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Ask The Wizard #87
Dear Mr. Wizard, I'm curious about the impact of minimum payout laws on video poker machines. Is it permissible for a casino to operate a VP machine without knowing the optimal strategy? And if a player makes particularly poor decisions—like discarding a winning pair or even a royal flush—can they take legal action against the casino if their strategy leads to payouts below state-mandated levels? Additionally, purely out of interest, what is the worst possible return a VP machine can yield, especially if one were to discard a royal flush or hold onto all five cards of a worthless hand? I really appreciate your time and insights on this matter.
According to Nevada Gaming Control Board regulation 14.040.1(a), gaming machines are required to have a minimum payout of 75% assuming the player employs the best strategy. In response to your second query, I adjusted my video poker software to simulate the least favorable moves. For instance, retaining all five cards of a non-winning hand and discarding parts of a strong hand. When using 9/6 Jacks or Better rules, this poor strategy yields a return of merely 2.72%, giving the house an overwhelming edge of 97.28%. Below is the complete return chart. A player making such irrational choices could not sue the casino since their poor play was to blame for their losses.
Jacks or Better - The Most Unfortunate Player Scenario
| Hand | Payoff | Number | Probability | Return |
|---|---|---|---|---|
| Royal flush | 800 | 48564 | 0.000000 | 0.000002 |
| Straight flush | 50 | 2058000 | 0.000000 | 0.000005 |
| 4 of a kind | 25 | 38040380 | 0.000002 | 0.000048 |
| Full house | 9 | 292922028 | 0.000015 | 0.000132 |
| Flush | 6 | 336550092 | 0.000017 | 0.000101 |
| Straight | 4 | 6239759724 | 0.000313 | 0.001252 |
| 3 of a kind | 3 | 12510891616 | 0.000628 | 0.001883 |
| Two pair | 2 | 34968642984 | 0.001754 | 0.003509 |
| Jacks or better | 1 | 334574728656 | 0.016785 | 0.016785 |
| Nothing | 0 | 19544266875156 | 0.980487 | 0.000000 |
| Total | 19933230517200 | 1.000000 | 0.023717 |
In the pai gow poker games I participate in, there is a $1 fee on a $25 wager, which translates to a 4% commission. What effect does this have on the house advantage?
With a 4% commission, the house edge is reduced by 0.29%.
I have a quick question that has me a bit puzzled, and I hope you can help! I recently won $12,000 from an online casino. Should I withdraw the entire amount at once or in parts? Also, do I have any tax reporting requirements related to this windfall? If I choose not to report it, could I face any consequences? How would you advise handling this situation? Thank you so much for your assistance!
The choice to cash out your winnings in one go or in installments ultimately lies with you. If you're a U.S. citizen, you must report this income in your upcoming tax return; failure to do so could lead to charges of tax evasion. That being said, it's mostly reliant on the honor system. You are also allowed to claim any gambling losses incurred in the same fiscal year to offset your winnings.
Mr. Wizard, if 50 individuals each flip a coin 8 times, what percentage of these people is expected to achieve 8 heads or 8 tails in a row? Thank you in advance for your clarification.
The chance of any single individual flipping 8 heads or tails consecutively is calculated as follows: 2*(1/2) = 1 in 128. If 50 people are participating, on average, approximately 0.39 of them would end up with all heads or tails. The likelihood that at least one person achieves this outcome is about 32.44%.8I recently visited Las Vegas and experienced a phenomenal hand in blackjack. I started with an ace, then split, received another ace, split again, got a third ace, and split once more, ultimately receiving a fourth ace. Amazingly, all four hands resulted in blackjack! This is no exaggeration; my friends and I were in disbelief, and the Luxor's gaming deities were undoubtedly watching. What are the odds of this occurring? I played with a 6-card deck shoe while sitting in seat number 3 of a four-player game. Let's assume the deck was freshly shuffled.
Not many casinos allow resplitting aces, so you're lucky to have found one that does. Your position at the table doesn't influence the outcome. The probability of this scenario depends on drawing four aces in the first four cards and then receiving four tens afterward. The calculations show that the odds are (combin(24,4)/combin(312,4))*(combin(96,4)/combin(308,4)), leading to a combined probability of 1 in 4,034,213.
If seven players are each dealt seven cards, what is the likelihood that at least one of them will have a 7-card flush?
The chances that a single player achieves a 7-card flush stands at 4*combin(13,7)/combin(52,7), which equates to 1 in 19,491. Meanwhile, the probability that at least one of the seven players secures a 7-card flush is roughly 1 in 2,785.
Can you share the odds for holding 3 cards and drawing 2 more to complete a Royal Flush? My spouse and I often decide to discard a high pair to pursue a royal draw.
The odds stand at 1/combin(47,2), calculated to be approximately 1 in 1,081. In every instance I've analyzed, retaining a high pair offers a superior hand compared to having three cards towards a royal, unless playing the game 'Chase the Royal.'
I frequent a local casino featuring a six-deck game with h17, DAS, and DOA rules. However, they provide a 2-1 payout for suited blackjacks. How significantly does this affect the house edge? What mathematical approach would you use to ascertain this?
The odds of being dealt a suited blackjack in a six-deck game can be calculated using the formula: number of suits multiplied by the number of aces within that suit times the number of tens of the same suit, all divided by the total number of 2-card combinations from 312. This results in a probability of 4*6*24/combin(312,2) = 576/48,516, equaling approximately 1.19%. Assuming a push in cases of a blackjack tie, the probability of a suited blackjack occurring when the dealer does not have a blackjack is calculated to be 1.13%. Receiving an additional half unit 1.13% of the time diminishes the house edge by 0.57%, altering it from 0.62% to just 0.05%!
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