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Overview

Overview. Odds Pot Odds Outs Probability to Hit an Out Odds Against Hitting Your Hand Implied Odds Reverse Implied Odds Putting It Together. Odds. The odds represent the probability that an event does not occur.

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Overview

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  1. Overview • Odds • Pot Odds • Outs • Probability to Hit an Out • Odds Against Hitting Your Hand • Implied Odds • Reverse Implied Odds • Putting It Together

  2. Odds The odds represent the probability that an event does not occur. By extension, an odd measures the relationship between a potential winning and the associated risk. If the Cowboys have odds of 8-to-1 (8:1) to win the Superbowl, it means that for every bet on the Cowboys, there are 8 bets for some other team. If the Cowboys win the Superbowl, those that made this bet will win 9 times their bet (minus the rake taken by the bookmaker).

  3. Probability & Odds Probability « x % »  Odds « (1/x – 1) to 1 » Odds « x to 1 »  Probability « 1/(x+1)  »

  4. Pot Odds Pot odds are the odds the pot is giving you for calling a bet. Example: If there is $50 in the pot and the final bet was $10, you are getting 5-to-1 odds for your call. If you figure your chances of winning are better than 5-to-1, then it is correct to call. If you think your chances are worse then 5-to-1, you should fold. From: The Theory of Poker – D.Sklansky (Ch.5)

  5. Pot Odds Exercise: You have on the button You’re playing NL $200 (blinds $1/$2) and your stack is currently $140. All your opponents have you covered. An early position player bets $10, 2 players call. You raise $40. The blinds fold, but the early position raiser goes all in. Should you Call or Fold ?

  6. Pot Odds Answer: To answer, you must guess the probability to win the hand, and compare it to the pot odds. Pot odds: You had $140, and already bet $40. You still have $100. In the pot, there is : The $140 bet by your opponent + 2x $10 from the two callers + $40 from your raise = $200 (+ $3 from the blinds that we will ignore to keep the math simple). You must risk $100 to win 200. The pot odds are 200:100 = 2:1

  7. Pot Odds Answer: Pot odds = 2:1 If your chances to win are better than 2:1 (33%), you should call. Otherwise, you should fold. Equity calculated with PokerStove

  8. Pot Odds The pot odds will help you make the right decision … IF you can correctly estimate your winning probabilities. For your winning probabilities to be accurate, you must guess the ranges of your opponents with enough reliability (… that’s another story …)

  9. Outs Outs: Cards in the deck that give you the winning hand. Example: You have in a family-pot with 6 opponents (limpers). The flop is With 6 opponents, you probably don’t have the best hand right now. But any heart on the turn or river will give you the nut flush, and most likely the winning hand. (=> 9 outs) An ace gives you top-pair, but with a ridiculous kicker. « Top-pair – no kicker » will not be enough to win. (=> aces will not be counted as outs)

  10. Counting Outs

  11. Counting Outs Be careful about outs that could give you the second best hands. Sometimes, you have less outs than you might think. (0 outs  drawing dead) Discount bad outs or count them as partial outs.

  12. Counting Odds Sometimes, your opponent has a hand weaker than expected => you may have more outs than you think. You may have outs to a split-pot. Think about outs to a backdoor-draw (worth about one additional out on the flop). Counting outs is not an exact science (unless you know your opponents cards).

  13. Counting Outs Exercise: Your hand: Flop: What are your outs?

  14. Counting Outs Answer: Your hand: Flop: 9 hearts give you a flush - not the nut-flush (someone with the ace of heart can have the nut-flush, or redraw to the nut flush on the river). => count these 9 hearts as partial outs 3 kings and 3 jacks would give you two pairs (max-min) - but it’s still a marginal holding Backdoor straight draw Risk: a made full house or a draw to a full house could make you loose a lot of money.

  15. Counting Outs Exercises: 1) Your hand:Opponent’s hand: Board: 2) Your hand: Opponent’s hand: Board: What are your outs in each situation?

  16. Counting Outs Answers: 1) Your hand:Opponent’s hand: Board: Outs: 12 (3 aces, 3 queens, 3 eights, 3 fours) 2) Your hand: Opponent’s hand: Board: Other interesting exercises :Small Stakes Hold’em – Miller/Sklansky/Malmuth (Part 3) • Outs: 3 for a win (3 deuces) • 22 for a split (1 ace, 3 kings, 4 queens, 4 jacks, 4 tens, 3 nines, 3 fours)

  17. Probability to Hit an Out Hitting On The Turn: 2 known cards in your hand. 3 cards on the board (flop). 47 hidden cards (among the deck or your opponents hands). Probability = Outs / 47. Hitting On The River: Probability = Outs / 46.

