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Ask The Wizard #166
I've recently started playing 3-card guts online, where they do have live game options available for play money. My query is: where can I find a resource that outlines what would be considered a decent starting hand in a game with 10, 9, 8, and fewer players? The rankings of hands are identical to those in three card poker. Although I've accessed the probabilities for three card poker on your website, I'm uncertain how to delve further to identify the average expected hand. Could you assist me with this?
Below is the median strongest hand depending on the player count. While this estimation assumes that hands are independent, which they aren't, it still serves as a reasonable approximation.
Median Hand in Guts
| Players | Median Hand |
| 1 | K,10,2 |
| 2 | A,Q,8 |
| 3 | 5,5,K |
| 4 | 9,9,7 |
| 5 | J,J,Q |
| 6 | K,K,5 |
| 7 | A,A,7 |
| 8 | 8,5,3 flush |
| 9 | 10,8,6 flush |
| 10 | J,10,6 flush |
Today, I experienced significant losses while playing Cryptologic Blackjack. I don’t suspect any rigging, but one aspect of the game appeared to fall way outside normal probability. In just 35 hands, the dealer displayed a six seven times and emerged victorious each time. This has been confirmed through the game's records. Given that a dealer's chance of busting with a six showing is estimated at 56%, my calculations indicate that the odds of this happening consecutively six times are merely 0.23%.
At Cryptologic They operate using eight decks of cards, with the dealer standing on a soft 17. Based on my calculations, blackjack appendix 2 the likelihood of the dealer failing when showing a six is roughly 0.422922. Therefore, the chance of the dealer not busting is 1 - 0.422922 = 0.577078. Consequently, the odds of not busting over seven attempts would be (0.577078)7= 2.13%.
When it comes to counting cards, what position on the table is considered most advantageous?
From a mathematical viewpoint, the third base position is advantageous because you’ve had a chance to see more cards before your turn, granting you a wealth of information. Nevertheless, among the six spots at the table, I personally favor the fourth position since it offers a clearer view of the entire game layout.
In your last column You previously mentioned that 'The probability of there being 5500 coins not including a 55 can be approximated closely as 0.9864012865500, or about 1 in 507 trillion.'
I take it you refer to it as an 'approximation' due to the diminishing effect of removal while going through the 5500 coins. This represents a very minor removal impact! It’s a classic case where the target coins become less likely to be present as non-target coins are eliminated, particularly since the removal effect is minimal compared to the larger probability of game fraud; in other words, if target coins have been withdrawn.
Indeed, I did say 'closely approximated' since the total number of pennies in existence is finite. Removing even a single non-55 penny increases the odds that each remaining penny is a 55. Had I not specified 'closely approximated,' I would have received corrections from at least three individuals. Although the effect is trivial, many of my audience members strive for precision and would be quick to Point out any inaccuracies.
How does this work?
- Grab a calculator; this isn't a mental math problem.
- Input the first three digits of your phone number, excluding your area code.
- Multiply by 80
- Add 1
- Multiply by 250
- Now add the last four digits of your phone number.
- Then, add those last four digits once more.
- Subtract 250
- Divide number by 2
Do you recognize the answer?
Let’s designate the first three digits of your phone number as x and the last four as y. Let’s examine what outcomes we achieve at each stage.
- Ready!
- X
- 80x
- 80x+1
- 250*(80x+1) = 20000x+250
- 20000x+250+y
- 20000x+250+2y
- 20000x+250+2y-250 = 20000x+2y
- (20000x+2y)/2 = 10000x+y
This calculation ultimately results in your complete phone number. We multiply 10000 by x to shift the prefix four digits to the left, and then we add the final four digits.
While I was using a triple-play deuce wild machine, I was pleasantly surprised to receive four deuces. I chose to keep the deuces and discard a queen before hitting the draw button. Naturally, I was compensated accordingly, but the stranger beside me became agitated, insisting that I should have retained the queen instead of drawing a different card. He argued that malfunctions void all payouts. Should I genuinely be concerned about potential malfunctions in such scenarios?
