A Puzzle for Blackjack Players
by Arnold Snyder
(Blackjack Forum Vol. III #1, March 1983)
© Blackjack Forum 1983
I’ve got some puzzles here for true blackjack fanatics. If you like working on puzzles, give them a try before looking at the answers. Some of these may take a while to work out, but all of them can be solved with just the data provided. (You don’t have to refer to any other blackjack books.)
If you have an intriguing blackjack puzzle, send it in to Blackjack Forum (along with the solution), and if it’s a good one, I’ll publish it. If enough puzzle-freaks are out there, we may make this a regular feature.
1. You are playing on a team with two other counters. You are sitting in the third base position. Your teammates are occupying two seats to your right at the same table. You are the Big Player, and currently have a table limit $1000 bet on the last spot. Your teammates are covering the other six spots with $10 bets. One of your teammates is keeping the Hi-Lo Count, and passes his running count to you with a secret signal. You generally use this information to size your bets. (The Hi-Lo Count values 2s, 3s, 4s, 5s, and 6s, as +1, and counts 10s and As as -1.) Your other teammate is keeping the Roberts unbalanced ten-count (which counts all non-tens, including aces, as +1, and counts 10s as -2). He also signals his running count to you, which you are generally only using to make perfect insurance decisions. Since he is starting his count at 0, you insure whenever his running count is greater than +4. Your job is to count the exact number of cards played, and to keep a side-count of aces. In this way, you can ace-adjust the Hi-Lo Count for more optimal playing decisions, with an exact true count.
The game you are playing is a single-deck game with Vegas Strip Rules and late surrender. Because your two teammates had split and resplit pairs on three of their second-round hands, by the time the dealer gets to you, there are only 6 cards which have not been played, including the burn card, the bottom card, and the dealer’s hole card. There are no remaining aces. You are holding a pair of 6s vs. a dealer 8. You look to the Hi-Lo counter, and he signals you that his running count is 0. The unbalanced ten-counter signals you that his running count is -2. Should you stand? Hit? Double? Split? or Surrender?
2. After years of studying a Las Vegas dealer, you have finally figured out her tell. (A “tell” is a mannerism which a dealer might unconsciously display after checking her hole card, which would indicate to the aware player whether the dealer was pat or stiff.) To your great joy, the tell is 100% dependable. To your dismay, it requires a new counting system to decode. The dealer wears an uncomfortable pair of contact lenses. Her eyes are often blinking and squinting uncontrollably. What you have discovered is that she will indicate whether she is pat or stiff, after checking her hole card, according to whether her left eye or her right eye is twitch indicating the prediction, however, is the fact thatwith every card she deals, she reverses her “indicator”.hus, if her left eye is indicating pat, and her right eye isindicating stiff, and any odd number of cards are dealt fromthe deck, her left eye would now indicate stiff, and her righteye would indicate pat. If an even number of cards are dealtfrom the deck between n tells”, however, then the left and right indicators remain the same as for the last prediction.You are the only player at the table. You have been dealt a pair of tens vs. her upcard of a ten. You watch for her tell, and soon the twitching in her left eye indicates that she is stiff. You split and resplit your tens, until you have four hands, consisting of 10-5, 10-8, 10-7, and 10-2. She turns up her down-card, a 5, and hits it with a 4, thus beating all four of your hands. Noting that you had $500 bet on every hand, the pit boss romps you to dinner. The dealer gathers the cards and without reshuffling, deals another round. This time, you receive a pair of 7s, vs. her upward of 9. Her right eye is twitching. What is your best play?
3. On page 68 of Lawrence Revere’s Playing Blackjack As A Business, Revere provides a chart of “The Fine Points of Basic Strategy.. Based on Julian Braun’s computer analyses of the optimum basic strategy decisions for single-deck play, Revere advises that although the correct basic strategy is to hit 12 vs. a dealer 3, you would be better off to stand on 12 vs. 3, if two of your cards are: A-3, A-4, A-5, A-6, 2-4, 2-5, 2-6, 3-4, 3-5, 3-6, 4-4, 4-5, 4-8, or 5-7. Instead of memorizing these 14 pairs, what simple rule could be substituted, which, if followed, would enable you to play in 100% agreement with Revere’s advice. Note: there are 58 possible combinations of cards which would make up a hand totaling hard 12. Your simplified rule would advise you to stand with and only with the exact same combinations of cards as if you were following Revere’s rule, and using his 14 pairs to make decisions.
