July 9th, 2018 at 1:14:36 PM
permalink

This was a thread yesterday but I cannot find it, so here it is again. There was some progress made on it, but then it "died" I think.

Double deck, dealer hits soft 17.

First hand (solo player) gets two tens and dealer has an ace up. Player stands. Dealer flips over the hole card (cannot be 7-10 of course), draws a third card, draws a fourth card, and draws a fifth card that is exactly 21. You lose! Darn!

I started off with all 10,000 different way for the dealer to expose the hole card and the next three cards (4 cards having one of 10 values is 10^4=10,000).

This part I did on a spreadsheet. I started with AAAAA, then AAAA2, AAAA3, etc., all the way to ATTTT.

Then, starting at the bottom, I deleted all the ones that start with AT since that is dealer blackjack. Then I deleted more, starting from the bottom, as those would be A9xyz (soft 20 with no more cards), same for A8xyz, and A7xyz. Now my last row is A6TTT. That one is three cards ending in hard 17 (the fourth and fifth cards are irrelevant but part of the entire set of A+ 4 cards of any value). Delete A6Txy. Now my last row is A69Tx, which is bust.

At this point I decided to write a VBA (Visual Basic for Access) program to analyze the 590 possibilites. I don't like Excel Visual Basic. Access can handle millions of rows in a table (limit 2GB of data in a table, something that would bog down Excel for an eternity).

Anyway, I wrote the program, acting like the dealer, where I start with A (score of 11), flip over the hole card, add its score (if A, it must be 1 since I already used 11), and so on. If a soft score>21, switch to hard total and subtract 10 (e.g. A3T4x is hard 18, no 5th card needed).

For each row, the program output the result, which is bust, 3 card 21 (e.g. A64), 4 card 21, 3 cards soft 18-20, 3 cards hard 17-20, 4 cards soft 18-20, and 4 cards soft 17-20. What is left is 4 cards that add up to soft 17 or 16 or less. Now I can easily calculate what the 5th card must be (e.g. soft 17 on 4 cards, draw a 4 to get to 21 in 5 cards).

I ended up with 135 possibilities: (sorry for the bad formatting; haven't figured that out yet)

