Ask The Wizard #43

This is a great website!. FYI - A guy missed the Megabucks jackpot (7.9M) yesterday because he had just two coins in. To the best of your knowledge, when does the RNG stop and determine your outcome? If it stops on the first coin, then he blew it. If it is on the last coin, he could have had an entirely different outcome. My guess that the stop time is set by the individual manufacturer, and there is no regulation telling him when to do so. Just wondering if you knew different.

Andy from Bloomfield, USA

Thanks for the compliment. The outcome of the game is determined when the player initiates the spin. The game is constantly drawing random numbers, even when not played. The random numbers chosen at the moment the button is pressed to spin the reels determine where the reels stop, which determines what the player wins. So, if the player bet three coins he would have pressed the button at a different moment, causing a different outcome.
What are your casino choices in Atlantic City for craps and Spanish 21? When you mention that it is wise to take full odds on a bet while playing craps, do you mean to match your bet with an equal odds bet, or to make the highest allowed odds bet along with your bet (ex: at a table with 10x max odds place a $1 bet with a $1 free odds bet, or a $1 bet with a $10 free odds bet). I'm a little confused on that. I love your site, and honestly see it as "a diamond in the rough" among gambling advice web sites. Personally, I like to know what the mathematical odds are when it comes to wagering my hard earned money! Thanks in advance for answering my questions!

Dave from Roanoke, Virginia

Thanks for the compliment. The Spanish 21 rules are the same across Atlantic City. I only know of two that have the game, the Tropicana and the Claridge, but there could be others by now. If I'm not mistaken, the best craps game is at the Sands, which offers 5X odds. When I say to take the maximum odds I mean bet the maximum allowed on the odds. For example, $50 after a $10 line bet. Keep in mind that you won't win more money by taking the odds, you just get to bet more without losing more in the long run.
Are there any Internet casinos with looses dueces wild and which casino has the best payouts for dueces wild. Thank you.

Mike from Montana

Atlantic Interbet has full pay deuces wild (return of 100.77%). I think their highest coinage is 50 cents in that game.
I know that you have the casino advantage for blackjack listed on your web site in the case that a person plays the basic strategy, but I was wondering what the casino advantage was on average against a typical beginner. Also, can you formulate what the best advantage a casino could have over the worst of players, assuming that they would never hit anything higher than a hard sixteen? Thank You Kindly.

John from Storrs, Connecticut

According to Extra Stuff by Peter Griffin the cost due to player mistakes of the average player is 1.41%. This is above whatever the house edge is assuming proper basic strategy. It also varies by place, Atlantic City players are better than Las Vegas players, for example. Your other question about bad strategies was such a good one I added information to my blackjack section about it. See my remarks on bad strategies.
Have you noticed when you look sideways past the right reel on IGT games there are 4-5 counters inside the machine labeled "coins in, coins out, jackpots" or similar wording? I was just wondering what your experience with the counters was. Is there any way to get helpful information from those? Thanks for your time.

Chris from Madison, USA

No, that information won’t help you at all. Your odds are always the same on every spin, regardless of the counters.
I read on your web site that you recently had a chance to visit Tunica, Mississippi. I play very often at the Grand. I am sure you have heard of the side bet known as Triple 7s. I don't consider myself a good card counter, or even an average one, but say no 7s had been played at all in six hands would the odds not be in my favor to play the side bet?

Austin from Germantown, Tennessee

Yes, I've seen that bet in Tunica. I address it in my blackjack appendix 8. I agree that side bet would seem very countable.
First of all, thanks for your very informative, comprehensive, and overall helpful site. I have a couple of questions for you. I have noticed in your tables of probabilities and expected returns for video poker, that the probabilities (and corresponding number of hands) for each hand vary for the same type (jacks or better, for example) from one pay out chart to another. For example, on the first jacks or better chart, the probability of forming a three-of-a-kind is 0.074344, but on the second that same probability is listed as 0.074449. Why would this discrepancy exist? It seems that the only possibility is that the game is being played with a different strategy. Otherwise, the probability of forming any hand should be the same in that type of game, no matter what the pay outs are. If you have indeed devised a unique playing strategy for each pay out schedule, would you mind sharing that info with us?

Secondly, I am wondering which, if any, online casinos currently advise the player of a shuffle in blackjack (multi-deck, of course). Also, do you know, among the majority who do not, which shuffle after each hand and which just do not advise of a shuffle (although it actually occurs after many hands)? It would be great to have this knowledge. A follow up question would be, if they do indeed shuffle at regular casino intervals, can a player assume that if he enters a private table that he beings with a full shoe? Thanks again for your great web site, and I look forward to your response to my questions.

Tony from Columbus, Ohio

Thanks for the kind words. Yes, the probability of a three of a kind depends on the pay table, which affects player strategy. My video poker program always makes the optimal play for every hand by looping through all the possible cards on the draw. However, creating a strategy in writing is very time consuming.
Top notch site you are running! My question to you is: by how much does the house edge in blackjack increase if the player cannot afford to split or double?

Martin from Odense, Denmark

Thanks for the compliment. That is a good question. Not having enough money to double or split, but otherwise playing correctly, adds 1.9% to whatever the house edge is.
I'd really like to know how to read odds like 12 to 1, or 3 to 2. Which one shows the best chances of winning? 12 to 1 or 3 to 2?

Louis from Montreal, Canada

I don't like using probabilities in that form but they are generally used in this kind of syntax, "The odds against drawing a royal flush are 649,739 to 1." That means there are 649,739 ways you can't draw a royal flush and 1 way you can. In your examples 12 to 1 is a probability of 1/13, or 7.69%, and 3 to 2 is 2/5, or 40.00%, so the 3 to 2 is the better chance of winning.
If multiple choice questions have possible answers of a,b,c,d,and e: what is the probability that among 100 guesses, there will be at least 25 correct responses?

Daniel from Portales, USA

The probability of getting exactly x right in your example is combin(100,x)*(1/5)x*(4/5)(100-x). To get the exact answer you have to calculate this for all values of x from 0 to 24, add them up, and take the difference from 1. The answer is 13.14%.
Are the craps probability numbers with the odds taken 100% reliable. Also is the gaming industry your full time profession, and do you visit Atlantic City often? Also, how do you simulate billions and billions of hands, spins, and rolls. Is it computer generated and if so with which software?

DB from New York, USA

Well, anyone can make a mistake, but craps is an easy game to analyze mathematically so I would be very confident my odds on craps are right. Yes, gambling in one way or another is my full time self-employed profession. I have been to Atlantic City many times in the last few years but two months ago I moved to Las Vegas. So, I'm afraid I wouldn't be gracing Atlantic City with my presence much any longer. I prefer a combinatorial approach as opposed to random simulations whenever I can. Either way, I roll my own software with Visual C++. For random numbers I use a Mersenne Twister.
Could you tell me how the total number of combinations in Caribbean, 19,933,230,517,200 are arrived at? I followed your 5-card poker combinations to get the 2,598,960. From there how do I continue? Thank you in advance.

Claudio from Punta del Este, Uruguay

You correctly calculated the number of player combinations as combin(52,5)=2,598,960. From there, the dealer can have combin(47,5)=1,533,939 possible hands. Then any one of five dealer cards can be face up. So 2,598,960*1,533,959*5=19,933,230,517,200.