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Microgaming has a new blackjack game called "Lucky Sevens" where you get bonuses for having your first card a 7, first two cards 7’s, and first 3 cards 7’s. It also has a progressive pot which you win if you get all 3 7 of diamonds. The bad part is that you have to ante \$1 for each hand. You have no choice on this if you play the game. My question is: at what size progressive jackpot does this become a positive expectation game. Thanks!

Bryan from Austin, Texas

Good question. "Triple Sevens Blackjack" is played with five decks with a \$1 mandatory side bet. Following is the side bet return table, based on a meter of \$41,227 (the amount on August 31, 2002).

### Microgaming Triple Sevens Side Bet

 Hand Permutations Probability Pays Return 1 seven 1238400 0.07128 5 for 1 0.3564 2 unsuited 7’s 72000 0.004144 25 for 1 0.103605 2 suited 7’s 19200 0.001105 50 for 1 0.055256 3 unsuited 7’s 6600 0.00038 250 for 1 0.094971 3 suited 7’s 180 0.00001 1000 for 1 0.01036 3 diamond 7’s 60 0.000003 41227 for 1 0.142377 Non-paying hand 16037280 0.923077 0 0 Total 17373720 1 0.76297

If the player splits two sevens the connectivity is lost and the player begins each hand with one seven for purposes of the side bet. The player should never split sevens in this game at low bet levels (\$40 or less). The house edge on the side bet is 37.94%, less 3.45% for every \$10,000 in the meter. When I checked at the Golden Tiger casino on August 31, 2002, the meter was at \$41,227, for a return of 76.30%, or a house edge of 23.70%. For the side bet to have no house edge the meter would need to reach \$109,862. This does not consider the 0.0057% cost of deviating from basic strategy by not splitting two sevens. Assuming the player is betting \$2 on the blackjack hand (the minimum) the meter would need to reach \$113,196 for the combined game to have no house edge.

I recently rolled, during a game of backgammon, double sixes four consecutive times. What are the odds of this happening again?

David from Sunland, USA

With every new roll the probability the next four rolls will be all double sixes is (1/36)4 = 1 in 1679616.

Where can I buy nicely printed and lamenated credit card sized versions of your basic strategy tables for 21? If you don’t offer them--please do!

Steve from Tuscon, U.S.A.

I’m glad you asked. You can get them through Custom Strategy Cards. These are my own blackjack and video poker strategies on nice wallet sized laminated cards.

Nov. 13, 2007 update: The Custom Strategy Cards site is now defunct.

In Blackjack, what is the difference between early surrender and late surrender?

Dan from Brooklyn, USA

In early surrender you can surrender before the dealer checks for blackjack. With late surrender you only have the option after the dealer checks for blackjack. Early surrender is much better because you can still save half your bet when the dealer does have blackjack. As far as I know no casino on the land or Internet currently offers early surrender.

Hi Wizard. In your opinion, which sites offer the best payouts regarding video poker? Also, which software do you prefer for video poker? Thank you kindly for always being there with your indispensable wealth of knowledge.

Barry from Brooklyn, New York

Two questions from Brooklyn in a row, what are the odds of that? The best video poker odds are with Microgaming and Real Time Gaming. It depends on your specific game of choice. Of these two I prefer the Real Time Gaming interface better.

What is the probability of getting a straight by a single throw of 5 dice?

Teodoro C. Deocares from Dagupan, Philippines

There are two possible spans: 1 to 5 and 2 to 6. Each of these spans can be ordered in 5!=120 ways. There are 65 = 7776 ways to roll five dice. So the probability is 2*120/7776 = 3.09%. The probability of this seems to be much higher right after I put mark 0 for large straight during a game of Yahtzee.

What do you think about the strategy of add 50% after second winnings in blackjack, ex, 2-2-5-7-11-15-22-33....

KYK from Hong Kong

As I have said many times, in the long run all betting systems are equally worthless.

You have a great site. Thank you for spending so much of your time helping people to learn the math behind the games. I think I am missing something on your ’Buy’ bets payouts, however. For example, the ’Buy 4’, which you have listed as 39:21. This implies that a winning player would have 21+39, or 60, if they win. But a winning player only has 59 (because they pay the \$1 fee). Should this not be 38:21? Then you lose 21 or have 59. I can’t wait to find out exactly how much of a doofus I am.

Dave from Northfield, Minneapolis

Don’t be so hard on yourself. Very few Internet casinos implement the buy bet odds correctly. When I say the odds are 39-21 I mean that if you bet \$21 (including the commission) you will get back \$39 plus the original \$21 if you win. So if you win you get back \$60. Consider making a \$20 buy bet, plus the \$1 commission. The \$1 is gone forever, but if you win you get back \$40 in winnings plus the original \$20, for a total of \$60. Either way you risk \$21 and get back \$60 if you win.