$500 Flatbet session at Phoenician

[cipher]

This session consists of 548 hands with a flat bet of $500.00 on all hands. You'll want to pay particular attention to the "double downs" (25 Wins out of 63 attempts) and the "splits" (3 Wins out of 9 attempts) that account for $14,500.00 out of the total loss of $23,500.00.

Check out the RCA (Relative Card Averages) values. The All Player Cards bar graph and the Player's First Two Cards bar graph are nearly identical even to the fact of both of those categories being not random with a 95% degree of confidence. Have a good one.

 

[bethug]

cipher, is that real money? it looks like u lose over 23000

 

[cipher]

cipher, is that real money? it looks like u lose over 23000

You know me better than that I hope Bethug. All of the strands that I've done over the last 60 days or so on Phoenician or Nostalgia are in free play.

I'm working on a large sample of RTG hands that have been sent to me by several players over the last couple of months and those sessions are for real money. Have a good one.

 

[Simmo!]

You'll want to pay particular attention to the "double downs" (25 Wins out of 63 attempts) and the "splits" (3 Wins out of 9 attempts) that account for $14,500.00 out of the total loss of $23,500.00.

It would be interesting to see the combined results from all the players hands you have. You can't conclude anything from 3 out of 9 (expected 4.5 I assume) or 25 out of 63 (expected 31.5 I assume) but a sample of 100,000+ would provide interesting results indeed.

As an aside, you are implying that RTG software is weighted in the casino's favour more heavily than the House Edge alone Cipher, yes?

 

[cipher]

It would be interesting to see the combined results from all the players hands you have. You can't conclude anything from 3 out of 9 (expected 4.5 I assume) or 25 out of 63 (expected 31.5 I assume) but a sample of 100,000+ would provide interesting results indeed.

As an aside, you are implying that RTG software is weighted in the casino's favour more heavily than the House Edge alone Cipher, yes?

I'm from a different school of thought than most Simmo. I don't need to see hundreds of thousands of hands being played in order to recognize very real and very factual trends. I utilize the data that I record in very real sessions of play on a daily basis.

"You are implying that RTG software is weighted in the casino's favour more heavily than the House Edge alone Cipher, yes?"

The data that I'm seeing indicates to me that each RTG casino has the ability to set the individual parameters for such things as splits and double downs.

Have a good one.

 

[Johnny Empire]

Trend

I calc odds of losing 47 bets or worse in 548 hands as 5.07%. You'll need more than that to prove a casino is rigged.

If you really want a statistical sample, play 100,000 hands. If you lose more than 2,000 bets, the chance of that happening randomly is .0006%. Then I'd believe it.

But then I don't play at a casino unless they give me a bonus offer equal to a 3%+ player edge anyway. Why take chances?

 

[DeMango]

You SHOULD win more splits and double downs than lose. This plus BJ's are what in theory make a game where you lose 52.5% of all hands only lose .5% of money wagered assuming flat bets.

 

[cipher]

You SHOULD win more splits and double downs than lose. This plus BJ's are what in theory make a game where you lose 52.5% of all hands only lose .5% of money wagered assuming flat bets.

I agree Demango. In this particular session the incidence of blackjack for the house and the player were both 26. But the huge disparity in the win loss ratio incident to splits and double downs is just way too peculiar for me. Have a good one.

 

[summertime]

You're still the man Cipher

Cipher,

I have to thank the guy who taught you to count 4 decks(can't remember his name) and thank you for continuing to help others in his name. Many posters on this board work hard to help guilelss newbies or small bettors like me not lose money and I appreciate each one, including Caruso. I especially like the way you simply post facts, point out trends that your sets of facts seem to indicate and by gosh, give us a copy so that we can print it and look at it!

You have saved me much money (by my NOT betting) simply in showing me that it requires a sophistication that I don't possess. (I sure wish I'd read your posts before I lost that first $600.)

I get a little peeved when folks respond to you about sample sizes and rigging, etc. You really do just provide a FREE service as a jumping off point for thoughtful decisionmaking.

Okay, I'm done

 

[Flavio4321]

splits and doubles question

hey to Cipher or anybody who knows, What is the average ( percentage ) amonut of hands that one should win after double downs on a fair BJ game?
Same question regarding splits?

I want to know this for different rules, specifically RTG and Cryptologic.

I looked for the answer on the wizard's site and I didnt find it.

Thanks in advance if anybody knows the answer.

 

[cipher]

hey to Cipher or anybody who knows, What is the average ( percentage ) amonut of hands that one should win after double downs on a fair BJ game?
Same question regarding splits?

I want to know this for different rules, specifically RTG and Cryptologic.

I looked for the answer on the wizard's site and I didnt find it.

Thanks in advance if anybody knows the answer.

Hey Flavio; Good to hear from you. But I'm going to yield to Caruso or Grand Master on this one. Have a good one.

 

[jerseyguy11]

interesting as always cipher old buddy . thanks for sharing

 

[cipher]

interesting as always cipher old buddy . thanks for sharing

Good to hear from you Jersey. Have a good one.

 

[cipher]

Cipher,

I have to thank the guy who taught you to count 4 decks(can't remember his name) and thank you for continuing to help others in his name. Many posters on this board work hard to help guilelss newbies or small bettors like me not lose money and I appreciate each one, including Caruso. I especially like the way you simply post facts, point out trends that your sets of facts seem to indicate and by gosh, give us a copy so that we can print it and look at it!

