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Ask The Wizard #113

If you're considering a seat at the Caribbean poker table, which spot is ideal? Is there a notable impact based on your position? Are there typically six available seats?

anonymous

For optimal strategy, you should position yourself as far left as you can, especially if you intend to place side bets. However, if side bets aren’t part of your game plan, your position won't really affect your odds. This is important because if two other players achieve a straight flush or better, the player sitting furthest to the left stands to gain the full payout since the dealer pays out from right to left. The players following will receive a lesser amount after paying the first player. For instance, in scenarios with two royal flushes, the initial player claims the full payout while the second only receives a reset amount of $10,000. However, achieving such outcomes is highly improbable. Personally, I'd recommend sitting where you feel comfortable and are distanced from any smokers. And indeed, there are usually six seats.

In the Netherlands, there’s a baccarat variant where the banker’s bet pays even money, but a successful bet on 5 pays out at a 1 to 2 ratio. What is the house edge for this specific variation?

anonymous

The house edge for this game stands at 0.93%. You can find further information in my document. baccarat appendix 6 .

I’m preparing to take a professional licensure exam. The regulations specify that:

  1. The exam will cover seven distinct subjects.
  2. Participants will face 60 multiple-choice questions for each subject.
  3. Each multiple-choice question will offer four answer options, but only one will be the correct choice.
  4. To pass, a candidate must achieve a minimum overall average of 75% and cannot score below 65% in any individual subject.

I’m curious, if a test-taker guesses all answers, what are their chances of passing the exam? In other words, what is the probability of succeeding through chance alone?

anonymous

To meet the 75% threshold, a candidate needs at least 315 correct answers out of 420 questions. The expected number of correct answers from random guessing is calculated as 420 multiplied by 0.25, which equals 105. The standard deviation is derived from the formula (420*0.25*0.75)^0.5, yielding approximately 8.87412. Therefore, the candidate would need to exceed expectations by 210 questions, equating to 210 divided by 8.87412, resulting in roughly 23.66432 standard deviations. The chances of achieving this are exceedingly rare. If every single person on the planet took this test and answered randomly, I highly doubt anyone would pass. I won't even begin to address the other criteria.

In your opinion, is online poker inherently fair? Should I trust it or steer clear altogether? It seems nearly impossible to determine whether the casino or fellow players are attempting to cheat.

anonymous

I question whether the casino would resort to cheating—what would be the incentive? The more pressing concern lies with the other players. It’s relatively easy for them to coordinate via phone or instant messaging. Whether such collusion occurs is uncertain. The risk might be more significant at higher-stakes tables.

Quit gambling.

anonymous

But it is so much fun.

I’ve noticed a keno game with various side bets. What do you know about these options?

HEADS - wager that between eleven and twenty numbers will appear from the upper half - pays even money.
TAILS - wager that zero to nine numbers will appear from the upper half - pays even money.
EVENS - wager that exactly ten numbers will appear from the upper half - pays 3 to 1.

anonymous

The likelihood of winning the tie bet can be calculated as combin(40,10) multiplied by combin(40,10) over combin(80,20), which equals approximately 0.203243. Since it pays 3 to 1, the house edge is 18.703%. For heads or tails bets, the winning probability is calculated as (1 - 0.20343) divided by 2, resulting in 0.398378. Since it pays even money, the house edge here is 20.324%.

I’ve got a collection of 100 coins, one of which is double-sided. If I randomly select a coin and observe it flip heads ten times consecutively, what are the odds that the coin I chose is the two-headed one?

anonymous

This is a classic question of Bayesian conditional probability. In essence, the probability of A given B can be calculated by finding the probability of both A and B divided by the probability of B. Here, A stands for flipping 10 heads in a row, while B represents selecting the two-headed coin. The chance of both A and B happening is 1 in 100, reflecting that there’s a 1% possibility of selecting the two-headed coin, which guarantees that if chosen, it will land heads 10 times. The general probability of flipping 10 heads consecutively, given a randomly picked coin, would be (1/100)*1 + (99/100)*(1/2).10This delineation arises because there’s a 1% chance of having chosen the two-headed coin (which will assuredly turn up heads 10 times) and a 99% chance of having selected a fair coin that offers a (1/2) probability of achieving 10 heads in a row. Consequently, the probability that you’ve selected the two-headed coin after flipping heads 10 times is computed as 0.01 divided by (0.01*1 + 0.99*0.000977), yielding approximately 0.911843.10I’ve heard that casinos do not disburse jackpots for progressive machines; instead, these are paid out by the game manufacturers. Is that accurate, and does it also apply to other slot machine jackpots?

That is indeed the case for the exceptionally large jackpots like Megabucks and Wheel of Fortune. When a player wins, a representative from IGT, the manufacturer of the slot, verifies the legitimacy of the win before the payout is made. A portion of each wager contributes to a fund designated for funding the progressive payouts.

anonymous

I encountered a video poker game where all victories are tripled for the next nine hands following any occurrence of three of a kind in threes. The three threes qualify as a full house, however, they don’t meet the criteria for four of a kind. How might I assess the impact of this rule?

The probability of achieving any three of a kind or full house in a '9/6' jacks or better game approximates 0.085961. To simplify, I’ll divide this value by 13 to determine the chance of specifically getting threes as the rank of the three of a kind. This approach likely inflates the probability, given that higher ranks like jacks through aces will typically appear more frequently due to optimal strategy favoring holding those cards. Thus, 0.085961 divided by 13 equates to 0.006612. Tripling the winnings over nine games effectively grants you 18 free games—a boost of 18 multiplied by 0.006612 results in 0.119023. I’d apply a corrective factor to adjust for the reduced occurrence of threes, maybe around 75%, leading to an adjusted return of 0.119023 multiplied by 0.75, which equals 0.089267. Thus, you should multiply your standard return rate by 1.089.

anonymous

Are there any resources that cover the etiquette and subtleties of gambling in Europe, particularly in comparison to typical American casinos? I'm especially interested in German casinos and, specifically, Blackjack and Poker. I’ll have a chance to gamble on an upcoming journey to southern Germany, and I’d like to be prepared for what to expect.

I’ve gambled in Berlin, Hamburg, and Monte Carlo, and generally, the etiquette feels quite similar to what you find in the U.S. The one notable distinction is that I didn’t observe much tipping towards the dealers in these places. Contemplating further, the German players seemed to approach gambling with a serious demeanor, and the casinos—Berlin's particularly—had an unusually subdued atmosphere. In contrast, the renowned Grand Casino in Monte Carlo has a rather formal and rigid ambiance, while the Paris Casino and Sun Casino are more vibrant and lively, akin to American casino experiences. Have a wonderful time!

anonymous

Do you ever conduct tests on slot machines in Ontario, Canada? I’m concerned that since the government has a monopoly over gambling in the region, they might be tightening the machines.

I haven't personally tested machines in Ontario, but I did try one in Montreal. Given that Quebec casinos are also government-operated, similar concerns apply there as well. The 5-cent machine I used (equivalent to about 3 U.S. cents) was set to 89.975%. For such low denominations, this rate isn’t too unfavorable and aligns with machines on the Las Vegas Strip. I’ve also gambled on blackjack at casinos in both Niagara Falls and Montreal, discovering the rules mirror those offered in Atlantic City, resulting in a house edge of 0.41%. This indicates that the government's monopoly isn't unfairly taking advantage of players but is offering reasonable odds. For more insights, check my document.

anonymous

Strategies and information that are mathematically sound for casino games including blackjack, craps, roulette, and numerous others. slot machine appendix 3F for more information.