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Ask The Wizard #151
When discussing your strategy for Blackjack, it's likely that you're referring to the fundamental strategy for the initial cards dealt to you (the first two cards of the player and the dealer’s face-up card). Yet, once you draw additional cards or split your hand, the composition of the deck shifts, which may alter the basic strategy you'd typically follow. It might be beneficial to adopt a comprehensive strategy for the game of blackjack that takes into consideration what happens after you hit or split. Are there circumstances where your initial basic strategy for your hand differs from a strategy for the overall game?
Indeed, my basic strategy charts are crafted to represent the optimal moves based on the initial pair of cards. This is generally how basic strategies are constructed, as it allows for precise calculation of the expected values for each action, facilitating comparison with other analyses. However, you raise a significant concern, which I decided to discuss with Don Schlesinger, the writer of Blackjack Attack , to see if there’s any instance where the optimal play for the starting hand diverges from that which maximizes the expected value across the entirety of a blackjack game. He noted a scenario where holding a soft 18 against a dealer's ace, in a double-deck situation where the dealer stands on a soft 17, serves as such an example. According to my blackjack appendix 9 , the expected value when standing is -0.100502 while hitting is -0.100359, leading to a marginal preference for hitting by 0.000143 based on the first two cards. However, the composition of a soft 18 can vary; this table illustrates all the possible combinations that could lead to a soft 18.
Soft 18 Vs Ace Combinatorial Analysis
| Player cards |
Conditional Probability |
Hit EV |
Stand EV |
Hit Return |
Stand Return |
| A7 | 0.621139169 | -0.100359 | -0.100502 | -0.062336906 | -0.062425729 |
| A6A | 0.036728229 | -0.11202 | -0.116009 | -0.004114296 | -0.004260805 |
| A52 | 0.146912917 | -0.111299 | -0.103382 | -0.016351261 | -0.015188151 |
| A43 | 0.146912917 | -0.114804 | -0.103721 | -0.01686619 | -0.015237955 |
| A5AA | 0.001827682 | -0.111395 | -0.105122 | -0.000203595 | -0.00019213 |
| A42A | 0.016814677 | -0.116975 | -0.108233 | -0.001966897 | -0.001819903 |
| A33A | 0.007356421 | -0.132142 | -0.107256 | -0.000972092 | -0.00078902 |
| A322 | 0.020470041 | -0.134229 | -0.11004 | -0.002747673 | -0.002252523 |
| A4AAA | 0.000073486 | -0.117554 | -0.110984 | -0.000008639 | -0.000008156 |
| A32AA | 0.001028802 | -0.134775 | -0.112433 | -0.000138657 | -0.000115671 |
| A222A | 0.000709873 | -0.136788 | -0.114993 | -0.000097102 | -0.00008163 |
| A3AAAA | 0.000002238 | -0.135313 | -0.114821 | -0.000000303 | -0.000000257 |
| A22AAA | 0.000023502 | -0.137312 | -0.117376 | -0.000003227 | -0.000002759 |
| A2AAAAA | 0.000000046 | -0.137859 | -0.119823 | -0.000000006 | -0.000000006 |
| Total | 1 | -0.105806844 | -0.102374694 |
Explanation of column titles
Player cards: Cards in player’s hand
Conditional probability: Given that a player holds a soft 18 versus a dealer ace, what are the chances of achieving that particular hand composition?
Hit EV: Expected value by hitting
Stand EV: Expected value by standing
Hit Return: Multiply the probability by the expected value of hitting
Stand Return: Multiply the probability by the expected value of standing
The values in the right two cells of the bottom row indicate that, overall, the expected value of hitting stands at -0.105807, while for standing it is -0.102375. This suggests that the statistics lean slightly toward standing, with an advantage of 0.00343.
To validate these findings, I conducted two simulations based on the specified rules: one where I hit and one where I stood. I only considered those instances where a soft 18 against a dealer's ace was in play. Here are the outcomes from my simulations.
Soft 18 Vs Ace Simulation
| Soft 17 | Hands Played |
Total Win |
Expected Value |
| Stand | 3857490 | -396224 | -0.102715 |
| Hit | 3208390 | -337572 | -0.105215 |
Therefore, the simulation results indicate a slight preference for standing, with an advantage of 0.0025 across all possible scenarios for this hand. Consequently, for practical purposes in gameplay, the advisable action is to stand, despite what my basic strategy chart may suggest.
I’m a student from Germany and I've been searching for an article that ranks the world's top 100 casinos (in real life), but I haven’t been able to find one. Could you assist me with my inquiry?
- 50 St. James, London, England
- Atalantis at Paradise Island, Nassau, Bahamas
- Casino Baden-Baden, Germany
- Casino Bellevue Marienbad, Czech Republic
- Casino de Montreal, Montreal Quebec
- Le Casino, Monte Carlo
- St. James Club, Antigua
- Taleon Club, Saint Petersburg, Russia
- Venetian, Las Vegas, Nevada
My partner and I have had an on-and-off relationship for two years. We share a child and have cohabitated for the past five months. It frustrates me greatly that after work, my boyfriend spends about three hours at the gym twice a week. I often comment, expressing that a gym visit shouldn’t take that long. He usually goes with a friend, raising my suspicions that their gym time might involve more than just working out. Tonight he mentioned he would be working late and claimed he told his employer he would only put in three hours of overtime. Am I possibly overreacting, or is there something beyond normal behavior here? What could possibly occupy him for three hours, two times a week? I appreciate your help in advance.
