Ion Saliu (aka Parpaluck), Advantage Gambling Renaissance Man or Charlatan?

[Parpaluck]

Click on the links, pal! The text files (.txt) open directly in your browser. There they are again:

This text file shows all blackjack hands as combinations based on Dealer’s rules. Total cards: 13 (only one suit, from 2 to Ace). Link to the file: http://saliu.com/freeware/BjAllHands1-11Combos.TXT

This text file shows all blackjack hands based on Dealer’s rules as arrangements. Total cards: 13 (only one suit, from 2 to Ace). Link to the file: http://saliu.com/freeware/BjAllHands1-11Ord.TXT

Fuqe you! waste my time with a bunch of sh*ty brains!
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[Dodo]

Probability Theory, Live! (179) indicates the following, "My latest blackjack software (2009) undeniably proves that the percentage of the bust hands is, at least, 41.97%. The bust hands were generated following the dealer’s rule: Hit all hands under 16 and stand on all hands 17 or higher. In this case, the house advantage (HA) at blackjack becomes 41.97% x 41.97% = 17.6%. That HA figure is valid only for one player against the dealer. If we deduct the traditional 4% gained by the basic strategy player, we reach a 14% house advantage at blackjack."

Suppose that the percentage of dealer bust hands were actually to be 90% instead of 28% (or 42%). Using this calculation process, the HA becomes 90% x 90% = 81%. Would you want to play in a game where the house advantage is 80%, even though the dealer busts 90% of the time? [I am assuming that "house advantage" means "player disadvantage" as a player is given 4% less house advantage by playing "basic strategy."] As a gambler, should I celebrate when the dealer does not bust against me?

[zengrifter]

Fuqe you! waste my time with a bunch of sh*ty brains!

Now now, Doctor. We did help you work through some "tech issues," please be patient with ours.

[zengrifter]

Probability Theory, Live! (179) indicates the following, "My latest blackjack software (2009) undeniably proves that the percentage of the bust hands is, at least, 41.97%.

I still suspect that DD may be right - that he forgot to subtract the player bust % from the dealer bust percentage, yes/no?

[Katz]

Fuqe you! waste my time with a bunch of sh*ty brains!
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Whoa! Hey Pluck, we can't help it if we don't have your Genius-level Math Intellect. We are trying to unnerstand! For this unnerstand, your Book is not always clear, when it comes to how you actually arrived at 41.97% dealer busts and +300M possible hands in one 52-card deck.

Can you please try to explain again, slowly this time, without jargon, so that us mere mortals can try to grasp the gist of it... ERIC & I want to know...

[Dodo]

This text file shows all blackjack hands as combinations based on Dealer’s rules. Total cards: 13 (only one suit, from 2 to Ace). [BjAllHands1-11Combos.TXT]

This text file shows all blackjack hands based on Dealer’s rules as arrangements. Total cards: 13 (only one suit, from 2 to Ace). [BjAllHands1-11Ord.TXT]

I will focus on BjAllHands1-11Ord.TXT as the usefulness of counting straight arrangements (not combinations) is more clear. The following is the summary statistics located at the end of that file.

Total BJ Actions: 9532
Total Draws (Hits): 1674
Total Non-Bust Hands: 2794
Total Dealer BUSTS: 5064 (53.13%)
Total Complete BJ Hands: 7858
Total BlackJacks (10+A): 8 (5.13%)

Without generating an equivalent file to verify it, BjAllHands1-11Ord.TXT appears to contain all the proper lines. I have verified the summary statistic that there are 7858 lines (complete dealer hands) and that 2794 are non-bust hands with the remainder (5064) being dealer bust hands. I will ignore the fact that the meaning of "Draws (Hits)" eludes me. An "action" apparently can either be a draw, non-bust, or bust. This is where the percentage of dealer busts comes from dealer busts / actions instead of the (possibly) more natural percentage of dealer busts / complete hands.

The first clue (to me) that something is wrong with this method of probability analysis of dealer hands is that the frequency of arrangements containing a certain card in first or second position varies with the value of the card. Since the dealer's hand is dealt from a 1/4 deck containing the cards of one suit only, the first card should be equally likely to be of any value with a 10 value four times as likely. The actual frequencies of first (and second) cards are as follows: (2: 1518; 3: 1396; 4: 1088; 5: 882; 6: 644; 7: 446; 8: 329; 9: 253; 10: 664: 11: 638). This means that each arrangement in BjAllHands1-11Ord.TXT is not equally likely to occur. For example, if the "11" is the relative standard frequency, each sequence beginning with a "2" should be weighted by (about an average of) 40%; "9" by 250%; "10" by 385%; etc.

