Wizard Recommends
100 % up to
2250zł +200 spins- Massive gaming platform
- Crypto-friendly
- Loyalty program
120 % up to
1200zł +50 spins- Welcome bonus package
- Loyalty Program
- Join slot tournaments featuring huge prize pools.
Ask The Wizard #18
What are the chances of obtaining a Royal Flush in video poker if I hold two cards and draw three more for the flush?
The combinations for selecting 3 cards from the remaining 47 in the deck amounts to combin (47,3)=16,215. Out of these, only one combination will yield the three cards needed for the royal flush, making your odds 1 in 16,215.
Can you explain the house edge for put bets when 20 times odds are available? If such odds are allowed, a player could wager $1,000 while having $20,000 on every number. Your insights would be greatly appreciated. Thanks, the site is fantastic.
For those who may not know, a put bet is a wager placed after a point has been established, and the player can choose which point it will be. Even though a player can immediately place an odds bet on top of a put bet, they miss the opportunity to win on the initial roll. This works similarly to a place bet or buying odds, but the house edge differs based on the odds multiples. With 20 times odds, the house edge for put bets on the 4 and 10 is 1.59%, on the 5 and 9 it’s 0.95%, and on the 6 and 8 it’s only 0.43%. These high odds make all put bets preferable to the equivalent place or buy bets. This strategy should never be employed in a casino that allows less than 5 times odds. At exactly 5 times odds, the put bet on the 6 and 8 marginally beats the place bet, while at 10 times odds or higher, all put bets are superior to their place or buy counterparts. I plan to enhance my section on craps to include information about put bets, so thank you for the suggestion.
Regarding the various blackjack strategies featured on your website, does the standard deviation vary significantly among them? I suspect that allowing Double After Split (DAS) increases the variability in results, but to what extent? Is there a recommended book that provides variance statistics for different basic strategies in blackjack?
That’s a valid inquiry. However, I do not possess precise standard deviation statistics tied to specific rule variations. The rules I reference on my site are based on the generally favorable regulations found on the Vegas Strip. I concur that allowing doubles after a split tends to elevate the standard deviation, whereas the surrender option tends to lower it. I apologize for not providing more detailed information. 1.15 figure While I understand the difficulty in giving a precise answer, I’m curious about the average daily player count for Cash Splash and the odds I face. Additionally, do online progressive slots tend to offer better odds of hitting jackpots compared to their land-based counterparts?
You're correct; it's challenging for me to provide those statistics without insights from Microgaming regarding the weighting of their reels. I’ve inquired with several major software companies for this kind of data, but so far, no one has shared any specifics. However, I can share that the average payout for all slot games at the Golden Palace was 95.67% in March 2000. You can find this data at the
website; just click on the Price Waterhouse Coopers monthly payout report. Golden Palace Greetings Mr. Wizard! I've been a regular visitor to your site for about a year now, and I want to take a moment to express my gratitude. Thank you for not only creating such a useful platform but also for consistently updating it with fresh and informative content. I can only guess how much time you dedicate to this endeavor.
I have several questions I’d like to ask. Firstly, regarding the banners, how can we optimize your income through banner clicks? Are you compensated based on the number of hits, unique visitors, a flat fee, or some other method? At the moment, I only click on ads if they’re something novel, but I’d be willing to click on a few each visit if it could help support your revenue.
My subsequent inquiries focus on your ideal strategy for Jacks or Better and the practice Jacks or Better game. I apologize if this seems elementary, but it hasn’t stopped me from asking before. Where on the table do you identify the value of a hand with just one high card (A, K, Q, J) and no penalty cards? My second related question is about the best move according to the practice game, which suggests holding K and Q while discarding A along with the low cards. I initially thought keeping the Ace was the wiser choice. What’s the rationale for letting go of the Ace, and how can I determine the optimal move based solely on the table?
Thanks, Denis, for your encouraging words and for your eagerness to help keep the website financially viable. When you first looked into it, simply clicking on my banners was beneficial. However, as of 2013, what really contributes to my financial well-being is account acquisitions. Clicking a banner without signing up for an account and ideally making a deposit doesn’t help much.
there’s a singular category listed for a 'one high card.' This is due to the fact that any card between Jack and Ace holds a similar value.
