## Wizard Recommends

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How is the house advantage affected by "free Ace" coupons (promotional tools) used with a continuous shuffler?

"Anonymous" .

I have been asked this enough time to add a section about it. The short answer is that the coupon is worth just over half of its face value. Visit my blackjack appendix 14 for all the details.

I’d like your opinion on an NFL pool. Tickets cost \$25 each and consist of three random teams, in a given order. Each week the ticket holder with the highest three scoring teams, in the correct order, wins \$1000. What is the actual value of each ticket?

"Anonymous" .

There are 17 regular weeks in the NFL season and 32 teams. The probability of winning any given week is 1 in 32*31*30 = 29760. The expected value of each ticket is \$1000*17/29760 = 57.12 cents. So the expected return is 2.28%, or a house edge of 97.72%!

Michael, a person asked you if they are not counting cards in blackjack, what difference does it make how many decks are being used. You stated the difference had mostly to do with the number of stiff hands possible, due to the fact that if a small card came out it was more likely a large card would follow and vice-a-versa. How could that be? Would it still not be a random event with the possibility of a small or large card coming out being equal, if you are not counting?

"Anonymous" .

Every legitimate blackjack expert agrees the house edge decreases as the number of decks goes down, all other rules being equal. However it is hard to explain why. First, it is true that you are more likely to get one small card and one big card in single-deck than multiple-deck. For example if we define a small card as 2 through 6, and a large card as any 10-point card or ace then the probability of getting one of each in single deck is 2*(20/52)*(20/51) = 30.17%. The probability in 8-decks is 2*(160/416)*(160/415) = 29.66%. Although stiffs can cut both ways the player has the free will to stand, the dealer must always hit them.

Is there software that will count cards as you input them? Can this be used to play online blackjack? Or does online blackjack shuffle after each hand?

"Anonymous" .

Yes. Have a look at Beejack. Most, but not all, casinos shuffle after every hand. I don't know if it practical to actually use this product. If you try it please let me know how you do, I might like to try it myself.

Note: The link to Beejack was removed in 2014, due to a potential virus with that site. Proceed there with caution.

You’ve already shown me how to be profitable playing Craps. Thanks! Now your site is teaching me Blackjack. One question: When you’ve got, say, two 5’s and you want to Double Down, you say to put an additional wager next to your original bet. How does the dealer know you don’t mean to split? Thanks! Your site rocks!

"Anonymous" .

Thank you for the compliment. To answer your question the dealer will just ask you what you want to do. Normally all decisions in blackjack must be visible, however this is the only exception I can think of. However if you want to avoid being asked when it is your turn simply hold up you index finger to denote that you want one card. Most dealers know what this means. Coincidentally I just learned yesterday that in Bulgaria if you wish to double you put your extra bet behind the original bet, and if you want to split you put it next to the original bet.

Another reader wrote in to state that in North Dakota it is the state law to follow the Bulgarian rule for doubling and splitting.

Here in Ontario, people have the opportunity to "piggyback" a blackjack player instead of waiting for a spot at a full table. When the primary player doubles or splits, the piggybacker has the option but not the obligation to do so. If the primary player splits and the piggybacker doesn’t, the piggybacker’s original bet moves to the primary player’s first new (post-split) hand. This seems like it would be beneficial in some cases, for example 8,8 vs 10. In this case, E(16 vs 10) < E(8 vs 10) < 0, so the primary player should split but the piggybacker shouldn’t. In this case, the piggybacker has turned his 16 into an 8 for free. Assuming the primary player plays perfect basic strategy, what is the house edge for the piggybacker? If the primary player colludes with the piggybacker to maximize total winnings, and primary bets \$5 while piggybacker bets \$100, is it possible to overcome the house edge?

"Anonymous" .

I have seen this rule at the casino in Montreal as well. Yes, this is a good opportunity for player collusion, where the seated player bets small and makes sacrificial plays for the big bettor in back. Basic Blackjack by Stanford Wong goes into great depth on this topic. There are lots of changes to the splitting strategy, for example the seated player should always split twos and then the back bettor should play both hands against a 4 to 6, otherwise play only one. Using Wong’s full strategy reduces the house edge by 0.2%.

Does losing a hand at blackjack increase the probability that the composition of the deck is in your favor? More specifically, is your expected return on one hand ever positive after a given net loss since the last shuffle?

"Anonymous" .

Without knowing anything else, if you lost the last hand in blackjack then it is slightly more likely that more small cards than large just left the deck. This would make the remaining deck more large card rich and thus lower the house edge. However I speculate this is an extremely small effect. Yet it does go to show that if you must use a betting system one that increases the bet after a loss is better than one that increases after a win. I hesitate to put this in writing at all because again the effect is probably very small and I fear system sellers will misquote me and imply I endorse any system, which I DO NOT.

I read your review of casinos and want to try Club Dice. Regarding the terms on their website, they mention bonus will be deduct from the account once you make the cash-in even you fulfill the wager requirement. I wonder then what is the meaning of this bonus?

"Anonymous" .

This is what is called a "sticky bonus" and is not confined to Internet casinos. When I went to Germany I had to pay 20 Duetchmarks to get in. However if purchased 100 Duetchmarks in chips they gave me a free 20 in sticky chips. A sticky bonus or sticky chip is one that can never be cashed out. However if you bet it and win the winnings are real money. They way to get rid of sticky chips is to keep betting them until you lose them. In the case of Internet casinos you will need to keep cashing out winnings and always leave the sticky bonus in your account, then go back and play again.

Recently at the Miami Beach casino I did a 100% promotion for a \$1000 deposit. Eventually I lost \$1650 and tried to cash out my last \$350. They declined it, stating in effect that the \$1000 bonus was sticky. So I played more and kept cashing out when my balance was significantly above \$1000. In the end I cashed out 7 or 8 times for a total of \$4700.

"Anonymous" .

In the long run sticky bonuses just force the player to bet more. The expected value of a sticky bonus is close to 100% less 2 times the house edge in even money based games.