up card hole card third card fourth card 5th card

A A A A 7

A A A 2 6

A A A 3 5

A A A 4 4

A A A 9 9

A A A 10 8

A A 2 A 6

A A 2 2 5

A A 2 3 4

A A 2 8 9

A A 2 9 8

A A 2 10 7

A A 3 A 5

A A 3 2 4

A A 3 7 9

A A 3 8 8

A A 3 9 7

A A 3 10 6

A A 4 A 4

A A 4 6 9

A A 4 7 8

A A 4 8 7

A A 4 9 6

A A 4 10 5

A A 5 5 9

A A 5 6 8

A A 5 7 7

A A 5 8 6

A A 5 9 5

A A 10 A 8

A A 10 2 7

A A 10 3 6

A A 10 4 5

A 2 A A 6

A 2 A 2 5

A 2 A 3 4

A 2 A 8 9

A 2 A 9 8

A 2 A 10 7

A 2 2 A 5

A 2 2 2 4

A 2 2 7 9

A 2 2 8 8

A 2 2 9 7

A 2 2 10 6

A 2 3 A 4

A 2 3 6 9

A 2 3 7 8

A 2 3 8 7

A 2 3 9 6

A 2 3 10 5

A 2 4 5 9

A 2 4 6 8

A 2 4 7 7

A 2 4 8 6

A 2 4 9 5

A 2 9 A 8

A 2 9 2 7

A 2 9 3 6

A 2 9 4 5

A 2 10 A 7

A 2 10 2 6

A 2 10 3 5

A 3 A A 5

A 3 A 2 4

A 3 A 7 9

A 3 A 8 8

A 3 A 9 7

A 3 A 10 6

A 3 2 A 4

A 3 2 6 9

A 3 2 7 8

A 3 2 8 7

A 3 2 9 6

A 3 2 10 5

A 3 3 5 9

A 3 3 6 8

A 3 3 7 7

A 3 3 8 6

A 3 3 9 5

A 3 8 A 8

A 3 8 2 7

A 3 8 3 6

A 3 8 4 5

A 3 9 A 7

A 3 9 2 6

A 3 9 3 5

A 3 10 A 6

A 3 10 2 5

A 4 A A 4

A 4 A 6 9

A 4 A 7 8

A 4 A 8 7

A 4 A 9 6

A 4 A 10 5

A 4 2 5 9

A 4 2 6 8

A 4 2 7 7

A 4 2 8 6

A 4 2 9 5

A 4 7 A 8

A 4 7 2 7

A 4 7 3 6

A 4 7 4 5

A 4 8 A 7

A 4 8 2 6

A 4 8 3 5

A 4 9 A 6

A 4 9 2 5

A 4 10 A 5

A 5 A 5 9

A 5 A 6 8

A 5 A 7 7

A 5 A 8 6

A 5 A 9 5

A 5 6 A 8

A 5 6 2 7

A 5 6 3 6

A 5 6 4 5

A 5 7 A 7

A 5 7 2 6

A 5 7 3 5

A 5 8 A 6

A 5 8 2 5

A 5 9 A 5

A 6 5 A 8

A 6 5 2 7

A 6 5 3 6

A 6 5 4 5

A 6 6 A 7

A 6 6 2 6

A 6 6 3 5

A 6 7 A 6

A 6 7 2 5

A 6 8 A 5

Back to Excel, I calculated the probability of each occurrence. I have 4 tables of deck compositions, starting with the same for everyone, 30 tens, 7 aces, and 8 of everything else. The 2nd table has the deck composition after the hole card, and so on, until the last table with the deck composition after the 4th card has been drawn (to calculate the probability of the 5th needed card being drawn). I calculated the probability of that particular hand happening (e.g. AA23T5 as 1.13851693510761E-06).

Add them all together, and I get 5.00105E-05, or 1 in 19995.78.

Fun! :)

Double deck, dealer hits soft 17.

First hand (solo player) gets two tens and dealer has an ace up. Player stands. Dealer flips over the hole card (cannot be 7-10 of course), draws a third card, draws a fourth card, and draws a fifth card that is exactly 21. You lose! Darn!

I started off with all 10,000 different way for the dealer to expose the hole card and the next three cards (4 cards having one of 10 values is 10^4=10,000).

This part I did on a spreadsheet. I started with AAAAA, then AAAA2, AAAA3, etc., all the way to ATTTT.

Then, starting at the bottom, I deleted all the ones that start with AT since that is dealer blackjack. Then I deleted more, starting from the bottom, as those would be A9xyz (soft 20 with no more cards), same for A8xyz, and A7xyz. Now my last row is A6TTT. That one is three cards ending in hard 17 (the fourth and fifth cards are irrelevant but part of the entire set of A+ 4 cards of any value). Delete A6Txy. Now my last row is A69Tx, which is bust.

At this point I decided to write a VBA (Visual Basic for Access) program to analyze the 590 possibilites. I don't like Excel Visual Basic. Access can handle millions of rows in a table (limit 2GB of data in a table, something that would bog down Excel for an eternity).

Anyway, I wrote the program, acting like the dealer, where I start with A (score of 11), flip over the hole card, add its score (if A, it must be 1 since I already used 11), and so on. If a soft score>21, switch to hard total and subtract 10 (e.g. A3T4x is hard 18, no 5th card needed).

For each row, the program output the result, which is bust, 3 card 21 (e.g. A64), 4 card 21, 3 cards soft 18-20, 3 cards hard 17-20, 4 cards soft 18-20, and 4 cards soft 17-20. What is left is 4 cards that add up to soft 17 or 16 or less. Now I can easily calculate what the 5th card must be (e.g. soft 17 on 4 cards, draw a 4 to get to 21 in 5 cards).

I ended up with 135 possibilities: (sorry for the bad formatting; haven't figured that out yet)