You can see from my 9-6 jacks or better strategy As you've observed, the player benefits in single-deck blackjack. Numerous casinos in Las Vegas offer this variant, yet I doubt they’re providing a losing game. Is your information incorrect, or are these casinos counting on players’ lack of familiarity with basic blackjack strategy? My friend and I are debating this matter. Also, is it true that a skilled blackjack player can consistently profit in the long run using even a basic card counting method? I appreciate your assistance.
On your blackjack page, in the House Edge section You raise a valid point. When you originally posed this question, I based my house edge evaluation on a fixed rule set that only varied with the number of decks used. In reality, single-deck games often have stricter rules. I've updated the house edge chart in the blackjack section to include a broader range of rules. Typically, a Las Vegas single-deck game doesn't allow doubling after a split and has the dealer hitting on a soft 17, resulting in a house edge of 0.18%. The outstanding single-deck game can be found at Slots-a-Fun, which stands next to Circus Circus, where the dealer stands on soft 17, giving players a 0.01% edge. Next door, at Westward Ho, doubling after a split is allowed, but the dealer performs a hit on soft 17, creating a 0.04% house edge. Regarding card counting, it is simply not true; even adept card counters face frequent losses. A complete month can end in a deficit. Only over an extended duration does the probability of showing a profit increase.
Note: Since this information was written, the Westward Ho has been dismantled, and Slots-a-Fun now features only slot machines.
Dear Wizard! I'm about to engage in a game of Blackjack on a Finnish site with the following conditions:
Do these rules work to my advantage? What is the corresponding house edge? I appreciate your feedback.
- 4 decks
- 9-11 double
- one split only
- double after split allowed
- one card to split aces
- dealer stands on soft 17
- European card rule= none
- no surrender
What are the chances of being dealt a Royal Flush? And what are the odds of getting a SEQUENTIAL Royal Flush (in either direction)?
The house edge in this game is 0.51%.
The likelihood of being dealt any Royal Flush is calculated by taking the number of possible Royals, which is four (one for each suit), and dividing it by the total combinations of 5 cards from a deck of 52, which is
The probability of receiving a sequential Royal Flush can be expressed as (number of suits) multiplied by (number of directions) divided by (total permutations of 5 cards selected from 52) = 4 * 2 / combin (52,5)=2,598,960. So, the answer is 4/2,598,960 = 0.00000153908, or 1 in 649,740.
the overall count of possible Royals, which is four (each corresponding to one suit), multiplied by the number of potential arrangements divided by the total number of ways to select 5 cards from the 52-card deck, which is permut (52,5) = 8 / 311,875,200 = 8 /
I’ve been pondering how to adjust the dice in a game of craps to ensure a roll of 7 or 11 every time. Can you assist me with this? Thank you. permut (52,5)=311,875,200. So, the answer is 4/311,875,200 = 0.00000002565, or 1 in 38,984,400.
Modify the dice so that one die has six faces all showing six, while the other die shows only ones and fives.
I've left college to pursue a mathematics degree but obtained an MCSE certification and found better financial opportunities. Nevertheless, I have a strong passion for statistics and currently work at a consulting firm within an Indian casino. I had no idea what actuaries were until I found this website. What’s the pathway to becoming an actuary?
To become an actuary, you'll need to pass a series of examinations. The initial set of tests focuses heavily on mathematics, while the subsequent tests delve into investment theory, actuarial science, pensions, and related subjects. However, securing a position in this field is typically challenging without a college degree. Most actuaries hold at least a Master’s degree in mathematics. Although your Microsoft certification may add some value, it won’t sufficiently compensate for the absence of a degree. For more information, check out the
Update: Since this inquiry was made, the Society of Actuaries has changed the examination criteria. There are now fewer exams, but they are more challenging. That’s the extent of my knowledge on this topic. Society of Actuaries web site .
Accurate mathematical strategies and insights for casino games like blackjack, craps, roulette, and a multitude of others that one can participate in.