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Ask the Wizard #141

Why do people insist on believing in betting systems and beating house odds when they know better? There are plenty of folks who are unaware of either rules or probabilities, but some of us know both well and still insist that through a betting system, timing, or some other fallacious method that the house can be beat. I know that your degree is in math, not psychology, but by your experience you also must have some insight into the gambler’s mind that gives you an idea about what motivates this line of thinking... right?

Brendan from Winston Salem, North Carolina

Good question. I have run across numerous system believers and the one thing they all seem to have is a lot of conceit. Despite the fact that they never seem to have gone much past algebra, if they made it that far, they all think they know better than greatest names in mathematics. This inability to consider contradicting evidence or other points of view is certainly not confined to betting system chasers. The more ridiculous a belief is the more tenaciously it tends to be held, and there is no shortage of ridiculous things for weak-minded people to believe in.

I have been playing online poker for a while and I have noticed that premium hands and especially premium pocket pairs (As,Ks,Qs,Js) come up very often. I am aware that you should be dealt pocket aces on average once every 220 hands, but I think it occurs more often than this. I have friends who have (allegedly) tracked their pocket ace occurrence and have an average somewhere in the neighborhood of once every 125-150 hands, over 10,000 hands. I have a feeling this may below standard deviation and may in fact be very unlikely in an honest game. I was wondering if you have ever conducted any research yourself on this subject? Also what are the odds of having an average of pocket aces every 150 hands over the course of 10,000 hands (67 pocket aces in 10,000 hands)?

Jonah from Davis, California

The probability of pocket aces is combin(4,2)/combin(52,2) = 6/1326 = 1 in 221. Over 10,000 hands you could expect to get pocket aces 10,000/221 = 45.25 times. The standard deviation over 10,000 hands would be (10,000*(1/221)*(1-(1/221)))1/2 = 6.71149. 67 pocket aces would be (67-45.25)/6.71149=3.24 standard deviations above expectations. The probability of results this skewed or more is 0.06%, or 1 in 1673.

Are you a Packers fan at heart? I am. It looks like you are betting with your heart and the packers are killing your great NFL picks. Great percentage even with the packers not coming through for you. Just thought you might like the observation.

Stan from Coconut Creek

The reason has nothing to do with team loyalty. My program rated them the fifth best team at the close of the 2004 season, and that I carry that power rating over into the 2005 season. However maybe it is too slow too react to recent history. Something for me to think about.

Hello oh great and powerful Wizard. Love your site and the great education it has given me. Today I am asking a question regarding the math for determining the odds of certain "groups" of wagers. For instance, the groups of 2 bets wagering on both the 6 and 8 in craps, or the group of 4 bets wagering as an "inside" bet in craps. We know that for the 6 OR the 8, ((5/11)*7 + (6/11)*(-6))/6 = 1.515 %. BUT what if we wager on both the 6 and the 8 at the same time? Using a formula similar to that above: (((10/36)/(10/36+6/36))*7+(((6/36)/(6/36+10/36))*-12))/12 = -1.04167%. - 10 chances to win 7, and 6 chances to lose 12. No? Am I out to lunch?! Thanks for considering this problem.

Andy from Hollywood

I get a lot of questions about combinations of craps bets. Normally I don’t answer them but when you address me as "the great and powerful Wizard" it greatly improves your odds of getting a reply. Your mistake is that both bets are not resolved all of the time. When you win either the 6 or 8 you are taking the other bet down, which brings down the expected loss because you are betting less. So your math is right but you are comparing apples to oranges.

Would you consider doing an analysis on Texas Hold’em Bonus? This game is all over Atlantic City and is also in the Las Vegas Flamingo. Thank you.

Roger from Atlantic City

It just so happens that I have four computers cranking away on that game right now. The number of combinations in that game is so huge the game requires about 56 days of computer time to cycle through them all. I should have the analysis completed about October 20.

What are the chances of a dealer hitting 5 of the same number in 10 spins of the roulette wheel?

Spence from Red Deer, Alberta

The chances of any number occurring exactly 5 times in 10 spins in a double-zero roulette game could be closely approximated by 38*combin(10,5)*(1/38)5*(37/38)5 = 1 in 359275.

A follow-up to the recent question about the person who walked up to the hot craps table and wanted to play. I understand, of course, why the history of the table means nothing. However, why wouldn’t you recommend he place a come bet right away? My understanding is that it would result in the exact same expectation as waiting for a new come-out roll, but the eager better wouldn’t have to wait.

Gary from Milwaukee, Wisconsin

You’re right. A come bet would have been just as good and require no waiting. I should have added that.

Am I pregnant?

Lauren from Fort Worth

I don’t think so. I set the lines at yes +240, no -300.

Very simple question on the online gaming side. Casino states that their RNG gives back for example 96.7. We’re all aware that payment companies charge them as a merchant, let’s say an industry avg. 3.5% transaction fee on the drop (not on the take). So where is the operator making all their money or are the RNG’s all playing with us?

Josh from Stamford

The 96.7% applies to total money bet and transaction fees generally only apply to deposits and/or withdrawals. Players generally circulate through the same money and thus bet much more than they deposit. As I discussed in the September 18, 2005, column a player could bet through about 1.5 million dollars with a $10,000 bankroll and betting $5 at a time in blackjack. In this case the casino would make their profit based on 1.5 million in bets but pay expenses based only on $10,000.