob = 0.0334164
RC = 7 prob = 0.0225508
RC = 8 prob = 0.0142621
RC = 9 prob = 0.00843541
RC = 10 prob = 0.00465399
RC = 11 prob = 0.00238778
RC = 12 prob = 0.00113497
RC = 13 prob = 0.000497512
RC = 14 prob = 0.000199986
RC = 15 prob = 7.32012e-005
RC = 16 prob = 2.41812e-005
RC = 17 prob = 7.12598e-006
RC = 18 prob = 1.8444e-006
RC = 19 prob = 4.10306e-007
RC = 20 prob = 7.59528e-008
RC = 21 prob = 1.11106e-008
RC = 22 prob = 1.16274e-009
RC = 23 prob = 6.88095e-011
cards = 24
RC = -24 prob = 2.30952e-011
RC = -23 prob = 4.11429e-010
RC = -22 prob = 4.11359e-009
RC = -21 prob = 2.93613e-008
RC = -20 prob = 1.65372e-007
RC = -19 prob = 7.74515e-007
RC = -18 prob = 3.11653e-006
RC = -17 prob = 1.10131e-005
RC = -16 prob = 3.47206e-005
RC = -15 prob = 9.8811e-005
RC = -14 prob = 0.000256154
RC = -13 prob = 0.000609227
RC = -12 prob = 0.00133702
RC = -11 prob = 0.00272025
RC = -10 prob = 0.00515072
RC = -9 prob = 0.00910543
RC = -8 prob = 0.0150681
RC = -7 prob = 0.0233939
RC = -6 prob = 0.0341368
RC = -5 prob = 0.0468892
RC = -4 prob = 0.0606989
RC = -3 prob = 0.0741244
RC = -2 prob = 0.0854532
RC = -1 prob = 0.093047
RC = 0 prob = 0.0957222
RC = 1 prob = 0.093047
RC = 2 prob = 0.0854532
RC = 3 prob = 0.0741244
RC = 4 prob = 0.0606989
RC = 5 prob = 0.0468892
RC = 6 prob = 0.0341368
RC = 7 prob = 0.0233939
RC = 8 prob = 0.0150681
RC = 9 prob = 0.00910543
RC = 10 prob = 0.00515072
RC = 11 prob = 0.00272025
RC = 12 prob = 0.00133702
RC = 13 prob = 0.000609227
RC = 14 prob = 0.000256154
RC = 15 prob = 9.8811e-005
RC = 16 prob = 3.47206e-005
RC = 17 prob = 1.10131e-005
RC = 18 prob = 3.11653e-006
RC = 19 prob = 7.74515e-007
RC = 20 prob = 1.65372e-007
RC = 21 prob = 2.93613e-008
RC = 22 prob = 4.11359e-009
RC = 23 prob = 4.11429e-010
RC = 24 prob = 2.30952e-0116 decks HiLo RC probs after seeing 25 or 26 cards
These are for 25 and 26 cards.
