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Ask The Wizard #94
Is it wise to consider a 'double-up' option in video poker games?
Absolutely! The double-up feature is among the rare bets that don't favor the house. Just like I support certain bets in craps, I also endorse the double-up in video poker. However, if you're engaging in a game that offers returns exceeding 100%, I would advise against it. Additionally, if you can't handle the heightened risk associated with using the double-up function, it's best to forgo it. Furthermore, it's worth noting that while traditional casinos don't offer cash back on double-up bets, Playtech online casinos give you a 0.1% cashback on all wagers, including double-ups.
I'm not planning to, but if I were to attempt card counting, wouldn't it be simpler and equally effective to focus solely on the high cards instead of tracking high versus low cards? Assuming, of course, that I can accurately estimate how many cards remain in the shoe.
No, it would actually be more challenging and less effective to only monitor the high cards. You might be misunderstanding how the plus/minus counting system operates. High cards are counted as -1, while low cards count as +1, with you keeping a cumulative total throughout your play. This means that most cards balance each other out, resulting in the running count remaining close to zero, simplifying your calculations to just one number. If you were to concentrate solely on the high cards, your total would skew high, and you would then need to carefully divide it by the remaining number of cards, which could be quite difficult, even if you're good at estimating.
If I roll a certain number of dice, what are the chances that at least one will show a one?
The probability of none of the dice landing on a one is (5/6). Therefore, the chance of getting at least one die showing a one is calculated as 1 - (5/6).nFor instance, if you roll five dice, the calculation for this would be 1 - (5/6).nHi there, I appreciate the incredible site you’ve created! Thank you for providing such valuable insights that help all of us avoid unnecessary losses on poor bets. We definitely need more individuals like you who can enlighten the general public. I hail from Southern California, and rather than taking a 5% cut on winnings, the local casinos here charge a commission based on each hand played ($1 for every $100 wagered). I’m curious, what is the house edge for both the banker and player bets in this scenario?5= 59.81%.
I appreciate your kind words! As I mention in my section about pai gow poker, the odds for a banker win stand at 29.98%, while the player win sits at 28.55%, and ties account for 41.47%. Therefore, if you're charged a 1% fee, the expected return for the banker in a direct matchup would be .2998 - .2885 - 0.01 = 0.0043, translating to a player advantage of 0.43%. Conversely, if you're the player, your expected return would be .2855 - .2998 - 0.01 = -0.0243, indicating a house edge of 2.43%.
You highlighted the remarkably low house edge in Spanish 21, but I find it quite difficult to engage with the game due to the verbal assaults I endure when trying to apply your strategy. Not that I doubt your gambling advice, but you were completely right about the risk involved in hitting on a 17 against an Ace. I once faced immense backlash from a player wagering $400 on split 8s against a 3; they ended up with two 11s, doubled down, and drew 19 on both. Meanwhile, I attempted to hit my 14 versus a 3, busted with a ten, while the dealer had 13 and pulled an 8. It was truly tense—security had to be almost called due to the situation.
I also often face verbal hostility when I play Spanish 21. During my time in Baltimore, I frequently played it in Atlantic City because it has a lower house edge than blackjack there. Sadly, the individuals who hurl insults at me lack an understanding that subtracting tens from the decks actually lessens the chance of busting when hitting. Attempting to explain this logic is pointless as it won't penetrate their stubborn minds. I used to keep quiet in these confrontations, but next time I might not be so accommodating.
Not long ago, I visited a Microgaming casino (Viper version) for high-stakes baccarat, and focusing solely on banker bets yielded some unfortunate results:
What is the likelihood of such an outcome occurring? I would appreciate your insights, and if possible, could you provide the formula so I can calculate these odds myself in future instances?
Player 44 (64.7%)
banker 19 (27.9%)
Tie 5 (7.4%)
Total 68
It's generally poor practice to analyze previous gameplay and question the odds. Instead, I prefer establishing a premise and then collecting data to validate or invalidate it. However, should we need to consider your case, I would phrase your inquiry as: 'I placed banker bets 68 times and incurred a loss of 25.95 units (44 - 0.95 * 19). What is the likelihood of losing this amount or more?'
To respond to your query, we first need to ascertain the variance associated with a single banker bet. The probable outcomes and their corresponding probabilities can be found in my baccarat section, according to the Microgaming single-deck rules.
The variance for 68 of these bets is simply 68 multiplied by the variance for a single bet, which results in 68 * 0.861468877 = 58.57988361. The standard deviation over these 68 bets can be calculated as the square root of the variance, yielding a result of 58.57988361.
Win: 45.96%
Loss: 44.68%
Push: 9.36%
So the variance on a single wager is .4596*(.95)2+ .4468*(-1)2 +.0936*02- (-0.010117)2= 0.861468877.
In a single deck game, the house edge for the banker bet is calculated at 1.01%. Therefore, over the course of 68 bets, one might expect to lose around .67 units. You, however, lost 25.95 units—25.28 units more than anticipated. This deviation puts your results at 25.28 / 7.653749644 = 3.30 standard deviations below the expected outcome. To determine the probability of this occurrence, you would consult a normal distribution table. In Excel, you can easily perform this calculation by entering: =normsdist(-3.30) in any cell, which would yield a result of 0.000483424, or 1 in 2069. This figure represents the probability of losing as much, or more, than you did. I appreciate that you didn't accuse anyone of cheating, but had you done so, the evidence may not have supported such claims—it could simply be chalked up to unfortunate luck.1/2= 7.653749644.
Here are mathematically validated strategies and insights for various casino games like blackjack, craps, roulette, and many others.