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Poker1 library
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: beginner)
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What are the odds against beginning with three of a kind in seven-card stud
(a) 424-to-1;
(b) 1400-to-1;
(c) 220-to-1;
(d) exactly 190.7-to-1.
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What are the odds against beginning with suited cards in hold ’em?
(a) 3.25-to-1;
(b) 3-to-1
(c) 4-to-1;
(d) 12-to-1.
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What are the odds against beginning with a pair in hold ’em?
(a) 16-to-1;
(b) 25-to-1;
(c) 47-to-1;
(d) 3-to-1.
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What are the odds against beginning with three suited cards in seven-card stud?
(a) 90-to-1;
(b) 42-to-1;
(c) 18.3-to-1;
(d) 5.7-to-1.
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Your odds against starting with a pair in any poker game depend on the number of players who are dealt in:
(a) true;
(b) false.
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What are the odds against starting with a pair of aces in hold ’em?
(a) 19.8-to-1;
(b) 220-to-1;
(c) 403-to-1;
(d) 1,279-to-1.
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What are the odds against starting with a pair of deuces in hold ’em?
(a) 19.8-to-1;
(b) 220-to-1;
(c) 403-to-1;
(d) 1,279-to-1.
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If the board is 8-7-2-A in hold ’em and you hold 10-9, what are the odds against you making a straight on the last card (assuming you know nothing about the cards opponents may be holding)?
(a) 5.75-to-1;
(b) 11.25-to-1;
(c) 3.5-to-1;
(d) 4.75-to-1.
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If you hold a pair to start with in hold ’em, what are the odds against flopping four of a kind?
(a) 1,003-to-1;
(b) 407-to-1;
(c) 80-to-1;
(d) 13-to-1.
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If you start with a pair in hold ’em, what are the odds against flopping a straight or a flush?
(a) 2,540-to-1;
(b) 19-to-1;
(c) 402-to-1;
(d) none of the above.
Answers and explanations (with questions repeated for convenience)
Odds (level: beginner)
-
What are the odds against beginning with three of a kind in seven-card stud
(a) 424-to-1;
(b) 1400-to-1;
(c) 220-to-1;
(d) exactly 190.7-to-1.
Answer: (a). It’s 424-to-1 against beginning with three of a kind in seven-card stud. This type of problem is particularly easy. Think about it this way… The first card counts no matter what, because it must be some rank. After that, there are 51 cards left of the original 52, and since there are four cards of each rank to begin with, there are now three matching your first rank. Three out of 51 is the same as 1 out of 17 (divide 51 by 3, if you doubt this). So, there’s one chance in 17 that the first two cards will constitute a pair. If that happens (and only if that happens) do we care what the third card is – at least, for the purposes of this calculation. If you now have a pair, then there are 50 cards remaining that are unknown to you and only two that complete your three of a kind. That’s the same as one in 25. Now, we just multiply the chances – 17 times 25 = 425. That’s a universe of 425 chances and only one that qualifies as three of a kind. So, it’s 424-to-1 against.
I won’t go into this depth with the other answers, but it’s interesting to note that some calculations – like this one – can be relatively simple to reason out. When I did my collection of 50 poker tables for Doyle Brunson’s Super/System in 1977, some were extraordinarily complex and others were just as easy as this. But most of the poker literature of the day was oddly wrong, even when citing some of the simplest statistics. -
What are the odds against beginning with suited cards in hold ’em?
(a) 3.25-to-1;
(b) 3-to-1
(c) 4-to-1;
(d) 12-to-1.
Answer: (a). The odds against beginning suited in hold ’em are 3.25 to 1.
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What are the odds against beginning with a pair in hold ’em?
(a) 16-to-1;
(b) 25-to-1;
(c) 47-to-1;
(d) 3-to-1.
Answer: (a). The odds are 16-to-1 against beginning with a pair in hold ’em.
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What are the odds against beginning with three suited cards in seven-card stud?
(a) 90-to-1;
(b) 42-to-1;
(c) 18.3-to-1;
(d) 5.7-to-1.
Answer: (c). The odds are 18.3-to-1 against beginning with three cards of the same suit in seven-card stud.
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Your odds against starting with a pair in any poker game depend on the number of players who are dealt in:
(a) true;
(b) false.
Answer: (b). It’s false. The odds against starting with a pair in any poker game are completely independent of the amount of cards dealt or the number of opponents. It makes no difference whether unknown cards remain in the deck or are dealt facedown to others – they are still unknown and must be accounted for as such.
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What are the odds against starting with a pair of aces in hold ’em?
(a) 19.8-to-1;
(b) 220-to-1;
(c) 403-to-1;
(d) 1,279-to-1.
Answer: (b). It’s 220-to-1 against starting with a pair of aces in hold ’em.
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What are the odds against starting with a pair of deuces in hold ’em?
(a) 19.8-to-1;
(b) 220-to-1;
(c) 403-to-1;
(d) 1,279-to-1.
Answer: (b). It’s also 220-to-1 against starting with a pair of deuces (or any other pair) in hold ’em. Aces are no harder to get than any other rank. We just care more about them, because we’ve arbitrarily decided they’re worth more.
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If the board is 8-7-2-A in hold ’em and you hold 10-9, what are the odds against you making a straight on the last card (assuming you assume nothing about the cards opponents may be holding)?
(a) 5.75-to-1;
(b) 11.25-to-1;
(c) 3.5-to-1;
(d) 4.75-to-1.
Answer: (d). It’s 4.75-to-1 against hitting an open-end straight on the river in hold ’em (if you make no assumption about opposing cards).
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If you hold a pair to start with in hold ’em, what are the odds against flopping four of a kind?
(a) 1,003-to-1;
(b) 407-to-1;
(c) 80-to-1;
(d) 13-to-1.
Answer: (b). It’s 407-to-1 against flopping four of a kind in hold ’em if you begin with a pair.
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If you start with a pair in hold ’em, what are the odds against flopping a straight or a flush?
(a) 2,540-to-1;
(b) 19-to-1;
(c) 402-to-1;
(d) none of the above.
Answer: (d). It’s impossible to flop a straight or flush in hold ’em if you begin with a pair.