4. A new game has just opened up on the Vegas Strip: Blackjacarat. In this game, all rules are exactly the same as in standard, single-deck, Vegas Strip blackjack, except that you may place your bet on either the player’s or the dealer’s hand. Note: since all other rules are the same, house rules are followed in playing the dealer’s hand, even when your money is bet on the dealer’s hand. Likewise, you make all decisions on the player’s hand, regardless of where your money is bet. You estimate that in the standard Strip game you can get an edge of about 1% over the house from card counting with a 1-to-3 spread. Approximately what kind of an edge could you get in Blackjacarat using the optimum strategy, and the same spread? a) 2% b) 4% c)50% d)100%
5. You discover that a certain dealer, due to his highly mechanized shuffle, always has the cards in a predictable order. If you can determine the pattern of the cards, you will always know the next card to be dealt. What card will be dealt next after this sequence: K, 10, 9, J, Q, J, 8, Q, J, Q, 7, K?
Solutions
1. You know that there are only 6 cards remaining, since you are counting the exact number of cards played. If your teammate who is keeping the unbalanced ten-count is accurate in signaling that his running count is -2, then you know that all remaining cards must be non-tens. (This count system will always end at a running count of +4 if you count down a full deck. Only 6 non-tens, valued at +1 each, could bring about this result.) Since you are keeping a side-count of aces, and you know that all 4 aces have been played, then all remaining cards can only be 2s, 3s, 4s, 5s, 6s, 7s, as, or 9s. Since the Hi-Lo counter has signalled you that his running count is 0, and you know that no tens or aces are remaining, then all remaining cards must be valued at 0 in the Hi-Lo count system. You cannot have any Hi-Lo plus-valued cards remaining, or the Hi-Lo running count would not equal 0. Therefore, you know that all six remaining cards, including the dealer’s hole card, are 7s, 8s or 9s. Since your hand totals hard 12, any hit you take will have to give you a total of 19, 20, or 21. Since the dealer has an 8 up, and either a 7, or 8, or 9 in the hole, he will either have a pat 17 (8-9), or he will be stiff, take a hit, and bust. You cannot lose this hand if you take just one card, so your correct play is to double down.
2. Since the dealer’s up-card is a 9, the dealer will not check her hole card. (Hole cards are checked only when the dealer has a 10 or Ace, remember?) No dealer can give a tell, if she does not know what her hole card is, so your best play is to hit.
3. If you examine all possibilities, the first thing you would discover is that it is virtually impossible to hold any combination of cards totaling hard 12, which contains either a 4 or a 5, without also containing one of Revere’s 14 listed pairs. Since 10 of Revere’s pairs contain a 4 or a 5 (or both), you can eliminate all 10 of these pairs with the simple rule: Stand on 12 vs. 3 if any one of your cards is a 4 or 5. The next thing you would notice is that of the 4 remaining pairs, any combination of cards which would contain any one of these pairs, and equal 12, would contain one of two of the 4 remaining pairs: A-3, or 2-6. Thus, the simplified rule would be: Stand on 12 vs. 3 if two of your cards are A-3 or 2-6, or if one of your cards is a 4 or 5.
4. d) Your optimum strategy in Blackjacarat, as described, would be to place all bets on the dealer’s hand, then continue to hit every player hand, including naturals, until you busted. This would give you an advantage of 100% over the house. Experts may employ a few fine points of basic strategy, such as splitting and resplitting all pairs, then hitting all of these hands until they busted. The one exception would be that you would never split aces, since these hands would draw only one card each, often resulting in a player win. You could increase your 5-per-hour win rate by employing a number of sophisticated double-down strategies. While it would be profitable to double down on hard hands of 12 through 20 vs. any dealer up-card, these plays would lower your win rate to slightly under 100%, since the player would occasionally win. But we’ll get into these fine points of play as soon as Vegas World offers a version of this game.
5. The pattern here becomes obvious if you list the cards in sets of four, then read down the columns. The next card to be dealt is a 10:
K, 10, 9, J,
Q, J, 8, Q,
J, Q, 7, K,
?
Scoring
Give yourself 20% for each correct answer. No partial credit. If you scored:
100%: Perfect! You are indeed a blackjack expert. You’d be a welcome addition to any professional team . . . as long as you didn’t cheat!
80%: You’re far above average in your dedication to, and comprehension of, blackjack in particular and puzzles in general. You’d probably be a millionaire if you weren’t so obsessed with this game. Don’t you have anything better to do with your brilliant mind?
60%: This score may have flunked you in high school, but in this test it’s a good, solid pass. But don’t gloat. You just made it, bub.
40%: Yeah, but can you count cards? I mean, hey, so you didn’t have the time to spend on this silly test. After reading the answers you knew you would have gotten them all correct if you just would have put your mind to it, right? Right?
20%: Your subscription to Blackjack Forum is hereby cancelled. You must donate S100 to the First Church of Blackjack to reinstate your subscription.
0%: I hear they’re hiring pit bosses for the $2 games in Fargo, North Dakota. Send for an application form. You qualify. ♠