Three hours at the gym does seem questionable, especially paired with overtime that matches the duration. If he is indeed unfaithful, incessantly nagging him with indirect evidence is unlikely to deter him; it may only prompt him to become more secretive. My suggestion is to act as though you trust him, and consider hiring a private investigator to discreetly follow him. This way, he will be less guarded, making it easier to gather information. If you discover infidelity, it's often best to distance yourself from such a partner. Until then, you lack substantial evidence to level accusations.
Hi, I think your site is fantastic! Please keep up the excellent work. I am trying to determine the risk of ruin statistics for various combinations of betting units and number of hands played. Currently, if the specific pair of values doesn't appear in your RoR [Risk of Ruin] table in the Blackjack appendix, I'm left without an accurate percentage for potential ruin. Could you possibly share the formula with us? Thank you!
Thank you! I provide an explanation of how I compute the risk of ruin in video poker in my video poker appendix 1 . However, for games with fluctuating bet amounts, calculations can become quite complex, necessitating the use of computer simulations.
At Bally’s in Atlantic City, there’s a $1 9/6 JoB [Jacks or Better] video poker game featuring a progressive royal flush payout starting at 4k. Given that non-progressive 9/6 JoB games offer a return rate of 99.54% with optimal play, at what point does the progressive payout elevate the total return above 100%?
My Jacks or Better section shows the return for a 940/9/6 game as 0.999030. The contribution from the royal flush is noted at 0.024686. Therefore, the return from other hands must equal 0.999030 - 0.024686 = 0.97434. The depicted probability of hitting a royal flush is stated as 0.000026, but that’s rounded to two significant digits. Let’s determine the probability by utilizing the return divided by the win, or 0.024686/940, to solve for the jackpot amount j using this equation:
1=0.97434 + j*(0.024686/940)
j = (1-0.97434)/(0.024686/940) = 977.33182.
Thus, the breakeven point would be at 977.33 betting units, equating to $4886.66. This calculation assumes an impeccable 940/9/6 strategy; however, few players are aware of this strategy. If adhering to an 800/9/6 strategy, we would refer to the 800/9/6 table:
1 = (0.99543904-0.01980661) + j*(0.01980661/800)
j = (1 - (0.99543904-0.01980661))/(0.01980661/800)
j = 984.2197
So if using 800/9/6 strategy The jackpot would then need to amass to 984.22 betting units or $4921.10.
What steps can I take to prove that an online casino is cheating in blackjack?
As I’ve mentioned previously, it's essential to gather sufficient evidence. If you're uncertain how the cheating is occurring, a simple tally of the total initial bets placed and the corresponding losses will be adequate. It's advisable to flat bet one hand at a time, playing the optimal basic strategy, without including the money bet from doubling or splitting in the total bet count. Should your records show that the likelihood of your losses is less than 1 in 10,000, there may be grounds for suspicion, and I would be interested in reviewing your findings to help confirm them. With a house edge of 0.5% and a standard deviation of 1.15, here’s how much you should be down depending on the number of hands played since you began tracking.
0.01% Losing Percentile in Blackjack
| Hands | Net Loss |
| 100 | 43 |
| 200 | 61 |
| 500 | 98 |
| 1000 | 140 |
| 2000 | 201 |
| 5000 | 327 |
| 10000 | 478 |
What is the reason casinos typically use green felt for their tables? Has research been conducted on this, and if so, where can I locate the results?
I asked Barney Vinson, author of Ask Barney: An Insider’s Guide to Las Vegas this inquiry. He suggested it might stem from the era of illegal gambling, though he wasn't aware why those illicit tables were covered in green felt. This remains a theory, but I believe it is due to the prevalence of green felt in pool tables. The manufacturers of gambling tables likely found green felt readily available due to the high number of pool tables. This however raises another question: why is green felt the standard for pool tables? My research brought me to this explanation:
"Billiards has a long and rich history, played by individuals from all walks of life—kings, commoners, presidents, and others. It evolved from a croquet-like outdoor game around the 15th century in Northern Europe, especially in France. The game transitioned indoors onto wooden tables draped with green fabric to mimic grass, surrounded by a simple border.\" - Dolly’s Pro Shop
Hello, I truly appreciate your help with this. Now, onto my question. I was friends with this girl back in high school. As our friendship was waning, I developed feelings for her but never acted on them, thinking she wouldn’t feel the same. Fast forward three years, she found me on a social network, was excited to reconnect, and even sent me a friend request. We engaged in conversations, and she repeatedly expressed how thrilled she was to have found me again. That’s when she asked if I ever had a crush on her. I suggested she go first, and she admitted that she indeed had a crush on me. I confessed my feelings too, and everything felt like it was moving in a positive direction. However, a few days later, her communication frequency dramatically decreased. She no longer emails me as frequently and doesn’t engage like she used to, making me feel forgotten. I’m puzzled about what’s going on. What’s your take on this? How should I proceed?
Both of you put each other in an awkward position with that question, which tends to backfire often. Perhaps she was merely seeking closure on some curiosity or trying to boost her self-esteem. Once the excitement faded, the intrigue dissipated. I suspect she is pulling back because she sees no further benefit in maintaining the connection. My suggestion would be to move forward and let it go.