up card hole card third card fourth card 5th card

A A A A 7

A A A 2 6

A A A 3 5

A A A 4 4

A A A 9 9

A A A 10 8

A A 2 A 6

A A 2 2 5

A A 2 3 4

A A 2 8 9

A A 2 9 8

A A 2 10 7

A A 3 A 5

A A 3 2 4

A A 3 7 9

A A 3 8 8

A A 3 9 7

A A 3 10 6

A A 4 A 4

A A 4 6 9

A A 4 7 8

A A 4 8 7

A A 4 9 6

A A 4 10 5

A A 5 5 9

A A 5 6 8

A A 5 7 7

A A 5 8 6

A A 5 9 5

A A 10 A 8

A A 10 2 7

A A 10 3 6

A A 10 4 5

A 2 A A 6

A 2 A 2 5

A 2 A 3 4

A 2 A 8 9

A 2 A 9 8

A 2 A 10 7

A 2 2 A 5

A 2 2 2 4

A 2 2 7 9

A 2 2 8 8

A 2 2 9 7

A 2 2 10 6

A 2 3 A 4

A 2 3 6 9

A 2 3 7 8

A 2 3 8 7

A 2 3 9 6

A 2 3 10 5

A 2 4 5 9

A 2 4 6 8

A 2 4 7 7

A 2 4 8 6

A 2 4 9 5

A 2 9 A 8

A 2 9 2 7

A 2 9 3 6

A 2 9 4 5

A 2 10 A 7

A 2 10 2 6

A 2 10 3 5

A 3 A A 5

A 3 A 2 4

A 3 A 7 9

A 3 A 8 8

A 3 A 9 7

A 3 A 10 6

A 3 2 A 4

A 3 2 6 9

A 3 2 7 8

A 3 2 8 7

A 3 2 9 6

A 3 2 10 5

A 3 3 5 9

A 3 3 6 8

A 3 3 7 7

A 3 3 8 6

A 3 3 9 5

A 3 8 A 8

A 3 8 2 7

A 3 8 3 6

A 3 8 4 5

A 3 9 A 7

A 3 9 2 6

A 3 9 3 5

A 3 10 A 6

A 3 10 2 5

A 4 A A 4

A 4 A 6 9

A 4 A 7 8

A 4 A 8 7

A 4 A 9 6

A 4 A 10 5

A 4 2 5 9

A 4 2 6 8

A 4 2 7 7

A 4 2 8 6

A 4 2 9 5

A 4 7 A 8

A 4 7 2 7

A 4 7 3 6

A 4 7 4 5

A 4 8 A 7

A 4 8 2 6

A 4 8 3 5

A 4 9 A 6

A 4 9 2 5

A 4 10 A 5

A 5 A 5 9

A 5 A 6 8

A 5 A 7 7

A 5 A 8 6

A 5 A 9 5

A 5 6 A 8

A 5 6 2 7

A 5 6 3 6

A 5 6 4 5

A 5 7 A 7

A 5 7 2 6

A 5 7 3 5

A 5 8 A 6

A 5 8 2 5

A 5 9 A 5

A 6 5 A 8

A 6 5 2 7

A 6 5 3 6

A 6 5 4 5

A 6 6 A 7

A 6 6 2 6

A 6 6 3 5

A 6 7 A 6

A 6 7 2 5

A 6 8 A 5

Back to Excel, I calculated the probability of each occurrence. I have 4 tables of deck compositions, starting with the same for everyone, 30 tens, 7 aces, and 8 of everything else. The 2nd table has the deck composition after the hole card, and so on, until the last table with the deck composition after the 4th card has been drawn (to calculate the probability of the 5th needed card being drawn). I calculated the probability of that particular hand happening (e.g. AA23T5 as 1.13851693510761E-06).

Add them all together, and I get 5.00105E-05, or 1 in 19995.78.

Fun! :)

July 9th, 2018 at 2:05:37 PM
permalink

This is the thread you're referring to. Good work on the calculation. I suggest you go there and re-post your work, as I can't combine this thread to that one.

This thread is closed.

See:https://wizardofvegas.com/forum/questions-and-answers/math/31103-blackjack-5-card-charlie-probability-question/2/#post659609

This thread is closed.

See:https://wizardofvegas.com/forum/questions-and-answers/math/31103-blackjack-5-card-charlie-probability-question/2/#post659609

If the House lost every hand, they wouldn't deal the game.

- Jump to:
DEFUNCT CASINOS Bill's Gambling Hall & Saloon MonteLago O'Sheas Sahara Western FORUM INFO Announcements Help Rules GAMBLING Betting Systems Big Wins Blackjack Craps Dice Setting Gambling with an Edge Online Gambling Other Games Poker Slots Sports Betting Table Games Trip Reports Video Poker GAMBLING OUTSIDE VEGAS Asia Atlantic City California Eastern U.S. Europe/Africa Mississippi Nevada (other) Oceania The Americas Western U.S. GAMING BUSINESS Boyd Gaming Caesars Entertainment Game Inventors Corner MGM/Mirage Other Sands Station Casinos Wynn LAS VEGAS ATTRACTIONS Deals Food and Restaurants Night Clubs Other Attractions/Entertainment Relaxation and Rejuvenation Shopping Shows Strip Clubs Thrill Seeking LAS VEGAS CASINOS Aliante Casino Aria Arizona Charlie's Casinos Bally's Barcelona Bellagio Binion's Boyd Gaming Casinos Caesars Palace Cannery Casinos Casino Royale Casuarina Circus Circus Cosmopolitan D Las Vegas El Cortez Ellis Island Excalibur Flamingo Four Queens Golden Gate Golden Nugget Hard Rock Hilton Hooters Jean/Primm Casinos Longhorn Casino Luxor M Mandalay Bay MGM Grand Mirage Monte Carlo New York, New York Palms Paris Planet Hollywood Plaza Poker Palace Quad, The Rampart Rio Riviera Silver Nugget Silver Sevens Silverton Skyline Small Casinos South Point Station Casinos Stratosphere Treasure Island Tropicana Tuscany Vegas Club Venetian and Palazzo Wynn and Encore OFF-TOPIC Adult Discussions Free Speech Zone General Discussion GLBT Corner Gripes Kiosk Off-Topic Other Casinos Religion QUESTIONS AND ANSWERS Advice All Other Casual Corner Gambling Las Vegas (other than gambling) Math