Ask The Wizard #79

Can You tell me the expected return in Black Jack if a player wagers all his money in one hand and not having money for split’s or double’s. Thank You.

Ruben from Copenhagen, Denmark

If you can’t double or split that adds 1.9% to whatever the house edge is otherwise. This just goes to show that you should always have double or split money available if you need it.

Dear Sir, We are avid Keno players. It is our intuitive belief that if we play two or more keno machines using the same numbers that our chances for hitting those numbers are significantly increased. Can you enlighten us with some statistics to support our intuition? Thank you.

Gene & Rosie from Bayside, WI

Your overall expected return is the same regardless of how many games you play. Of course it is more likely to hit a number the more machines you play, but if they all miss you lose more money.

I’ve been playing blackjack for quite awhile using basic strategy, mostly betting an even unit each hand. Occasionally I will increase the bet because I "feel" like I am going to win the next one. I would think that just about all recreational players bet on feel once in a while at least. I was reading through some of your past Ask the Wizard columns and saw your calculation of the probability of a string of losses in the August 4, 2002 Column. You know those emotional thoughts that pop in head while gambling (well maybe not your head), "I’m due for a win!"

That column seemed to put the mathematics to that "feeling" a player can get. In that columns’ example of a player losing 8 consecutive hands of blackjack the odds were (.5251^8 or about 1 in 173). My question though is what does that really mean? Is it that when I sit down at the table, 1 out of my next 173 playing sessions I can expect to have an 8 hand losing streak? Or does it mean that on any given loss it is a 1 in 173 chance that it was the first of 8 losses coming my way?

I know, I know, its some sort of divine intervention betting system I am talking about and no betting system affects the house edge. I’m still curious though. Besides every once in awhile throwing down a bigger bet just adds to the excitement and for some reason it seems logical that if you have lost a string of hands you are "due" for a win.

Steve from Phoenix, AZ

I have no problem with increasing your bet when you get a lucky feeling. What is important is that you play your cards right. Unless you are counting cards you have the free will to bet as much as you want. As I always say all betting systems are equally worthless so flying by the seat of your pants is just as good as flat betting over the long term. When I said the probability of losing 8 hands in a row is 1 in 173 I meant that starting with the next hand the probability of losing 8 in a row is 1 in 173. The chances of 8 losses in a row over a session are greater the longer the session. I hope this answers your question.

Is there any ways to cheat the slot machines?

Michael V.

Sure. There are lots of ways. Putting in fake coins just to name a simple one. Be warned that in Nevada cheating in a casino carries the same kind of penalty as bank robbery, or so I hear. Let the record show that I disapprove of all forms of cheating.

Mabuhay!! Great site!!! Ive learned a lot from you! Had I not learned the math behind the casino games, I probably would be a compulsive gambler by now. I used to gamble to win, but after learning that one cannot beat the house, I learned how to play for fun. I’m not sure if you are familiar with Super 6. Its a commissionless baccarat that pays 1:2 on a winning 6. What is the house edge (for banker and player) on this? Also, there’s this side bet which pays 12-1 on a winning 6, would this be a sucker’s bet? Thanks.

Thefamousv from Manila

Thanks for the nice words. I already address commission free baccarat in my baccarat section. Yes, the winning 6 is a sucker bet. The probability of the banker having a winning 6 is 5.39% and the probability of the player having a winning 6 is 6.26%. The house edge on the banker is 30.00% and on the player is 18.68%.

Hello. I’ve been an avid roulette gambler for some years now and for the first time ever I’m thinking of trying out a roulette system...Now I know how you feel about these so called "systems" and the scammers behind them, and belive me, I feel the same way, but I’ve come across two systems which can’t be ignored...

The first one is the 3q/A-strategy found in R.D Ellison’s book "Gamble to win: Roulette", which has a verified win rate of 7.94% (7500 spins). The system was tested and developed in conjunction with" Spin roultte Gold" by Frank Scoblete and "Roulette system tester" by Eric St. Germain.

The second one is Don Young’s roulette system which is verified to beat the Roulette System Tester from Zumma Publishing(15000 spins).

Now, I must say I’m still a bit sceptical about spending money on these systems, but since they've proved themselves over the long haul, I can't really see no reason why I shouldn’t. I mean, beating these testbooks have to mean something...

What’s your opinion on these systems? And do you think I should try them out??

Thanks alot! Have nice day. Best wishes


7500 spins? Is that it? Anyone can show a profit of 7.94% of total money bet over 7500 spins if they bet aggressively. Same is true about 15000 spins. Most systems are designed to have a lot of small wins and small number of large losses. A system requiring a huge bankroll can easily go 15000 spins and show a profit. Eventually the losses will come in and it won't pass the test of time. The big losses might also come at the beginning. The true way to put a system to the test is to play it over billions of trials. My opinion about these systems is the same as all systems, they are worthless. I have no problem with you trying them out but I do have a problem with anyone putting one dime in the pockets of those selling them.

Note: See the follow up to this question in the next column.

Dear sir, I’ve read your FAQs with great interest. I’ve a question of my own. In the game of baccarat how many times on average can you expect a B/P winning streak of nine times in a row. Can you show the mathematics of it. Thank you.


The probability of a single banker win is 0.50682483 and single player win is 0.49317517, ignoring ties. So the probability that the next 8 hands will be banker win, skipping ties, is 0.506824838 = 0.004353746 . The probability of the same thing on the player is 0.493175178 = 0.003499529.

I have something rather interesting to calculate. I was playing Deuces Wild Video Poker when I was dealt "Garbage". When I threw all five cards away, I was given 4 deuces on the draw, 1,000 coins! What is the probability for 4-Deuces to appear on the draw after throwing all 5 cards away on the deal? Thanks for your time and keep up the good work on your website! P.S. On the same machine, I switched to Deuces Wild Bonus Poker and was dealt 3 wilds w/4&5 of diamonds (straight flush), I threw away the 4&5 and hit 4 deuces w/Ace for another 2,000! What a lucky machine! This was at Soboba Casino in Southern California.

Anthony Saucedo

No problem. There are combin(47,5)=1533939 ways to arrange 5 cards out of the 47 left in the deck. 43 of those will result in four deuces (the 5th card has 47-4=43 possibilities). So the probability of getting four deuces on the draw is 43/1533939 = 1/35673 = 0.000028032. The probability of drawing a fourth deuce after keeping 3 is (47-1)/combin(47,2) = 46/1081 = 0.0426. In my video poker appendix 5 you can see how the probability distribution in deuces wild of the number of cards drawn to any given hand. For example 2.62% of all four deuces will be obtained by getting all four on the draw. The probability of this happening on any given hand is 0.000005. For more information on the combin function visit my section on probabilities in poker.