You have saved me much money (by my NOT betting) simply in showing me that it requires a sophistication that I don't possess. (I sure wish I'd read your posts before I lost that first $600.)

I get a little peeved when folks respond to you about sample sizes and rigging, etc. You really do just provide a FREE service as a jumping off point for thoughtful decisionmaking.

Okay, I'm done

Heh there little buddy;

That gentlemen was Jerry Patterson out of Vorhees, New Jersey at the Blackjack Academy and it was the 6 to 8 deck shoe. Have a good one.

 

[GrandMaster]

Hey Flavio; Good to hear from you. But I'm going to yield to Caruso or Grand Master on this one. Have a good one.

I have a program to calculate composition dependent strategy. It should only need some minor modification to calculate the probability of win/loss/push after doubling down. If I have time, I will post some numbers tonight, if not, then probably on Sunday.

 

[GrandMaster]

I promised some numbers, so here are some numbers.

The first column shows the player's total, the second the dealer's up card, the third the probability of this particular combination being dealt, the last three columns show the probability of the player winning, pushing or losing the double down. These numbers are for a 4 deck shoe, and don't include split hands, but the probabilities should not be too much different for 6 or 8 decks or for hands after a split.

For hard doubles, the probability of a win is usually 50-60%, the probability of a push is 6-9%, and the probability of a loss is usually 30-40%.


9, 3, 0.00271310, 0.50019495, 0.06888858, 0.430916457
9, 4, 0.00271310, 0.51841005, 0.06647686, 0.415113080,
9, 5, 0.00271310, 0.53664626, 0.06416847, 0.399185252,
9, 6, 0.00271310, 0.55280310, 0.06224455, 0.384952338

10, 2, 0.00314605, 0.554506, 0.0790360, 0.366458,
10, 3, 0.00314605, 0.569135, 0.0766647, 0.354201,
10, 4, 0.00314605, 0.584117, 0.0738528, 0.34203,
10, 5, 0.00314966, 0.600010, 0.0708573, 0.329132,
10, 6, 0.00314605, 0.614227, 0.0683477, 0.317426,
10, 7, 0.00314605, 0.564752, 0.0736985, 0.36155,
10, 8, 0.00314605, 0.536796, 0.0730063, 0.390198,
10, 9, 0.00320378, 0.493880, 0.0869117, 0.419209,

 

[cipher]

I promised some numbers, so here are some numbers.

The first column shows the player's total, the second the dealer's up card, the third the probability of this particular combination being dealt, the last three columns show the probability of the player winning, pushing or losing the double down. These numbers are for a 4 deck shoe, and don't include split hands, but the probabilities should not be too much different for 6 or 8 decks or for hands after a split.

For hard doubles, the probability of a win is usually 50-60%, the probability of a push is 6-9%, and the probability of a loss is usually 30-40%.


9, 3, 0.00271310, 0.50019495, 0.06888858, 0.430916457
9, 4, 0.00271310, 0.51841005, 0.06647686, 0.415113080,
9, 5, 0.00271310, 0.53664626, 0.06416847, 0.399185252,
9, 6, 0.00271310, 0.55280310, 0.06224455, 0.384952338

10, 2, 0.00314605, 0.554506, 0.0790360, 0.366458,
10, 3, 0.00314605, 0.569135, 0.0766647, 0.354201,
10, 4, 0.00314605, 0.584117, 0.0738528, 0.34203,
10, 5, 0.00314966, 0.600010, 0.0708573, 0.329132,
10, 6, 0.00314605, 0.614227, 0.0683477, 0.317426,
10, 7, 0.00314605, 0.564752, 0.0736985, 0.36155,
10, 8, 0.00314605, 0.536796, 0.0730063, 0.390198,
10, 9, 0.00320378, 0.493880, 0.0869117, 0.419209,

Thanks for the numbers. Have a good one.

 

[DeMango]

Thanks for the figures. I would like to work up my own, for one and two deck, B&M casino's. Need figures on doubling vs hitting, also H17 & S17. Do you have any formulas? I can get hand value probability from Professional BJ by Wong

 

[cipher]

Grand Master, are these figures based on Internet Blackjack or off known quantities incident to land based play? Have a good one.

 

[GrandMaster]

I calculated the numbers myself, I don't know if they can be found anywhere. They are exact numbers, not not the result of simulations. These numbers relate to a freshly shuffled 4 deck shoe, to this extent they are only applicable to online casinos that shuffle after every hand, but the averages at a casino that does not shuffle after every hand should not be much different. I forgot to mention that I assumed S17 rules. I will try to get a full set of figures, including soft doubles, tonight.

 

[GrandMaster]

Here are the complete numbers for the 4 deck, S17 game.

Probability of a double down opportunity: 0.0952521
Average probability of win/push/loss: 0.552009, 0.0695503, 0.380259

The first column shows the player's total, the second the dealer's up card, the third the probability of this particular combination being dealt, the last three columns show the probability of the player winning, pushing or losing.

