Targeted poker quiz 31: Odds (advanced)


Note: Not at the old Poker1 site. This 39-part series of quizzes, originally published (2004-2006) in Poker Player, is based on the Mike Caro University of Poker library of research and advice. In each entry, Mike Caro presents 10 questions covering a category of poker, targeted for beginner, intermediate, or advanced players. Answers with explanations appear below each quiz, with the questions repeated for easy reference.


The MCU Targeted Poker Quiz series

(See the index to this series)

Odds (level: advanced)

  1. From the 1930s to the 1980s, draw poker was a common form of legal poker in California. It was played with a 53-card deck, joker added. The joker wasn’t completely wild, though. It served as an ace or could be used to complete a straight or flush (including a straight flush). As such, what are the odds against being dealt five aces before the draw?

    (a) 45,003,721-to-1;

    (b) 2,869,684-to-1;

    (c) 962,403-to-1;

    (D) 14,200-to-1.

  2. Using the same joker-added deck and same rules as in question #1, what are the odds against being dealt a royal flush before the draw?

    (a) 14,801-to-1;

    (b) 50,403-to-1;

    (c)119,569-to-1;

    (d) 903-to-1.

  3. Using the same deck, California (which only permitted forms of draw poker) hosted many legal five-card draw lowball games. The ace was always considered low, and straights and flushes were ignored. As such 5-4-3-2-A of any suits was the best possible hand and 6-4-3-2-A of any suits was the next best. Using the same 53-card deck, in which the joker always fills the lowest, non-paring gap, what are the odds against getting 5-4-3-2-A (known as a “wheel” or a “bicycle”) before the draw?

    (a) 1,245-to-1;

    (b) 79,400-to-1;

    (c) 10,360-to-1;

    (d) 140,442-to-1.

  4. … and, what are the odds against getting 6-4-3-2-A (second-best possible hand) before the draw?

    (a) 658-to-1;

    (b) 19,010-to-1;

    (c) 4,003-to-1;

    (d) 1,243-to-1.

  5. In seven-card stud, what are the odds against starting with any three parts of a straight flush (meaning 3-5-7 of diamonds, 10-J-A of clubs, and 6-7-8 of hearts all equally qualify)…

    (A) 888-to-1;

    (b) 4,779-to-1;

    (c) 278-to-1;

    (d) 85-to-1.

  6. In seven-card stud, if you have one pair after the fifth card, what are the odds against finishing with four-of-a-kind?

    (a) 963,100-to-1;

    (b) 1,080-to-1;

    (c) 47-to-1;

    (d) 8,498-to-1.

  7. The number of possible combinations of two cards can be found by multiplying the total number of available cards times one less that number and then dividing by two?

    (a) true;

    (b) false.

  8. The odds against something happening twice in a row can be found by multiplying one more than the odds-to-one against it happening once times that same number and then subtracting one from the answer

    (a) true;

    (b) false.

  9. In hold ’em, if you have four parts of a flush – A-10-7-2 of clubs — after the flop, what percent of the time will you complete it?

    (a) 93;

    (b) 11;

    (c) 22;

    (d) 35.

  10. In hold ’em, if you have two overcards (unpaired cards ranking higher than anything on the board) after the flop, what are your odds against pairing both on the final two cards (the turn and the river)?

    (a) 119-to-1;

    (b) 118,441-to-1;

    (c) 600-to-1;

    (d) 40-to-1..


Answers and explanations (with questions repeated for convenience)

Odds (level: advanced)

  1. From the 1930s to the 1980s, draw poker was a common form of legal poker in California. It was played with a 53-card deck, joker added. The joker wasn’t completely wild, though. It served as an ace or could be used to complete a straight or flush (including a straight flush). As such, what are the odds against being dealt five aces before the draw?

    (a) 45,003,721-to-1;

    (b) 2,869,684-to-1;

    (c) 962,403-to-1;

    (D) 14,200-to-1.

    Answer: (b) Using the 53-card, joker-added deck that was commonly used is commonly used in California for draw poker games, the odds are 2,869,684-to-1 against being dealt five aces before the draw. The joker is used as the fifth ace.

  2. Using the same joker-added deck and same rules as in question #1, what are the odds against being dealt a royal flush before the draw?

    (a) 14,801-to-1;

    (b) 50,403-to-1;

    (c)119,569-to-1;

    (d) 903-to-1.