Another clue--one that may be easier for most persons to understand--that the likelihood of each arrangement in the BjAllHands1-11Ord.TXT file is not equally likely to occur is the relatively low frequency of dealer blackjack sequences in the file. The calculated frequency of blackjacks from a complete 1/4 deck is 5.13% (1*4 / C(13,2)). The BjAllHands1-11Ord.TXT contains 8 blackjack lines of the 7858 possible arrangements or 0.1%.

Conclusion: Parpaluck's analysis of blackjack dealer hand busting frequencies is flawed. Other conclusions based on the same starting assumption--that generated blackjack dealer hand card sequences are all equally likely to occur--are flawed, too.

[DDutton]

Total BJ Actions: 9532
Total Draws (Hits): 1674
Total Non-Bust Hands: 2794
Total Dealer BUSTS: 5064 (53.13%)
Total Complete BJ Hands: 7858
Total BlackJacks (10+A): 8 (5.13%)

Another clue--one that may be easier for most persons to understand--that the likelihood of each arrangement in the BjAllHands1-11Ord.TXT file is not equally likely to occur is the relatively low frequency of dealer blackjack sequences in the file. The calculated frequency of blackjacks from a complete 1/4 deck is 5.13% (1*4 / C(13,2)). The BjAllHands1-11Ord.TXT contains 8 blackjack lines of the 7858 possible arrangements or 0.1%.

Conclusion: Parpaluck's analysis of blackjack dealer hand busting frequencies is flawed. Other conclusions based on the same starting assumption--that generated blackjack dealer hand card sequences are all equally likely to occur--are flawed, too.

One supposes that it's possible that we are reading the file tabulation wrong ...
Or that Doc Pluck may need to check and re-present his numbers, there might be a typo or two?

[Dodo]

One supposes that it's possible that we are reading the file tabulation wrong ... Or that Doc Pluck may need to check and re-present his numbers, there might be a typo or two?

Nope. There can only be eight blackjacks in that file. "10" before "11" four times and "11" before "10" four times since there are only four "10" and one "11" in the 1/4 deck of cards. The only way this would be possible (were each sequence to be equally likely) would be for there to be only 156 arrangements, not 7858.

[DDutton]

A quarter-deck will deliver a BJ about once in 21 hands.
But according to your read of Doc Luc's numbers a BJ only occurs once in 1000 hands?
I guess the trade off is that if you believe in a dealer-break frequency in excess of 40% you only get BJ every 1000 hands.
Marquis Katzwisko, can you accept only one natural per 10 hours of play? Where's the fun?

[Parpaluck]

I will focus on BjAllHands1-11Ord.TXT as the usefulness of counting straight arrangements (not combinations) is more clear. The following is the summary statistics located at the end of that file.

Total BJ Actions: 9532
Total Draws (Hits): 1674
Total Non-Bust Hands: 2794
Total Dealer BUSTS: 5064 (53.13%)
Total Complete BJ Hands: 7858
Total BlackJacks (10+A): 8 (5.13%)

Without generating an equivalent file to verify it, BjAllHands1-11Ord.TXT appears to contain all the proper lines. I have verified the summary statistic that there are 7858 lines (complete dealer hands) and that 2794 are non-bust hands with the remainder (5064) being dealer bust hands. I will ignore the fact that the meaning of "Draws (Hits)" eludes me. An "action" apparently can either be a draw, non-bust, or bust. This is where the percentage of dealer busts comes from dealer busts / actions instead of the (possibly) more natural percentage of dealer busts / complete hands.

The first clue (to me) that something is wrong with this method of probability analysis of dealer hands is that the frequency of arrangements containing a certain card in first or second position varies with the value of the card. Since the dealer's hand is dealt from a 1/4 deck containing the cards of one suit only, the first card should be equally likely to be of any value with a 10 value four times as likely. The actual frequencies of first (and second) cards are as follows: (2: 1518; 3: 1396; 4: 1088; 5: 882; 6: 644; 7: 446; 8: 329; 9: 253; 10: 664: 11: 638). This means that each arrangement in BjAllHands1-11Ord.TXT is not equally likely to occur. For example, if the "11" is the relative standard frequency, each sequence beginning with a "2" should be weighted by (about an average of) 40%; "9" by 250%; "10" by 385%; etc.

Another clue--one that may be easier for most persons to understand--that the likelihood of each arrangement in the BjAllHands1-11Ord.TXT file is not equally likely to occur is the relatively low frequency of dealer blackjack sequences in the file. The calculated frequency of blackjacks from a complete 1/4 deck is 5.13% (1*4 / C(13,2)). The BjAllHands1-11Ord.TXT contains 8 blackjack lines of the 7858 possible arrangements or 0.1%.

Conclusion: Parpaluck's analysis of blackjack dealer hand busting frequencies is flawed. Other conclusions based on the same starting assumption--that generated blackjack dealer hand card sequences are all equally likely to occur--are flawed, too.

