# Targeted poker quiz 18: Odds (intermediate)

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

Strategy – odds (level: intermediate)

1. How many different combinations of two cards can you consider using from an Omaha starting hand?

(a) 10;

(b) 8;

(c) 21;

(d) 6.

2. If you sit down to play hold ’em, what are the odds against you having a pair on each of your first three two-card starting hands?

(a) 4,912-to-1;

(b) 104-to-1;

(c) 1,040,000-to-1;

(d) 80,455-to-1.

3. In hold ’em, which defines the likelihood that you will begin with either a pair of aces or kings versus ace-king suited…

(a) the chances are exactly equal;

(b) it’s four times more likely that you’ll have ace-king suited;

(c) it’s three times more likely that you’ll have either a pair of aces or kings;

(d) there’s one more chance of having either a pair of aces or kings than having ace-king suited to start with.

4. If your seven-card stud hand is 7-7-5-5-2-2, what are the odds against making a full house on the river (assuming no knowledge of other exposed cards)?

(a) 6.67-to-1;

(b) 11-to-1;

(c) 4.33-to-1;

(D) 12-to-1.

5. In draw poker, it’s harder to be dealt a full house before the draw if there are eight players dealt in than if there are two players dealt in…

(a) true;

(b) false.

6. In seven-card stud, it’s easier to be dealt three of a kind to start with if there are six players dealt in than if there are three players dealt in

(a) true;

(b) false

7. If you know your heads up opponent has a pair of aces to start, what are the odds that you also have a pair of aces?

(a) it’s impossible;

(b) 1,224-to-1 against;

(c) 8,403-to-1 against;

(d) 84-to-1 against.

8. Which statement is true about odds?

(a) over time, the number of full houses held by one player versus another are likely to be exactly the same;

(b) over time, two players are likely to have about the same percentage of full houses;

(c) over three years, everyone’s luck is almost exactly the same;

(d) in poker, you make your own odds

9. How many types of hold ’em starting hands are there? (Such as ace-king suited, jack-4 unsuited, 4-4, etc.)

(a) 221;

(b) 808;

(c) 55;

(d) 169.

10. It’s almost certain that nobody in the history of the world, in an honest game of hold ’em, has ever sat down and started with a pair on the first 10 hands in a row

(a) true;

(b) false.

Answers and explanations (with questions repeated for convenience)

Strategy – odds (level: intermediate)

1. How many different combinations of two cards can you consider using from an Omaha starting hand?

(a) 10;

(b) 8;

(c) 21;

(d) 6.

Answer: (d). There are six combinations of two cards contained in an Omaha starting hand. If the cards were labeled A, B, C, and D, then you can have these six two-card combinations: AB, AC, AD, BC, BD, CD.

2. If you sit down to play hold ’em, what are the odds against you having a pair on each of your first three two-card starting hands?

(a) 4,912-to-1;

(b) 104-to-1;

(c) 1,040,000-to-1;

(d) 80,455-to-1.

Answer: (a). It’s 4,912-to-1 against sitting down to play hold ’em and having a pocket pair on each of the first three hands.

3. In hold ’em, which defines the likelihood that you will begin with either a pair of aces or kings versus ace-king suited…

(a) the chances are exactly equal;

(b) it’s four times more likely that you’ll have ace-king suited;

(c) it’s three times more likely that you’ll have either a pair of aces or kings;

(d) there’s one more chance of having either a pair of aces or kings than having ace-king suited to start with.

Answer: (c). It’s three times more likely in hold ’em that you’ll begin with either a pair of kings or a pair of aces than with ace-king suited.

4. If your seven-card stud hand is 7-7-5-5-2-2, what are the odds against making a full house on the river (assuming no knowledge of other exposed cards)?

(a) 6.67-to-1;

(b) 11-to-1;

(c) 4.33-to-1;

(D) 12-to-1.

Answer: (a). Assuming no knowledge of other cards in opposing hands or in the deck, it’s 6.67-to-1 against making a full house in seven-card stud when you have three pair before the final (river) card.

5. In draw poker, it’s harder to be dealt a full house before the draw if there are eight players dealt in than if there are two players dealt in…

(a) true;

(b) false.

Answer: (b). It’s false that it’s harder to be dealt a full house in five-card draw if eight players are dealt in than if only two players are dealt in.

6. In seven-card stud, it’s easier to be dealt three of a kind to start with if there are six players dealt in than if there are three players dealt in

(a) true;

(b) false.

Answer: (b). It’s false that it’s easier to be dealt three of a kind in seven-card stud if there are six players dealt in than if only three players are dealt in. You see, in both this question and the previous one, the odds of getting certain hands are exactly the same, no matter how many opponents are dealt in. Your chances of being dealt anything are always the same, whether only two players are dealt in or a whole table full of players is dealt in. It doesn’t make any difference whether cards are dealt or remain in the deck, it doesn’t influence the odds unless you know (and can take into consideration) what opponents’ cards are.

7. If you know your heads up opponent has a pair of aces to start, what are the odds that you also have a pair of aces?

(a) it’s impossible;

(b) 1,224-to-1 against;

(c) 8,403-to-1 against;

(d) 84-to-1 against.

Answer: (b). If you’re playing heads-up hold ’em against an opponent who begins with a pair of aces, it’s 1,224-to-1 against you also beginning with a pair of aces.

8. Which statement is true about odds?

(a) over time, the number of full houses held by one player versus another are likely to be exactly the same;

(b) over time, two players are likely to have about the same percentage of full houses;

(c) over three years, everyone’s luck is almost exactly the same;

(d) in poker, you make your own odds.

Answer: (b). This statement was true: Over time, two players are likely to have about the same percentage of full houses.

9. How many types of hold ’em starting hands are there? (Such as ace-king suited, jack-4 unsuited, 4-4, etc.)

(a) 221;

(b) 808;

(c) 55;

(d) 169.

Answer: (d). When considering pairs, two specific non-paired ranks of mixed suits, and two specific non-paired ranks of the same suit as distinct hold ’em categories, there are 169 possible kinds of starting hands, ranging from ace-ace down to three-deuce of different suits.

10. It’s almost certain that nobody in the history of the world, in an honest game of hold ’em, has ever sat down and started with a pair on the first 10 hands in a row

(a) true;

(b) false.

Answer: (a). This statement is true: It’s almost certain that nobody in the history of the world, in an honest game of hold ’em, has ever started with a pair 10 hands in a row. The odds against that happening to start a given session (assuming you play at least 10 hands) are 2,015,993,900,449 — more than two trillion to one, using the American definition of the word “trillion.” Even if you estimated that 200 million people have played hold ’em (and not that many have) and that the average number of hold ’em sessions (of at least 10 hands) played by each person was 1,000 (and it’s way less than that), players still only have taken 200 billion shots at starting with a pair 10 times in a row. It would be about 9-to-1 against the event ever having happened. Actually, the odds against are much greater than that, and, so, it’s almost certain that nobody has ever started with 10 straight pairs.

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