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Ask the Wizard #52

I enjoy both Caribbean Stud and Blackjack. The element of risk for Stud is 2.56% and Blackjack is 0.38% or a ratio of 6.7. Assume I play $15 Blackjack and $5 ante Stud i.e., $15 at risk when I bet. Since the number of hands dealt per hour is many more for Blackjack versus Stud, does that mean that I will lose the same amount of my bankroll if the ratio of hands dealt per hour is 6.7?

John from Monsey, USA

No. If you’re interested in comparing expected loses it would be better to use the house edge. My section on the house edge shows the blackjack house edge to be 0.43% (Atlantic City rules) and that of Caribbean Stud Poker to be 5.22%. The expected loss for 1 hand of Caribbean Stud Poker at a $5 ante is $5 * 5.22% = 26.10 cents. The expected loss for 6.7 hands of blackjack at $15 per initial bet is 6.7 * $15 * 0.43% = 43.22 cents. So given these two options you will lose less in Caribbean Stud Poker. The ratio of the house edge of Caribbean Stud Poker to blackjack is about 12. So the expected loss of a $1 initial Caribbean Stud Poker bet is about the same as a $12 initial blackjack bet.

Mr. Wizard, your site is truly informative. There is a keno game here where we can bet on HEAD, TAIL or EVEN. HEAD meaning 11 numbers or more in the first forty numbers, TAIL meaning 11 numbers or more in the last forty numbers. EVEN meaning 10 numbers each in the first forty and last forty respectively. There are 20 numbers drawn each time. What are the odds of each bet winning? One more thing, since the house is negative according to you (for some online casinos), does that mean that a player can consistently win in the long run in the game of blackjack?

Tony from Malaysia

The probability of n numbers drawn in the first 40, last 40, or any given 40 is combin(40,n)*combin(40,20-n)/combin(80,20). So the probability of exactly 10 in the first 40 (and 10 in the last 40) is combin(40,10)*combin(40,10)/combin(80,20) = 0.203243. The probability of one half having more than the other is 1-.203243= 0.796757. The probability of a specific half having more is half this number, or 0.398378. If this bet paid even money the house edge would be 20.32%. If the even bet paid 3 to 1 then the house edge on that bet would be 18.70%. If it paid 4 to 1 the player would have a 1.62% edge. About positive expectation blackjack online the more the player plays the greater the probability of a net profit. The best game is currently Unified Gaming’s single deck, with a player edge of 0.16%. If the player flat bet one millions hands the probability of being down would still be about 8.6%. At Boss Media’s single player game with a player edge of 0.07% the probability of a loss after a million hands is about 27.5%.

I was just reading Peter Griffin’s Theory of Blackjack and found something in the back of the book that caught my attention. In his analysis of a baccarat count system in order to get true count he divided the running count by the number of cards remaining rather then the number of decks remaining. Is that correct? Thanks for your attention.

Ted from Las Vegas, USA

It is more accurate to divide by the exact number of cards remaining. He was trying to show that for all practical purposes baccarat was not countable, even for a computer perfect counter. So there was no need to devise a more practical count. If baccarat isn’t worth playing for a perfect counter then it certainly isn’t worth playing for a mere mortal.

I notice that all Boss Media multi-player casinos have a trend of dealer showing a face (10) the majority of the times, and other users complain about that as well. I figure that on average the dealer should show a face 4/13 of the times, does that make any sense? This is mostly while playing 1-3 hands vs the Dealer.

Jumbo from Canada

Although I address this kind of question in my FAQ and in past columns I’ll still comment. You need to give me some hard numbers to have this taken this seriously. For example if you played 1000 hands you would expect the dealer to have a 10 or face card up about 308 times. The probability of the actual number being within 50 of 308 is 99.93%. If you were outside of 50 then we could raise our eyebrows and if you were outside even more we could really get serious. However I can’t do much with "the majority." I indicate how to gather data a test for online cheating in my FAQ. Finally, I want to say that I strongly feel that Boss Media is playing a fair game.