Hard doubles
9, 3, 0.00271311, 0.500195, 0.0688886, 0.430916,
9, 4, 0.00271311, 0.51841, 0.0664769, 0.415113,
9, 5, 0.00271311, 0.536646, 0.0641685, 0.399185,
9, 6, 0.00271311, 0.552803, 0.0622446, 0.384952,
10, 2, 0.00314605, 0.554506, 0.079036, 0.366458,
10, 3, 0.00314605, 0.569135, 0.0766647, 0.354201,
10, 4, 0.00314605, 0.584117, 0.0738528, 0.34203,
10, 5, 0.00314966, 0.60001, 0.0708573, 0.329132,
10, 6, 0.00314605, 0.614227, 0.0683477, 0.317426,
10, 7, 0.00314605, 0.564752, 0.0736985, 0.36155,
10, 8, 0.00314605, 0.536796, 0.0730063, 0.390198,
10, 9, 0.00320378, 0.49388, 0.0869117, 0.419209,
11, 2, 0.00363672, 0.583131, 0.0775646, 0.339304,
11, 3, 0.00363672, 0.596393, 0.0751123, 0.328494,
11, 4, 0.00363672, 0.610303, 0.0727347, 0.316962,
11, 5, 0.00363672, 0.624988, 0.0699342, 0.305078,
11, 6, 0.00363672, 0.637111, 0.0664188, 0.296471,
11, 7, 0.00363672, 0.580056, 0.0735837, 0.346361,
11, 8, 0.00363672, 0.550088, 0.0740865, 0.375825,
11, 9, 0.00363672, 0.520139, 0.0731223, 0.406738,
11, 10, 0.0136244, 0.509769, 0.0682111, 0.42202,

Soft doubles
13, 5, 0.000923611, 0.514469, 0.0444979, 0.441033,
13, 6, 0.000923611, 0.525947, 0.0441305, 0.429922,
14, 5, 0.000923611, 0.514255, 0.0438567, 0.441888,
14, 6, 0.000923611, 0.525781, 0.0433085, 0.43091,
15, 4, 0.000865885, 0.526253, 0.0485226, 0.491891,
15, 5, 0.000923611, 0.51293, 0.0429624, 0.444108,
15, 6, 0.000923611, 0.524377, 0.0435193, 0.432103,
16, 4, 0.000923611, 0.492188, 0.0450182, 0.462793,
16, 5, 0.000865885, 0.545138, 0.0460823, 0.475446,
16, 6, 0.000923611, 0.526075, 0.0421066, 0.431819,
17, 3, 0.000923611, 0.47541, 0.0789189, 0.445671,
17, 4, 0.000923611, 0.493476, 0.0764925, 0.430032,
17, 5, 0.000923611, 0.514827, 0.0731548, 0.412018,
17, 6, 0.000865885, 0.558661, 0.0878082, 0.420197,
18, 3, 0.000923611, 0.50589, 0.0783217, 0.415789,
18, 4, 0.000923611, 0.525981, 0.0754427, 0.398576,
18, 5, 0.000923611, 0.540267, 0.0737333, 0.385999,
18, 6, 0.000923611, 0.560983, 0.0697132, 0.369304


I hope these numbers are useful for some people. They confirm that if you are not winning at least half of your doubles in a large enough sample, then there is definitely something fishy going on.

 

[cipher]

Thanks for the effort Grand Master. Have a good one.

 

[GrandMaster]

Here is the complete set of numbers for 1, 2, 4, 6 and 8 decks when the dealer stands on soft 17. Feel free to use them for any non-commercial purpose.

The first column shows the player's total, the second the dealer's up card, the third the probability of this particular combination being dealt, the last three columns show the probability of the player winning, pushing or losing.

1 deck

Probability of a double down opportunity: 0.105412
Average probability of win/push/loss: 0.558519, 0.0691201, 0.379229

Hard doubles
8 5 0.00205128 0.507200 0.0579973 0.434803
8 6 0.00205128 0.513786 0.0560803 0.430134
9 3 0.00265460 0.512993 0.0707678 0.416239
9 4 0.00265460 0.537406 0.0677714 0.394823
9 5 0.00265460 0.561326 0.0655239 0.37315
9 6 0.00265460 0.566147 0.0649941 0.368859
10 2 0.00301659 0.566833 0.0813652 0.351802
10 3 0.00301659 0.583931 0.0791053 0.336963
10 4 0.00301659 0.601270 0.0751574 0.323572
10 5 0.00307692 0.622773 0.0705145 0.306712
10 6 0.00301659 0.626582 0.0700365 0.303381
10 7 0.00301659 0.577143 0.0697794 0.353078
10 8 0.00301659 0.544200 0.06935180 0.386448
10 9 0.00325792 0.498236 0.0862284 0.415536
11 1 0.00260042 0.515977 0.0751604 0.408863
11 2 0.00361991 0.595919 0.0796485 0.324433
11 3 0.00361991 0.609710 0.0767755 0.313515
11 4 0.00361991 0.625674 0.0743888 0.299938
11 5 0.00361991 0.644429 0.0701494 0.285421
11 6 0.00361991 0.647753 0.0653464 0.286901
11 7 0.00361991 0.583192 0.0728303 0.343978
11 8 0.00361991 0.548466 0.0738811 0.377653
11 9 0.00361991 0.519951 0.0721283 0.407921
11 10 0.0141841 0.505768 0.0693089 0.424923