    Answer (c) Using the same 53-card deck where the joker can serve as an ace or be used to complete a straight or a flush, it’s 199,569-to-1 against being dealt a royal flush before the draw.

  3. Using the same deck, California (which only permitted forms of draw poker) hosted many legal five-card draw lowball games. The ace was always considered low, and straights and flushes were ignored. As such 5-4-3-2-A of any suits was the best possible hand and 6-4-3-2-A of any suits was the next best. Using the same 53-card deck, in which the joker always fills the lowest, non-paring gap, what are the odds against getting 5-4-3-2-A (known as a “wheel” or a “bicycle”) before the draw?

    (a) 1,245-to-1;

    (b) 79,400-to-1;

    (c) 10,360-to-1;

    (d) 140,442-to-1.

    Answer: (a) Using the same 53-card deck, but playing lowball draw, it’s 1,245-to-1 against being dealt the best-possible hand (5-4-3-2-A) before the draw.

  4. … and, what are the odds against getting 6-4-3-2-A (second-best possible hand) before the draw?

    (a) 658-to-1;

    (b) 19,010-to-1;

    (c) 4,003-to-1;

    (d) 1,243-to-1.

    Answer: (Correct choice, 1,400-to-1, demonstrating the intended point, wasn’t provided! MCU regrets the glitch, and you get credit for all answers. It was meant to be in slot D) … and it’s 1,400-to-1 against being dealt the second-best possible hand (6-4-3-2-A) before the draw. The reason it’s strangely harder to get the second best hand is that when you hold 4-3-2-A, the additional joker always serves as the lowest possible card – a five. You can’t use it as a six to make a 6-4-3-2-A. This means you’ll have more pat wheels than 6-4s.

  5. In seven-card stud, what are the odds against starting with any three parts of a straight flush (meaning 3-5-7 of diamonds, 10-J-A of clubs, and 6-7-8 of hearts all equally qualify)…

    (A) 888-to-1;

    (b) 4,779-to-1;

    (c) 278-to-1;

    (d) 85-to-1.

    Answer: (d) It’s 85-to-1 against starting with three parts of any possible straight flush in seven-card stud.

  6. In seven-card stud, if you have one pair after the fifth card, what are the odds against finishing with four-of-a-kind?

    (a) 963,100-to-1;

    (b) 1,080-to-1;

    (c) 47-to-1;

    (d) 8,498-to-1.

    Answer: (b) If you have one pair with two cards to come, it’s 1,080-to-1 against finishing with four-of-a-kind.

  7. The number of possible combinations of two cards can be found by multiplying the total number of available cards times one less that number and then dividing by two?

    (a) true;

    (b) false.

    Answer: (a – true) The number of possible combinations of two cards is determined mathematically by multiplying the number of cards you can receive times one fewer than that same number and then dividing the answer by two. For instance, to determine the number of possible hold ’em starting hand combinations, we multiply 52 x 51 and then divide the answer by 2, giving us 1,326 combinations.

  8. The odds against something happening twice in a row can be found by multiplying one more than the odds-to-one against it happening once times that same number and then subtracting one from the answer

    (a) true;

    (b) false.

    Answer: (a – true) You can find the odds-to-one against something happening twice in a row by adding one to the odds-to-one against it happening one time, multiplying that number times itself, then subtracting one. For instance, it’s 35-to-1 against rolling 12 on a pair of dice. So, the odds against rolling 12 twice in a row are 36 x 36 = 1,296. Now subtract one, and it’s 1,295-to-1 against.

  9. In hold ’em, if you have four parts of a flush – A-10-7-2 of clubs — after the flop, what percent of the time will you complete it?

    (a) 93;

    (b) 11;

    (c) 22;

    (d) 35.

    Answer: (d) In hold ’em, if you have four parts of a flush after the flop, you’ll complete it 35 percent of the time.

  10. In hold ’em, if you have two overcards (unpaired cards ranking higher than anything on the board) after the flop, what are your odds against pairing both on the final two cards (the turn and the river)?

    (a) 119-to-1;

    (b) 118,441-to-1;

    (c) 600-to-1;

    (d) 40-to-1.

    Answer: (a) In hold ’em, if you have two overcards after the flop, it’s 119-to-1 against you pairing both of them on the turn and the river.


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Known as the “Mad Genius of Poker,” Mike Caro is generally regarded as today's foremost authority on poker strategy, psychology, and statistics. He is the founder of Mike Caro University of Poker, Gaming, and Life Strategy (MCU). See full bio → HERE.

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