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Ask The Wizard #254
I've observed that many blackjack enthusiasts often hesitate to split pairs of eights when faced with a dealer showing a 9, 10, or an ace. Would you consider this decision to be among the most commonly misplayed? If you disagree, what do you believe is the most frequent mistake?
In my view, one of the plays most often mismanaged by blackjack players is the act of splitting a pair of fours against a dealer's 5 or 6, particularly when doubling after a split is permitted. The odds of encountering such a situation within a six-deck game is about 1 in 1135. If a player opts to hit instead of splitting, the expected value loss amounts to 2.83% against a 5 and 4.38% against a 6. Consequently, the overall house edge increases by 0.0032% each time this mistake is made. While it’s not a catastrophic blunder due to its low frequency, I’ve yet to witness another player successfully executing a split in this context. When I do, I often see eye-rolls from both the dealers and onlookers. I once overheard a fellow player erroneously advise the dealer, not realizing I could hear, that one should never split any hand starting with an F. blackjack appendix 9 If we were to discuss which mistake carries the most financial weight, taking into account both how often it occurs and its financial repercussions, I can only speculate. My guess would point to the number one blunder being the failure to execute a soft double when one is warranted. I rarely witness casual players doubling down on a soft 17 against a dealer's 6. The following chart illustrates the impact on house edge caused by four frequent errors. This table assumes that the player consistently opts for the second-best choice rather than correcting their play when the situation arises. Notably, I did not factor in a player standing with a pair of 6s against a 2 or 3.
This topic was brought up and debated in the forum of my associated website.
Frequent Blackjack Errors
| Error | Probability | Avg. Cost per Incident | Cost per Hand |
|---|---|---|---|
| Never soft double | 0.016430 | 0.054357 | 0.000893 |
| Stand on 12 against 2 or 3 | 0.000380 | 0.029955 | 0.000380 |
| Stand on soft 18 against 9-A | 0.000205 | 0.041605 | 0.000205 |
| Hit 8,8 against 9-A | 0.000194 | 0.081779 | 0.000194 |
If I were to place a pass or come bet during every roll in craps, how many bets would I have active at any given moment? I'm curious to find out what a reasonable average bet would look like for someone engaging in this style of play. Wizard of Vegas .
Typically, a player adopting this approach would have an average of 3.6 bets on the table whenever a roll occurs. If, for instance, they’re wagering $10 with each bet, the average fair amount wagered would equate to $36.
What are the chances of drawing 3 out of 10 straight flushes while holding three cards to a straight flush with one card being missing?
This situation can be analyzed using a binomial distribution model. The basic formula indicates that if the event's probability is p, and all outcomes are independent, the likelihood of it happening exactly w times in t attempts can be expressed as follows.
In this scenario, there are two ways to form the straight flush: you would need the 8 of diamonds along with either the 6 or the jack of diamonds. The number of combinations to draw 2 cards from the remaining 47 in the deck is combin(47,2)=1,081. Therefore, the chance of achieving a straight flush in a single hand is calculated as 2/1,081 = 0.0018501. To find out the probability of attaining 3 out of 10 attempts, we can use the formula combin(10,3)×0.0018501. combin (t,w)×pw×(1-p)t-w.
At a craps table featuring the Fire Bet, I witnessed a player successfully making every point except for 10, and they were still rolling. Assuming it was a come-out roll, what is the likelihood of securing a point on 10 before the player rolls a seven?3×(1-0.0018501)7= 0.000000750178, or 1 in 1,333,017.
During the come-out roll, there are three potential outcomes to consider at this stage.
Rolling a 10 on the come-out roll, followed by making that point.
- Sevening out.
- Repeating a point already made (4 to 9).
- We must consider the probabilities of the second and third outcomes only. The shooter will eventually establish a point, which they will then need to either make or risk rolling a seven. The odds of setting a point and then successfully hitting it stands at 4 to 9:
The probability of establishing a point of 10 and subsequently making it is derived as (3/24)*(1/3) = 0.041667.
(3/24)×(3/9) + (4/24)×(4/10) + (5/24)×(5/11) + (5/24)×(5/11) + (4/24)×(4/10) = 0.364394.
Let’s denote p as the likelihood of making a point on 10 before rolling a seven. If the shooter accomplishes any other point, they essentially return to their original position.
While I was engaged in video poker in Atlantic City, I could have sworn that occasionally I was dealt the same card I had discarded during the drawing process. If the machine were reinserting the discarded cards back into the deck, how would that influence the odds?
p = 0.364394 × p + 0.041667
p × (1-0.364394) = 0.041667
p = 0.041667/(1-0.364394)
p = 0.065554
If I were to place a pass or come bet during every roll in craps, how many bets would I have active at any given moment? I'm curious to find out what a reasonable average bet would look like for someone engaging in this style of play. Wizard of Vegas .
Certain online casinos, like Cryptologic, offer a game where discards are reintroduced into the deck, referred to as , and in this instance, the 40-20-9-6 Jacks or Better pay table yields a return of 95.2642%, not accounting for the redraw bonus feature, which I won’t delve into here. Comparatively, in standard video poker, that pay table offers a return of 98.2534%. Hence, using the discards in the deck diminishes the player’s potential return by nearly 3%. However, I seriously doubt this scenario was occurring on a machine in Atlantic City.
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If I were to place a pass or come bet during every roll in craps, how many bets would I have active at any given moment? I'm curious to find out what a reasonable average bet would look like for someone engaging in this style of play. Wizard of Vegas .