Soft doubles
13 4 0.000965309 0.505901 0.0457468 0.448352
13 5 0.000965309 0.531478 0.0431917 0.42533
13 6 0.000965309 0.535949 0.0432082 0.420843
14 4 0.000965309 0.507826 0.0389201 0.453254
14 5 0.000965309 0.530623 0.0405429 0.428834
14 6 0.000965309 0.535389 0.0401510 0.42446
15 4 0.000723982 0.666854 0.0562133 0.610266
15 5 0.000965309 0.525331 0.0368307 0.437838
15 6 0.000965309 0.529894 0.0405725 0.429533
16 4 0.000965309 0.495675 0.0399451 0.46438
16 5 0.000723982 0.690657 0.0508561 0.59182
16 6 0.000965309 0.536557 0.0352180 0.428225
17 2 0.000965309 0.462698 0.0812650 0.456037
17 3 0.000965309 0.479711 0.0775269 0.442762
17 4 0.000965309 0.500742 0.0757905 0.423468
17 5 0.000965309 0.533329 0.0733583 0.393313
17 6 0.000723982 0.701314 0.1083620 0.523657
18 3 0.000965309 0.508019 0.0784293 0.413552
18 4 0.000965309 0.540811 0.0747189 0.38447
18 5 0.000965309 0.549416 0.0757154 0.374869
18 6 0.000965309 0.559982 0.0724662 0.367552
19 6 0.000965309 0.585919 0.0694749 0.344606

2 decks

Probability of a double down opportunity: 0.100379
Average probability of win/push/loss: 0.552492, 0.0699694, 0.38104

Hard doubles
9 2 0.00269443 0.485699 0.0724685 0.441832
9 3 0.00269443 0.504405 0.0694854 0.42611
9 4 0.00269443 0.524541 0.0669148 0.408544
9 5 0.00269443 0.544626 0.0646156 0.390759
9 6 0.00269443 0.557147 0.0631108 0.379742
10 2 0.00310445 0.558532 0.0797687 0.361699
10 3 0.00310445 0.573985 0.0774371 0.348578
10 4 0.00310445 0.589792 0.0742625 0.335946
10 5 0.00311910 0.607483 0.0707312 0.321786
10 6 0.00310445 0.618426 0.0688761 0.312698
10 7 0.00310445 0.568865 0.0724517 0.358683
10 8 0.00310445 0.539118 0.0718466 0.389035
10 9 0.00322160 0.495261 0.0867356 0.418003
11 1 0.00256104 0.500546 0.0787338 0.42072
11 2 0.00363162 0.587231 0.0782163 0.334553
11 3 0.00363162 0.600742 0.0756279 0.32363
11 4 0.00363162 0.615321 0.0732537 0.311425
11 5 0.00363162 0.631353 0.0700010 0.298646
11 6 0.00363162 0.640723 0.0660502 0.293227
11 7 0.00363162 0.581210 0.0733315 0.345458
11 8 0.00363162 0.549553 0.0740425 0.376404
11 9 0.00363162 0.520051 0.0728255 0.407123
11 10 0.0138074 0.508497 0.0685628 0.422941

Soft doubles
13 5 0.000937193 0.520015 0.0440843 0.435901
13 6 0.000937193 0.529212 0.0438577 0.42693
14 5 0.000937193 0.519588 0.0427891 0.437622
14 6 0.000937193 0.528896 0.0422478 0.428856
15 4 0.000820044 0.566293 0.0507359 0.525828
15 5 0.000937193 0.516936 0.0409763 0.442088
15 6 0.000937193 0.526105 0.0426051 0.43129
16 4 0.000937193 0.493191 0.043397 0.463412
16 5 0.000820044 0.586541 0.047448 0.508868
16 6 0.000937193 0.529483 0.0398235 0.430694
17 3 0.000937193 0.476773 0.0784852 0.444742
17 4 0.000937193 0.495760 0.0762769 0.427963
17 5 0.000937193 0.520801 0.0732119 0.405987
17 6 0.000820044 0.599570 0.0937557 0.449531
18 3 0.000937193 0.506552 0.0783634 0.415085
18 4 0.000937193 0.530719 0.0752246 0.394057
18 5 0.000937193 0.543301 0.074378 0.382321
18 6 0.000937193 0.560856 0.070578 0.368566

4 decks


Probability of a double down opportunity: 0.0952521
Average probability of win/push/loss: 0.552009, 0.0695503, 0.380259

Hard doubles
9 3 0.00271311 0.500195 0.0688886 0.430916
9 4 0.00271311 0.518410 0.0664769 0.415113
9 5 0.00271311 0.536646 0.0641685 0.399185
9 6 0.00271311 0.552803 0.0622446 0.384952
10 2 0.00314605 0.554506 0.079036 0.366458
10 3 0.00314605 0.569135 0.0766647 0.354201
10 4 0.00314605 0.584117 0.0738528 0.34203
10 5 0.00314966 0.600010 0.0708573 0.329132
10 6 0.00314605 0.614227 0.0683477 0.317426
10 7 0.00314605 0.564752 0.0736985 0.36155
10 8 0.00314605 0.536796 0.0730063 0.390198
10 9 0.00320378 0.493880 0.0869117 0.419209
11 2 0.00363672 0.583131 0.0775646 0.339304
11 3 0.00363672 0.596393 0.0751123 0.328494
11 4 0.00363672 0.610303 0.0727347 0.316962
11 5 0.00363672 0.624988 0.0699342 0.305078
11 6 0.00363672 0.637111 0.0664188 0.296471
11 7 0.00363672 0.580056 0.0735837 0.346361
11 8 0.00363672 0.550088 0.0740865 0.375825
11 9 0.00363672 0.520139 0.0731223 0.406738
11 10 0.0136244 0.509769 0.0682111 0.42202