cards = 25
RC = -25 prob = 7.69841e-012
RC = -24 prob = 1.44345e-010
RC = -23 prob = 1.50843e-009
RC = -22 prob = 1.12287e-008
RC = -21 prob = 6.58636e-008
RC = -20 prob = 3.21007e-007
RC = -19 prob = 1.3436e-006
RC = -18 prob = 4.93796e-006
RC = -17 prob = 1.61908e-005
RC = -16 prob = 4.79288e-005
RC = -15 prob = 0.000129277
RC = -14 prob = 0.000320035
RC = -13 prob = 0.000731412
RC = -12 prob = 0.00155056
RC = -11 prob = 0.00306117
RC = -10 prob = 0.00564657
RC = -9 prob = 0.0097582
RC = -8 prob = 0.0158358
RC = -7 prob = 0.0241786
RC = -6 prob = 0.0347887
RC = -5 prob = 0.0472315
RC = -4 prob = 0.060573
RC = -3 prob = 0.0734426
RC = -2 prob = 0.0842398
RC = -1 prob = 0.0914496
RC = 0 prob = 0.0939847
RC = 1 prob = 0.0914496
RC = 2 prob = 0.0842398
RC = 3 prob = 0.0734426
RC = 4 prob = 0.060573
RC = 5 prob = 0.0472315
RC = 6 prob = 0.0347887
RC = 7 prob = 0.0241786
RC = 8 prob = 0.0158358
RC = 9 prob = 0.0097582
RC = 10 prob = 0.00564657
RC = 11 prob = 0.00306117
RC = 12 prob = 0.00155056
RC = 13 prob = 0.000731412
RC = 14 prob = 0.000320035
RC = 15 prob = 0.000129277
RC = 16 prob = 4.79288e-005
RC = 17 prob = 1.61908e-005
RC = 18 prob = 4.93796e-006
RC = 19 prob = 1.3436e-006
RC = 20 prob = 3.21007e-007
RC = 21 prob = 6.58636e-008
RC = 22 prob = 1.12287e-008
RC = 23 prob = 1.50843e-009
RC = 24 prob = 1.44345e-010
RC = 25 prob = 7.69841e-012
cards = 26
RC = -26 prob = 2.54826e-012
RC = -25 prob = 5.0214e-011
RC = -24 prob = 5.47908e-010
RC = -23 prob = 4.24921e-009
RC = -22 prob = 2.59297e-008
RC = -21 prob = 1.3137e-007
RC = -20 prob = 5.71318e-007
RC = -19 prob = 2.18114e-006
RC = -18 prob = 7.42867e-006
RC = -17 prob = 2.28447e-005
RC = -16 prob = 6.40248e-005
RC = -15 prob = 0.000164738
RC = -14 prob = 0.000391471
RC = -13 prob = 0.000863331
RC = -12 prob = 0.00177408
RC = -11 prob = 0.00340834
RC = -10 prob = 0.00613923
RC = -9 prob = 0.0103924
RC = -8 prob = 0.0165661
RC = -7 prob = 0.0249091
RC = -6 prob = 0.0353787
RC = -5 prob = 0.0475201
RC = -4 prob = 0.0604199
RC = -3 prob = 0.0727739
RC = -2 prob = 0.0830832
RC = -1 prob = 0.0899429
RC = 0 prob = 0.0923506
RC = 1 prob = 0.0899429
RC = 2 prob = 0.0830832
RC = 3 prob = 0.0727739
RC = 4 prob = 0.0604199
RC = 5 prob = 0.0475201
RC = 6 prob = 0.0353787
RC = 7 prob = 0.0249091
RC = 8 prob = 0.0165661
RC = 9 prob = 0.0103924
RC = 10 prob = 0.00613923
RC = 11 prob = 0.00340834
RC = 12 prob = 0.00177408
RC = 13 prob = 0.000863331
RC = 14 prob = 0.000391471
RC = 15 prob = 0.000164738
RC = 16 prob = 6.40248e-005
RC = 17 prob = 2.28447e-005
RC = 18 prob = 7.42867e-006
RC = 19 prob = 2.18114e-006
RC = 20 prob = 5.71318e-007
RC = 21 prob = 1.3137e-007
RC = 22 prob = 2.59297e-008
RC = 23 prob = 4.24921e-009
RC = 24 prob = 5.47908e-010
RC = 25 prob = 5.0214e-011
RC = 26 prob = 2.54826e-012
These are for 25 and 26 cards.