Doitser:

There was a real “flaw” here that saddened me. I received an alarming note from Kwitser via my Facebook. I accessed the ZenZone forum this morning (early evening Down Under) and I was met by a scary message: Account Suspended!

Your flaw, Doitser, occurred, however, before that cyber nuke!

“The BjAllHands1-11Ord.TXT contains 8 blackjack lines of the 7858 possible arrangements or 0.1%.”

That’s a really bad flaw, Doitser… on your part!

· The BJ natural is calculated exactly for the first 2 cards.

In the case of arrangements, the first 2-card possibilities in a total of 13 cards amount to: A(13, 2) = 13 * 12 = 156. There are 8 BJ naturals generated by that modified card deck. (Strangely enough, you did figure out correctly the number of naturals to be exactly 8.) Thusly, the (only) correct percentage is: 8 / 156 = 0.051282… approximately 5.13%.

“Conclusion: Parpaluck's analysis of blackjack dealer hand busting frequencies is flawed. Other conclusions based on the same starting assumption--that generated blackjack dealer hand card sequences are all equally likely to occur--are flawed, too.”

Actually, the correct conclusion is: You had your head deeply inserted in that barrel of whiskey! “… sequences are all equally likely to occur--are flawed, too.” Say, what??? Like a God of BJ decides that some sequences are not acceptable, although they are mathematically possible?! Like that heated argument in lotto: “The combination 1 2 3 4 5 6 does not have a probability p!”

… Hopefully my post goes thru… must stop here …

[DDutton]

Doitser:

There was a real “flaw” here that saddened me.

That’s a really bad flaw, Doitser… on your part!

· The BJ natural is calculated exactly for the first 2 cards.

In the case of arrangements, the first 2-card possibilities in a total of 13 cards amount to: A(13, 2) = 13 * 12 = 156. There are 8 BJ naturals generated by that modified card deck. (Strangely enough, you did figure out correctly the number of naturals to be exactly 8.) Thusly, the (only) correct percentage is: 8 / 156 = 0.051282… approximately 5.13%.

Actually, the correct conclusion is:“…sequences are all equally likely to occur--are flawed, too.” Say, what??? Like a God of BJ decides that some sequences are not acceptable, although they are mathematically possible?!

Now fur's gonna fly!

[Dodo]

I have nothing personally invested in this discussion or convincing anyone. I am satisfied with my analysis and conclusion as to how Parpaluck has generated incorrect dealer blackjack bust frequencies. I believe the sequences of numbers in BjAllHands1-11Ord.TXT speak for themselves, but am willing to help make them more intelligible to others who may be less than fully mathematically fluent. Ask a question(s) if you might be confused and have interest in getting more clarity.

[DDutton]

I have nothing personally invested in this discussion or convincing anyone. I am satisfied with my analysis and conclusion as to how Parpaluck has generated incorrect dealer blackjack bust frequencies. I believe the sequences of numbers in BjAllHands1-11Ord.TXT speak for themselves, but am willing to help make them more intelligible to others who may be less than fully mathematically fluent. Ask a question(s) if you might be confused and have interest in getting more clarity.

Ok, above Doc Pluck has stated to the effect that you misunderstodd his numbers and the only correct BJ frequency for the 13 card qtr-deck is 5.13% (which we all know already). But somehow you construed that his BJ frequency was only 0.1%, 1/50th of what we would expect.

Where is the error in your interpretation of Doctor Pluckmeister's data?
Or conversely, how did he fail to respond fully forthrightly above?

[Dodo]

Ok, above Doc Pluck has stated to the effect that you misunderstodd his numbers and the only correct BJ frequency for the 13 card qtr-deck is 5.13% (which we all know already). But somehow you construed that his BJ frequency was only 0.1%, 1/50th of what we would expect. Where is the error in your interpretation of Doctor Pluckmeister's data? Or conversely, how did he fail to respond fully forthrightly above?

That's a well-expressed question! Thank you. My argument generates a contradiction to falsify an assumption that underlies Parpaluck's dealer bust frequency claims. If we assume that every sequence of cards that the dealer receives is equally likely, then the likelihood of a dealer blackjack with an evenly distributed 1/4 deck must be about 0.1%. This is incorrect as Parpaluck emphatically asserts; the correct likelihood for a blackjack is 5.13%, as calculated, in this case. Therefore, the assumption that every possible sequence of dealer hands is equally likely to occur must be false because it generates a false conclusion (the incorrect blackjack likelihood). Consequently, it is invalid to use an unweighted counting argument involving the number of possible sequences of dealer-bust hands to calculate the likelihood of a dealer bust. Does this make sense to you? Please ask another question if necessary.

[zengrifter]

Therefore, the assumption that every possible sequence of dealer hands is equally likely to occur must be false because it generates a false conclusion (the incorrect blackjack likelihood).

Well, there are no two cards alike, no pair splits, why would every dealer hand not be equal?