Soft doubles
13 5 0.000923611 0.514469 0.0444979 0.441033
13 6 0.000923611 0.525947 0.0441305 0.429922
14 5 0.000923611 0.514255 0.0438567 0.441888
14 6 0.000923611 0.525781 0.0433085 0.43091
15 4 0.000865885 0.526253 0.0485226 0.491891
15 5 0.000923611 0.512930 0.0429624 0.444108
15 6 0.000923611 0.524377 0.0435193 0.432103
16 4 0.000923611 0.492188 0.0450182 0.462793
16 5 0.000865885 0.545138 0.0460823 0.475446
16 6 0.000923611 0.526075 0.0421066 0.431819
17 3 0.000923611 0.475410 0.0789189 0.445671
17 4 0.000923611 0.493476 0.0764925 0.430032
17 5 0.000923611 0.514827 0.0731548 0.412018
17 6 0.000865885 0.558661 0.0878082 0.420197
18 3 0.000923611 0.505890 0.0783217 0.415789
18 4 0.000923611 0.525981 0.0754427 0.398576
18 5 0.000923611 0.540267 0.0737333 0.385999
18 6 0.000923611 0.560983 0.0697132 0.369304

6 decks

Probability of a double down opportunity: 0.0952936
Average probability of win/push/loss: 0.550765, 0.0695135, 0.380927

9 3 0.00271916 0.498805 0.0686961 0.432499
9 4 0.00271916 0.516409 0.0663300 0.417261
9 5 0.00271916 0.534039 0.0640206 0.40194
9 6 0.00271916 0.551376 0.0619657 0.386658
10 2 0.00315958 0.553182 0.0788009 0.368017
10 3 0.00315958 0.567536 0.0764160 0.356048
10 4 0.00315958 0.582239 0.0737203 0.344041
10 5 0.00316118 0.597540 0.0709035 0.331556
10 6 0.00315958 0.612814 0.0681777 0.319008
10 7 0.00315958 0.563385 0.0741016 0.362514
10 8 0.00315958 0.536051 0.0733805 0.390568
10 9 0.00319788 0.493433 0.0869602 0.419606
11 2 0.00363831 0.581799 0.0773561 0.340845
11 3 0.00363831 0.594963 0.0749486 0.330088
11 4 0.00363831 0.608653 0.0725690 0.318778
11 5 0.00363831 0.622892 0.0699129 0.307195
11 6 0.00363831 0.635895 0.0665435 0.297562
11 7 0.00363831 0.579649 0.0736684 0.346683
11 8 0.00363831 0.550265 0.0740967 0.375638
11 9 0.00363831 0.520174 0.0732142 0.406612
11 10 0.0135642 0.510181 0.0680968 0.421723

Soft doubles
13 5 0.000919151 0.512647 0.0446313 0.442721
13 6 0.000919151 0.524874 0.0442146 0.430911
14 5 0.000919151 0.512504 0.0442052 0.44329
14 6 0.000919151 0.524762 0.0436630 0.431575
15 4 0.000880853 0.514091 0.0478473 0.48154
15 5 0.000919151 0.511621 0.0436119 0.444767
15 6 0.000919151 0.523824 0.0438103 0.432365
16 4 0.000919151 0.491884 0.0455449 0.462571
16 5 0.000880853 0.532569 0.0456675 0.465242
16 6 0.000919151 0.524957 0.0428640 0.432179
17 3 0.000919151 0.474970 0.0790572 0.445972
17 4 0.000919151 0.492743 0.0765608 0.430696
17 5 0.000919151 0.512878 0.0731373 0.413984
17 6 0.000880853 0.546183 0.0859854 0.41131
18 3 0.000919151 0.505679 0.0783066 0.416014
18 4 0.000919151 0.524444 0.0755111 0.400045
18 5 0.000919151 0.539261 0.0735218 0.387218
18 6 0.000919151 0.560984 0.0694358 0.36958

8 decks

Probability of a double down opportunity: 0.0953142
Average probability of win/push/loss: 0.550145, 0.0694953, 0.381262

Hard doubles
9 3 0.00272215 0.498112 0.068601 0.433287
9 4 0.00272215 0.515417 0.0662564 0.418327
9 5 0.00272215 0.532745 0.063947 0.403308
9 6 0.00272215 0.550667 0.0618281 0.387505
10 2 0.00316629 0.552524 0.078685 0.368791
10 3 0.00316629 0.566740 0.0762933 0.356967
10 4 0.00316629 0.581302 0.0736547 0.345043
10 5 0.00316718 0.596309 0.0709274 0.332764
10 6 0.00316629 0.612106 0.0680937 0.3198
10 7 0.00316629 0.562702 0.0743008 0.362997
10 8 0.00316629 0.535684 0.0735654 0.39075
10 9 0.00319494 0.493213 0.0869827 0.419805
11 2 0.00363908 0.581139 0.0772534 0.341607
11 3 0.00363908 0.594252 0.0748681 0.33088
11 4 0.00363908 0.607832 0.0724875 0.319681
11 5 0.00363908 0.621849 0.0699025 0.308249
11 6 0.00363908 0.635285 0.0666062 0.298109
11 7 0.00363908 0.579441 0.0737109 0.346848
11 8 0.00363908 0.550354 0.074101 0.375545
11 9 0.00363908 0.520193 0.0732589 0.406549
11 10 0.0135342 0.510384 0.0680402 0.421576