cards = 25
RC = -25 prob = 7.69841e-012
RC = -24 prob = 1.44345e-010
RC = -23 prob = 1.50843e-009
RC = -22 prob = 1.12287e-008
RC = -21 prob = 6.58636e-008
RC = -20 prob = 3.21007e-007
RC = -19 prob = 1.3436e-006
RC = -18 prob = 4.93796e-006
RC = -17 prob = 1.61908e-005
RC = -16 prob = 4.79288e-005
RC = -15 prob = 0.000129277
RC = -14 prob = 0.000320035
RC = -13 prob = 0.000731412
RC = -12 prob = 0.00155056
RC = -11 prob = 0.00306117
RC = -10 prob = 0.00564657
RC = -9 prob = 0.0097582
RC = -8 prob = 0.0158358
RC = -7 prob = 0.0241786
RC = -6 prob = 0.0347887
RC = -5 prob = 0.0472315
RC = -4 prob = 0.060573
RC = -3 prob = 0.0734426
RC = -2 prob = 0.0842398
RC = -1 prob = 0.0914496
RC = 0 prob = 0.0939847
RC = 1 prob = 0.0914496
RC = 2 prob = 0.0842398
RC = 3 prob = 0.0734426
RC = 4 prob = 0.060573
RC = 5 prob = 0.0472315
RC = 6 prob = 0.0347887
RC = 7 prob = 0.0241786
RC = 8 prob = 0.0158358
RC = 9 prob = 0.0097582
RC = 10 prob = 0.00564657
RC = 11 prob = 0.00306117
RC = 12 prob = 0.00155056
RC = 13 prob = 0.000731412
RC = 14 prob = 0.000320035
RC = 15 prob = 0.000129277
RC = 16 prob = 4.79288e-005
RC = 17 prob = 1.61908e-005
RC = 18 prob = 4.93796e-006
RC = 19 prob = 1.3436e-006
RC = 20 prob = 3.21007e-007
RC = 21 prob = 6.58636e-008
RC = 22 prob = 1.12287e-008
RC = 23 prob = 1.50843e-009
RC = 24 prob = 1.44345e-010
RC = 25 prob = 7.69841e-012
cards = 26
RC = -26 prob = 2.54826e-012
RC = -25 prob = 5.0214e-011
RC = -24 prob = 5.47908e-010
RC = -23 prob = 4.24921e-009
RC = -22 prob = 2.59297e-008
RC = -21 prob = 1.3137e-007
RC = -20 prob = 5.71318e-007
RC = -19 prob = 2.18114e-006
RC = -18 prob = 7.42867e-006
RC = -17 prob = 2.28447e-005
RC = -16 prob = 6.40248e-005
RC = -15 prob = 0.000164738
RC = -14 prob = 0.000391471
RC = -13 prob = 0.000863331
RC = -12 prob = 0.00177408
RC = -11 prob = 0.00340834
RC = -10 prob = 0.00613923
RC = -9 prob = 0.0103924
RC = -8 prob = 0.0165661
RC = -7 prob = 0.0249091
RC = -6 prob = 0.0353787
RC = -5 prob = 0.0475201
RC = -4 prob = 0.0604199
RC = -3 prob = 0.0727739
RC = -2 prob = 0.0830832
RC = -1 prob = 0.0899429
RC = 0 prob = 0.0923506
RC = 1 prob = 0.0899429
RC = 2 prob = 0.0830832
RC = 3 prob = 0.0727739
RC = 4 prob = 0.0604199
RC = 5 prob = 0.0475201
RC = 6 prob = 0.0353787
RC = 7 prob = 0.0249091
RC = 8 prob = 0.0165661
RC = 9 prob = 0.0103924
RC = 10 prob = 0.00613923
RC = 11 prob = 0.00340834
RC = 12 prob = 0.00177408
RC = 13 prob = 0.000863331
RC = 14 prob = 0.000391471
RC = 15 prob = 0.000164738
RC = 16 prob = 6.40248e-005
RC = 17 prob = 2.28447e-005
RC = 18 prob = 7.42867e-006
RC = 19 prob = 2.18114e-006
RC = 20 prob = 5.71318e-007
RC = 21 prob = 1.3137e-007
RC = 22 prob = 2.59297e-008
RC = 23 prob = 4.24921e-009
RC = 24 prob = 5.47908e-010
RC = 25 prob = 5.0214e-011
RC = 26 prob = 2.54826e-012
If the TC frequency's were about equal on both sides of the curve we would all be making a lot more money as the advantage would be in our favor more often.chessplayer said:
I'm no math expert but I don't see how the calculation for probabilities is equal to the TC frequency determined by a sim since the deck composition is always different in each shoe played.
In not one cvdata or cvcx sim is there any TC frequency close to even when comparing the + vs - integer until you get to the outer limits, say TC's +8/-8.