No, malfunctions in video gaming are extremely uncommon. Although they are somewhat more prevalent in slot machines that have physical components, the occurrence is still only about one in a million. In the case of video poker, failures during gameplay are virtually unheard of. Typically, the advice for keeping all five cards when dealt four deuces is predicated on the risk of making mistakes by incorrectly pressing buttons. In my opinion, the chances of such human error are far higher than encountering a malfunction.
I’d like to clarify something regarding a blackjack tournament where only the player with the largest stack at the conclusion receives a payout. Suppose 1000 players each start with $100 in chips and can place bets ranging from $1 to $10 across five hands. If nobody has any awareness of other players' chip stacks, what amount should you be aiming for before feeling content?
You haven't specified how many rounds are involved here. Regardless, my strategy would be to wager $10 on all five hands every round or go bankrupt trying. With a thousand participants and a relatively low maximum bet, you'll require as much variance as possible.
Could you clarify the table limits for roulette and explain the difference between the minimum limits for individual numbers and overall table limits? If you could provide examples, that would be great.
Roulette typically feature two distinct minimum bets: for example, $5 on outside bets and $1 on inside bets. Outside bets consist of all even money bets, column bets, and dozen bets. Inside bets refer to specific numbers, including combinations of 2, 3, 4, 5, and 6. In this scenario, the minimum for outside bets is $5 while for inside bets it is $1. It is important to note, however, that you must wager a minimum of $5 total for the inside bets or opt not to place any at all.
Question: I'm not a lawyer! Yet I have this idea that online gambling might breach certain legal regulations in the United States. If that's the case, aren't individuals essentially admitting to unlawful activity when they communicate in emails, etc., mentioning that they played at online casino X and won/lost Y dollars? Obviously, the legal system is likely preoccupied with more serious crimes, but it seems like if people openly confess in writing to breaking the law, it wouldn't be much work for authorities to pursue such cases in their jurisdictions.
As far as I'm aware, no one has been prosecuted for gambling online. Efforts have mainly focused on restricting the industry at the payment processing level, which has simply relocated those services abroad. Laws affecting players are not enforced. Numerous poker celebrities who have openly gained entry to significant poker tournaments through online play haven't faced prosecution to the best of my knowledge. However, it's worth noting that Washington State has recently classified online poker as a felony, which could be concerning for individuals in that area.
If everyone who engages in gambling ceased as soon as they generated a profit, I suspect there would be a number of casinos facing bankruptcy. Considering that bankrolls can fluctuate significantly, isn’t it likely that most gamblers will find themselves ahead at some point (which would imply the house is at a loss)?
I respectfully disagree, at least for the reason you presented. In your scenario, most players would indeed exit Vegas with winnings. However, there will always be players who lose their initial bet and continue to spiral into deeper losses until they deplete their bankroll entirely. Assuming consistent gameplay and strategy, the house edge remains unchanged, no matter how a player manages their funds. To address your inquiry, if everyone decided to stop playing once they were ahead, it would result in far less gambling activity. Even though the house edge would persist, it would apply to a reduced overall betting total, potentially impacting the casinos’ financial stability.
In one room, there are two tables. On the one table to the right, there are 100 coins, 20 of which have heads showing while the remaining 80 display tails. The other table is empty. The goal is to rearrange the coins to ensure that an equal number on both tables shows heads. You are not allowed to see the coins (it’s a dark room) or touch them to determine their orientation.
For the solution, please visit my other site, mathproblems.info (spoiler alert!).
As slots and video poker continue to grow in popularity along with new table games like 3 card poker, let it ride, and Caribbean stud, have any major casinos stopped providing the traditional table games such as blackjack, roulette, and craps?
Interestingly, the Casino Royale in Las Vegas does not offer any legitimate blackjack games. Instead, they feature four Blackjack Switch tables and one game with a 6 to 5 payout. However, they still offer craps and roulette.