Soft doubles
13 5 0.000916934 0.511741 0.0446973 0.443561
13 6 0.000916934 0.524340 0.0442554 0.431404
14 5 0.000916934 0.511634 0.0443782 0.443988
14 6 0.000916934 0.524256 0.0438405 0.431904
15 4 0.000888280 0.508210 0.0475202 0.476528
15 5 0.000916934 0.510972 0.0439342 0.445094
15 6 0.000916934 0.523552 0.0439534 0.432495
16 4 0.000916934 0.491737 0.0458058 0.462457
16 5 0.000888280 0.526492 0.0454671 0.460299
16 6 0.000916934 0.524402 0.043242 0.432356
17 3 0.000916934 0.474753 0.0791253 0.446122
17 4 0.000916934 0.492381 0.0765943 0.431024
17 5 0.000916934 0.511912 0.0731287 0.41496
17 6 0.000888280 0.540141 0.0851012 0.407016
18 3 0.000916934 0.505576 0.0782988 0.416125
18 4 0.000916934 0.523683 0.0755445 0.400773
18 5 0.000916934 0.538758 0.0734167 0.387825
18 6 0.000916934 0.560977 0.0692989 0.369724

 

[GrandMaster]

Here are the numbers for the case when the dealer hits soft 17.

1 deck

Probability of a double down opportunity: 0.108067
Average probability of win/push/loss: 0.556653,0.069276,0.38077

Hard doubles
8 5 0.00205128 0.507200 0.0579973 0.434803
8 6 0.00205128 0.511513 0.054980 0.433507
9 2 0.00265460 0.491245 0.0744982 0.434257
9 3 0.00265460 0.512993 0.0707678 0.416239
9 4 0.00265460 0.537406 0.0677714 0.394823
9 5 0.00265460 0.561326 0.0655239 0.37315
9 6 0.00265460 0.562512 0.0649121 0.372576
10 2 0.00301659 0.566833 0.0813652 0.351802
10 3 0.00301659 0.583931 0.0791053 0.336963
10 4 0.00301659 0.601270 0.0751574 0.323572
10 5 0.00307692 0.622773 0.0705145 0.306712
10 6 0.00301659 0.622996 0.0710390 0.305965
10 7 0.00301659 0.577143 0.0697794 0.353078
10 8 0.00301659 0.544200 0.0693518 0.386448
10 9 0.00325792 0.498236 0.0862284 0.415536
11 1 0.00260042 0.513961 0.0779953 0.408044
11 2 0.00361991 0.595919 0.0796485 0.324433
11 3 0.00361991 0.609710 0.0767755 0.313515
11 4 0.00361991 0.625674 0.0743888 0.299938
11 5 0.00361991 0.644429 0.0701494 0.285421
11 6 0.00361991 0.646305 0.0673829 0.286312
11 7 0.00361991 0.583192 0.0728303 0.343978
11 8 0.00361991 0.548466 0.0738811 0.377653
11 9 0.00361991 0.519951 0.0721283 0.407921
11 10 0.0141841 0.505768 0.0693089 0.424923

Soft doubles
13 4 0.000965309 0.505901 0.0457468 0.448352
13 5 0.000965309 0.531478 0.0431917 0.42533
13 6 0.000965309 0.540513 0.0419556 0.417531
14 4 0.000965309 0.507826 0.0389201 0.453254
14 5 0.000965309 0.530623 0.0405429 0.428834
14 6 0.000965309 0.539969 0.0396818 0.420349
15 4 0.000723982 0.666854 0.0562133 0.610266
15 5 0.000965309 0.525331 0.0368307 0.437838
15 6 0.000965309 0.535189 0.0391474 0.425664
16 4 0.000965309 0.495675 0.0399451 0.46438
16 5 0.000723982 0.690657 0.0508561 0.59182
16 6 0.000965309 0.540484 0.0355899 0.423926
17 2 0.000965309 0.462698 0.0812650 0.456037
17 3 0.000965309 0.479711 0.0775269 0.442762
17 4 0.000965309 0.500742 0.0757905 0.423468
17 5 0.000965309 0.533329 0.0733583 0.393313
17 6 0.000723982 0.707966 0.0928435 0.532523
18 3 0.000965309 0.508019 0.0784293 0.413552
18 4 0.000965309 0.540811 0.0747189 0.38447
18 5 0.000965309 0.549416 0.0757154 0.374869
18 6 0.000965309 0.554340 0.0723647 0.373295
19 6 0.000965309 0.581224 0.0708115 0.347964

2 decks

Probability of a double down opportunity: 0.103191
Average probability of win/push/loss: 0.551592,0.0697974,0.382016

Hard doubles
9 2 0.00269443 0.485699 0.0724685 0.441832
9 3 0.00269443 0.504405 0.0694854 0.42611
9 4 0.00269443 0.524541 0.0669148 0.408544
9 5 0.00269443 0.544626 0.0646156 0.390759
9 6 0.00269443 0.553813 0.0631039 0.383084
10 2 0.00310445 0.558532 0.0797687 0.361699
10 3 0.00310445 0.573985 0.0774371 0.348578
10 4 0.00310445 0.589792 0.0742625 0.335946
10 5 0.00311910 0.607483 0.0707312 0.321786
10 6 0.00310445 0.615146 0.0697247 0.31513
10 7 0.00310445 0.568865 0.0724517 0.358683
10 8 0.00310445 0.539118 0.0718466 0.389035
10 9 0.00322160 0.495261 0.0867356 0.418003
11 1 0.00256104 0.498786 0.0806685 0.420545
11 2 0.00363162 0.587231 0.0782163 0.334553
11 3 0.00363162 0.600742 0.0756279 0.32363
11 4 0.00363162 0.615321 0.0732537 0.311425
11 5 0.00363162 0.631353 0.070001 0.298646
11 6 0.00363162 0.639482 0.0674146 0.293103
11 7 0.00363162 0.581210 0.0733315 0.345458
11 8 0.00363162 0.549553 0.0740425 0.376404
11 9 0.00363162 0.520051 0.0728255 0.407123
11 10 0.0138074 0.508497 0.0685628 0.422941