Also keep in mind when flooring that counts at TC +0.7 are = to TC 0 and TC -0.4 are = to TC -1
BJC
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I believe the average pre-round HiLo RC is always negative due to the way blackjack is dealt so I think there is a preponderance of negative RCs particularly when a cut card is used. However, it's hard to believe count frequency would be <= -1 ~3.6%, = 0 ~60%, >= +1 ~36.4%.bjcount said:
Pre-round is when player must determine bet size. I think post shoe, when all rounds are dealt, would pretty much match the calculated RC count frequencies.
k_c,k_c said:
unless I am reading your sentence incorrectly X >=+1 should say (a true count X is greater then or equal to TC +1, 3.6% of the time and X<=-1 36.4% of the time.
look back at my original post which shows the sims TC frequencies ( the green background attachment). This is taken directly from the CVData sim I ran.
I think you guys are missing one critical factor, when you use flooring of the indices all those tiny positive 10 digit numbers you posted in the probability figures (+0.670394857 etc) are floored to TC 0 when using it in the sim.
and all those neg (-0.678019878 etc) are floored to TC -1.
BJC
bjc,bjcount said:
I guess you're talking about TC floored whereas I am showing RC and pen which can be computed to TC and rounded, say to 1 decimal place or it could be floored or grouped any way that is seen fit.
I was going to mention something to that effect but after I ran my program and entered the data it was time for me to leave for work, so I just left my post as it was with my initial impression.
The RC probabilities I posted would apply if from 1 to 26 cards from a full 6 deck shoe were randomly exposed and counted by a HiLo counter. Other counting systems could be similarly displayed and also other penetrations.
k_c
ok, after a good night sleep I looked back at your numbers and see that you are basically confirming what my first post stated, seeing a TC +1 or greater will occur ~ 1.5% (my sim result was ~3.65%) of the time just prior to the cut card point of 26 cards, otherwise the TC will be = to or less than 0 98.5% of the time when the counts are floored.
If you moved the cut card to the 13th card (played just a 1/4d per 6d game) we may see a "floored" TC+1 or greater less then 1% of the time. This would probably be in the realm of playing against a CSM game.
BJC
Edit: based on a lvl 2 count, RPC w/ 1/2dtc
ok, after a good night sleep I looked back at your numbers and see that you are basically confirming what my first post stated, seeing a TC +1 or greater will occur ~ 1.5% (my sim result was ~3.65%) of the time just prior to the cut card point of 26 cards, otherwise the TC will be = to or less than 0 98.5% of the time when the counts are floored.
If you moved the cut card to the 13th card (played just a 1/4d per 6d game) we may see a "floored" TC+1 or greater less then 1% of the time. This would probably be in the realm of playing against a CSM game.
BJC
Edit: based on a lvl 2 count, RPC w/ 1/2dtc
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chessplayer
Well-Known Member
After taking into account the flooring you written, based on either actual experience or logic, the frequency of TC +1 or more is significantly more than 3.65.
The probability given by kc of a RC + 6 is 3.5%.The probability of RC +7 is 2.4%. These two already makes it about 6%
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The probability given by kc of a RC + 6 is 3.5%.The probability of RC +7 is 2.4%. These two already makes it about 6%
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bjcount said:
Chessplayer,chessplayer said:
The numbers you quote above are on the last round of play which is the 26th card dealt, and thats if the last round ends once the 26th card is dealt. In essence a RC+6 is achieve 3.5% of the time when the 26 card is dealt. Your not considering all the hands/rounds where the percentage is lower or zero.
If you look at the RC +6 when the 9th card is dealt the RC+6 is acheived only 1% of the time. There is never a RC of +6 in the first 5 cards. What I believe you should do is average all the RC+6's probabilities and see what percentage of the time you see a RC+6. I came out with 1.79%. I would consider the results of my posted sim as accurate. (look at the TC distribution image in green)
If you add up all the RC greater then +6 which appear to be a rarity, I would guesstimate that you will come closer to my average 3.65% for all TC =>+1 then your single RC example which is taken from the extreme end.
Are there any other opinions out there from the math guys?
BJC
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chessplayer
Well-Known Member
I get your point now. However, I believe the OP was looking for info on the 26th cards all played at one go as in a CSM.
bjcount said: