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Ask The Wizard #33

I reviewed the potential payouts across the various deuces wild pay tables, but I couldn't locate the specific table I need. Could you provide me with the expected payout figures for a deuces wild game featuring this schedule:

Royal flush - 840
Four deuces - 200
Wild Royal - 20
Five of a kind - 12
Straight flush - 9
Four of a kind - 5
Full house - 3
Flush - 2
Straight - 2
Three of a kind - 1
I would take care of this on my own, but I'm unable to access the required software since I don't use Windows.

Ben from Henderson, Nevada

The return is 99.0251%.

My understanding of video poker is that it begins with a stack of 10 cards (actually encompassing all 52 cards) dealt from the top of the deck. The first five cards that comprise my initial hand are drawn from this stack, and if I choose to draw two additional cards regardless of their position in my hand, they are substituted with the next two cards from the stack. However, my brother-in-law argues that the five visible cards are dealt alongside the following five cards, which would then replace the discarded cards. This means that the selection of a new card would depend on where the card was discarded from, contributing to a different dynamic. While this concept unsettles me because it seems to disrupt the randomness of the deal, I can't precisely pinpoint why. Is there a negative conditional probability at play here?

George W. Bordner from Clarence, USA

From what I understand, the remaining 47 cards are shuffled constantly until the player decides which cards to draw. Thus, the cards drawn are not predetermined in any way. In mathematical terms, this does not create any significant difference.

Certain online casinos provide multiplayer options for Caribbean stud poker. Do you believe a coordinated group of skilled players with advanced computer technology could gain an advantage? If a team were to fill all five positions at a table, they would essentially have visibility into half the deck. A computer could analyze the visible 26 cards (five from each player plus the dealer's visible card) to determine the best move. I appreciate your gambling insights — I’ve been a keen follower for many years.

Peter from Ottawa, Canada

Someone previously posed this question in an earlier column. The book Finding the Edge features a paper by Peter Griffin and John Gwynn Jr. entitled \"An Analysis of Caribbean Stud Poker.\" They mention that if seven players successfully collaborated, they would enjoy a 2.3% edge over the house. However, they do not specify what the advantage would be in a five-player scenario. I suspect that the odds would revert in favor of the casino.

Could you clarify what the phrase \"Law of mathematical averages\" means? Thank you, and keep up the great work.

Dennis from Canada

I believe what you're referring to is commonly known as the \"Law of Large Numbers.\" This principle suggests that among a randomly selected set of n variables with average value x, the average of those variables, denoted as x', tends to approach x as the sample size increases indefinitely. We can think of each bet as a random variable. According to this law, as the total number of bets grows very large, the average outcome will start to align closely with the house's edge.nI continue to enjoy your website! I often turn to your content when I have questions, and I usually find the answers, though not always. While playing basic strategy blackjack, I recognize that I will experience fluctuations, and in the long term, I will likely break even. My question is, what exactly constitutes \"the long run\"? Is it a month, a year, or perhaps five years? Any insight would be appreciated.

Thank you for your positive feedback! You’ve brought up a great question, but there's no definitive answer. It varies in degree; the more you play, the closer your results will approximate the house edge. I recently updated my

Kim from Helsinki, Finland

to include information on standard deviation, which might help clarify your question. For instance, one table indicates that if you play 10,000 rounds of blackjack, there's a 90% probability that your results will be within 192 units of your starting bankroll after accounting for the expected loss due to the house edge. This means that over 10,000 hands, you are likely to end up winning or losing less than 2% of your total wagered money, due to random chance. However, if you increase that to one million hands, the probability of only a 0.2% variation due to luck is much higher. Generally, the variation in mean outcomes is inversely related to the square root of the number of hands played, assuming a flat betting strategy; otherwise, the calculations become considerably more complex. blackjack appendix 4 I've gone through all your insights regarding the Fortune side bet, but I'm still torn on whether engaging in it is a foolish decision. While I understand that the odds are not in my favor, it does present a fun opportunity to speculate. If you have any thoughts on this topic, I would greatly appreciate your input.

The essence of gambling should be enjoyment, so if you feel you derive 39.5 cents' worth of enjoyment from every $5 wagered, then it makes sense for you to place that bet. That's the amount you'd effectively be risking due to the house edge, assuming there are no competing players involved.

Richard

The InterCasino Double Bonus offers the following payout structure for a bet of 5 coins. What can be concluded about the return for this game? Royal-4200.

Do video poker systems, whether jacks or better or any wild variant, function like a regular deck of cards? Specifically, does the payout structure presented on the machine dictate its actual payback rate, or can internal computer chips alter the payout scheme, making it less reliable? Initially, I regarded this as deceptive until I read an article in Strictly Slots magazine acknowledging that this practice exists. If this is indeed the case, two identical video poker machines positioned side by side could be rigged to have different house advantages. I understand this is feasible in standard slot machines. If it is true, that would render all the payout percentages I've come across in magazines, software, and books ineffective.
St Flush-250
4 Aces-750
4/2,3,4-450
FourKind-250
Fullhouse-40
Flush-25
Straight-20
3Kind-10
2Pair-10
JacksBetter-5

anonymous

The return is 99.9367%.

I am quite confident that reputable video poker machine manufacturers ensure fairness and accuracy in their games. Is it entirely impossible for some dishonest machines or manipulative chips to exist? Certainly, that’s a possibility. I would be interested to see the article you mentioned.

Ray

What are the chances of a single player being dealt two four-of-a-kinds and a straight flush in a Texas Hold'em game involving ten players across 50 hands?

The likelihood of drawing four of a kind in seven cards stands at 0.00168067, while that of hitting a straight flush is 0.00027851. If we denote x as the probability of obtaining four of a kind and y as that for a straight flush, the overall probability you're interested in can be calculated as combin(50,2)*48*x.

Paul from Toronto, Canada

Mathematically accurate strategies and insights for casino games like blackjack, craps, roulette, and many others that can be enjoyed.2*y*(1-x-y)47. The answer comes out to .0000421845, or 1 in 23,705.