Soft doubles
13 5 0.000937193 0.520015 0.0440843 0.435901
13 6 0.000937193 0.533896 0.0425809 0.423524
14 4 0.000937193 0.499559 0.0428111 0.45763
14 5 0.000937193 0.519588 0.0427891 0.437622
14 6 0.000937193 0.533581 0.0414121 0.425007
15 4 0.000820044 0.566293 0.0507359 0.525828
15 5 0.000937193 0.516936 0.0409763 0.442088
15 6 0.000937193 0.531178 0.0412424 0.42758
16 4 0.000937193 0.493191 0.0433970 0.463412
16 5 0.000820044 0.586541 0.0474480 0.508868
16 6 0.000937193 0.533823 0.0394568 0.426721
17 3 0.000937193 0.476773 0.0784852 0.444742
17 4 0.000937193 0.495760 0.0762769 0.427963
17 5 0.000937193 0.520801 0.0732119 0.405987
17 6 0.000820044 0.605219 0.0795683 0.458069
18 2 0.000937193 0.490591 0.0805877 0.428821
18 3 0.000937193 0.506552 0.0783634 0.415085
18 4 0.000937193 0.530719 0.0752246 0.394057
18 5 0.000937193 0.543301 0.0743780 0.382321
18 6 0.000937193 0.554524 0.0708767 0.374599
19 6 0.000937193 0.580917 0.0701723 0.34891

4 decks

Probability of a double down opportunity: 0.0996404
Average probability of win/push/loss: 0.550091,0.0698818,0.3817660

Hard doubles
9 3 0.00271311 0.500195 0.0688886 0.430916
9 4 0.00271311 0.518410 0.0664769 0.415113
9 5 0.00271311 0.536646 0.0641685 0.399185
9 6 0.00271311 0.549600 0.0622734 0.388127
10 2 0.00314605 0.554506 0.079036 0.366458
10 3 0.00314605 0.569135 0.0766647 0.354201
10 4 0.00314605 0.584117 0.0738528 0.34203
10 5 0.00314966 0.600010 0.0708573 0.329132
10 6 0.00314605 0.611082 0.0691302 0.319788
10 7 0.00314605 0.564752 0.0736985 0.36155
10 8 0.00314605 0.536796 0.0730063 0.390198
10 9 0.00320378 0.493880 0.0869117 0.419209
11 1 0.00254106 0.491626 0.0819172 0.426457
11 2 0.00363672 0.583131 0.0775646 0.339304
11 3 0.00363672 0.596393 0.0751123 0.328494
11 4 0.00363672 0.610303 0.0727347 0.316962
11 5 0.00363672 0.624988 0.0699342 0.305078
11 6 0.00363672 0.635971 0.0674584 0.296571
11 7 0.00363672 0.580056 0.0735837 0.346361
11 8 0.00363672 0.550088 0.0740865 0.375825
11 9 0.00363672 0.520139 0.0731223 0.406738
11 10 0.0136244 0.509769 0.0682111 0.42202

Soft doubles
13 5 0.000923611 0.514469 0.0444979 0.441033
13 6 0.000923611 0.530652 0.0428591 0.426489
14 5 0.000923611 0.514255 0.0438567 0.441888
14 6 0.000923611 0.530485 0.0422691 0.427246
15 4 0.000865885 0.526253 0.0485226 0.491891
15 5 0.000923611 0.512930 0.0429624 0.444108
15 6 0.000923611 0.529281 0.0422053 0.428513
16 4 0.000923611 0.492188 0.0450182 0.462793
16 5 0.000865885 0.545138 0.0460823 0.475446
16 6 0.000923611 0.530602 0.0413128 0.428085
17 3 0.000923611 0.475410 0.0789189 0.445671
17 4 0.000923611 0.493476 0.0764925 0.430032
17 5 0.000923611 0.514827 0.0731548 0.412018
17 6 0.000865885 0.563830 0.0742583 0.428579
18 2 0.000923611 0.490039 0.0807251 0.429235
18 3 0.000923611 0.505890 0.0783217 0.415789
18 4 0.000923611 0.525981 0.0754427 0.398576
18 5 0.000923611 0.540267 0.0737333 0.385999
18 6 0.000923611 0.554324 0.0702220 0.375454
19 6 0.000923611 0.580704 0.0698856 0.34941

6 decks
Probability of a double down opportunity: 0.0996663
Average probability of win/push/loss: 0.548846,0.0698498,0.382457

Hard doubles
9 3 0.00271916 0.498805 0.0686961 0.432499
9 4 0.00271916 0.516409 0.066330 0.417261
9 5 0.00271916 0.534039 0.0640206 0.40194
9 6 0.00271916 0.548215 0.0620063 0.389779
10 2 0.00315958 0.553182 0.0788009 0.368017
10 3 0.00315958 0.567536 0.0764160 0.356048
10 4 0.00315958 0.582239 0.0737203 0.344041
10 5 0.00316118 0.597540 0.0709035 0.331556
10 6 0.00315958 0.609713 0.0689396 0.321348
10 7 0.00315958 0.563385 0.0741016 0.362514
10 8 0.00315958 0.536051 0.0733805 0.390568
10 9 0.00319788 0.493433 0.0869602 0.419606
11 1 0.00253436 0.489298 0.0823215 0.428381
11 2 0.00363831 0.581799 0.0773561 0.340845
11 3 0.00363831 0.594963 0.0749486 0.330088
11 4 0.00363831 0.608653 0.0725690 0.318778
11 5 0.00363831 0.622892 0.0699129 0.307195
11 6 0.00363831 0.634788 0.0674766 0.297735
11 7 0.00363831 0.579649 0.0736684 0.346683
11 8 0.00363831 0.550265 0.0740967 0.375638
11 9 0.00363831 0.520174 0.0732142 0.406612
11 10 0.0135642 0.510181 0.0680968 0.421723

Soft doubles
13 5 0.000919151 0.512647 0.0446313 0.442721
13 6 0.000919151 0.529580 0.0429474 0.427472
14 5 0.000919151 0.512504 0.0442052 0.44329
14 6 0.000919151 0.529467 0.0425530 0.42798
15 4 0.000880853 0.514091 0.0478473 0.48154
15 5 0.000919151 0.511621 0.0436119 0.444767
15 6 0.000919151 0.528664 0.0425149 0.428821
16 4 0.000919151 0.491884 0.0455449 0.462571
16 5 0.000880853 0.532569 0.0456675 0.465242
16 6 0.000919151 0.529544 0.0419202 0.428536
17 3 0.000919151 0.474970 0.0790572 0.445972
17 4 0.000919151 0.492743 0.0765608 0.430696
17 5 0.000919151 0.512878 0.0731373 0.413984
17 6 0.000880853 0.551195 0.0726436 0.41964
18 2 0.000919151 0.489860 0.0807692 0.42937
18 3 0.000919151 0.505679 0.0783066 0.416014
18 4 0.000919151 0.524444 0.0755111 0.400045
18 5 0.000919151 0.539261 0.0735218 0.387218
18 6 0.000919151 0.554219 0.0700155 0.375766
19 6 0.000919151 0.580625 0.0697946 0.34958


8 decks

Probability of a double down opportunity: 0.0996791
Average probability of win/push/loss: 0.548226,0.0698339,0.382802

9 3 0.00272215 0.498112 0.0686010 0.433287
9 4 0.00272215 0.515417 0.0662564 0.418327
9 5 0.00272215 0.532745 0.0639470 0.403308
9 6 0.00272215 0.547525 0.0618744 0.3906
10 2 0.00316629 0.552524 0.078685 0.368791
10 3 0.00316629 0.566740 0.0762933 0.356967
10 4 0.00316629 0.581302 0.0736547 0.345043
10 5 0.00316718 0.596309 0.0709274 0.332764
10 6 0.00316629 0.609026 0.0688457 0.322129
10 7 0.00316629 0.562702 0.0743008 0.362997
10 8 0.00316629 0.535684 0.0735654 0.39075
10 9 0.00319494 0.493213 0.0869827 0.419805
11 1 0.00253100 0.488145 0.0825215 0.429334
11 2 0.00363908 0.581139 0.0772534 0.341607
11 3 0.00363908 0.594252 0.0748681 0.33088
11 4 0.00363908 0.607832 0.0724875 0.319681
11 5 0.00363908 0.621849 0.0699025 0.308249
11 6 0.00363908 0.634195 0.0674864 0.298319
11 7 0.00363908 0.579441 0.0737109 0.346848
11 8 0.00363908 0.550354 0.074101 0.375545
11 9 0.00363908 0.520193 0.0732589 0.406549
11 10 0.0135342 0.510384 0.0680402 0.421576
13 5 0.000916934 0.511741 0.0446973 0.443561
13 6 0.000916934 0.529047 0.0429908 0.427963
14 5 0.000916934 0.511634 0.0443782 0.443988
14 6 0.000916934 0.528961 0.0426947 0.428344
15 4 0.000888280 0.508210 0.0475202 0.476528
15 5 0.000916934 0.510972 0.0439342 0.445094
15 6 0.000916934 0.528359 0.0426677 0.428974
16 4 0.000916934 0.491737 0.0458058 0.462457
16 5 0.000888280 0.526492 0.0454671 0.460299
16 6 0.000916934 0.529018 0.0422217 0.42876
17 3 0.000916934 0.474753 0.0791253 0.446122
17 4 0.000916934 0.492381 0.0765943 0.431024
17 5 0.000916934 0.511912 0.0731287 0.41496
17 6 0.000888280 0.545074 0.0718626 0.415321
18 2 0.000916934 0.489772 0.0807909 0.429437
18 3 0.000916934 0.505576 0.0782988 0.416125
18 4 0.000916934 0.523683 0.0755445 0.400773
18 5 0.000916934 0.538758 0.0734167 0.387825
18 6 0.000916934 0.554159 0.0699144 0.375926
19 6 0.000916934 0.580584 0.0697499 0.349666

 

[DeMango]

Grandmaster: Thank you so very much for your excellent Work!!!

Cipher: Looking at 8 decks H17 overall results. Player wins 58.88% of all DD's not including pushes. How does this stack up against your RTG accumulation of results?