  18. Probability to Hit an Out Hitting On The Turn OR On The River: 1 – Probability to hit neither on the turn nor on the river Probability not to hit on the turn = (47-outs) / 47 Probability not to hit on the river = (46-outs) / 46 Probability = 1 – ((47-outs)/47) x ((46-outs)/46)

  19. Probability to Hit an Out Rule of 2 and 4: The Rule of 2 and 4 is an approximation. With one card to come (turn or river only), the probability to hit an out is: about outs x 2 % With two cards to come (turn & river), the probability to hit an out is: about outs x 4 %. This approximation is close up to 8 outs. It is too high above 8 outs. But, in general, this approximation is enough.

  20. Odds Against Making Your Hand The probability to hit one of your outs is used to determine the odds against making your hand. If you have x% to hit one of your outs: Odds against making your hand = (1/x)-1 to 1 Example: 25% to hit an out  Odds 3-to-1 10% to hit an out  Odds 9-to-1

  21. Odds Against Making Your Hand Example: Your hand: Board: Number of outs: 9 outs But if the villain has two pair or a set, a or could give him a full-house  we will consider these two cards as fractional outs, worth ½ an out each. Discounted outs: 8 outs Probability to hit an out = 8 x 2% = 16% Odds against making your hand = about 5-to-1.

  22. Odds Against Making Your Hand Example (cont.): Odds = 5-to-1 If the villain bets $100 in a $400 pot: Pot odds are 500-to-100 (5-to-1) => Calling is OK (pot odds are good enough) If the villain goes all-in for $200 in a $400 pot: Pot odds are 600-to-200 (3-to-1) => Calling is NOT OK (pot odds are NOT good enough) => In the long run, calling makes you loose money

  23. Effective Odds When there are more betting rounds to come (or other opponents that could raise), you must consider the effective odds. Effective odds take into account future bets that you’ll have to call until the showdown. Example: Your hand: with effective stacks of $200Pot: $20 Flop: For some reason, you know the villain will bet ½ pot on the flop ($10) and on the turn ($20), and he will check the river. Effective Odds = 20 (pot) + 10 (flop bet) + 20 (turn bet) to 10 (call flop) + 20 (call turn) = 50 to 30 = 1.67-to-1 If you think you will win the pot more than 3 times out of 8, you have effective odds good enough to call on the flop & turn.

  24. Outs & Odds

  25. Outs & Odds It’s up to you to complete …

  26. Implied Odds Implied odds include future betting that will take place after you bet. - by another player yet to speak - on the next street if you hit one of your outs Implied Odds can justify a call where expressed odds would dictate a fold. Pot odds = ratio of current pot to the cost of calling a bet Implied odds = ratio of expected winnings (if your card hits) to the cost of calling a bet.

  27. Implied Odds Example: Your hand: Flop: (2 players on the flop) Your stack: $200 (you are covered) There is $40 in the pot, your opponent bets $20 Your pot odds are 3-to-1 ($20 to call in a $60 pot) You have 8 outs (4 eights and 4 threes that would give you the nuts) => 16% to hit on river => about 5-to-1 to hit one of your outs. If you don’t consider implied odds, it’s a clear fold.

  28. Implied Odds Example (cont.): But if you hit one of your 8 outs on the river, you think that you’ll be able to get another $60 from your opponent. If you don’t hit, you plan to fold. You are risking $20 to win $60 from the pot + $60 on the river. Your implied odds are 120-to-20, or 6-to- 1. Your implied odds are greater than the odds against making your hand… calling is OK.

  29. Reverse Implied Odds When you have an made hand versus a draw… You are in a situation where you can: - win a small pot - OR loose a big pot (if you cannot fold your hand) You have reverse implied odds.

  30. Reverse Implied Odds Example: NL$200 (blinds $1/$2), effective stacks about $200 Your hand: Opponent’s hand: ??? (for example ) Board: You chose to slow play pre-flop and on the flop to trap your opponent. You plan to call any bet on the river. The pot is $15. You are in a situation with huge reverse implied odds. Even if you bet the pot on the turn, your opponent will have implied odds of about 12:1 (enough for even a inside straight draw to correctly call). The trap closes on the trapper!

  31. Reverse Implied Odds Exercise: NL$200 (blinds $1/$2), effective stacks about $200 Your hand: in Middle Position You raise pre-flop to $8. The button reraises to $24. The blinds fold. What do you do? Let’s say you called the reraise (pot = $51) The flop comes What’s your plan?

  32. Reverse Implied Odds Answer: Pre-flop: fold facing this reraise! The main reason comes from your big reverse implied odds. On the flop, except for some rare two-pair hand, trips, or boat, you are in a precarious situation: • if there is an ace on the flop, you will win a small pot or loose a big one (kicker problem). • if a 9 comes, you have a weak pair and could be facing an over-pair. • if the flop misses you, you play out-of-position in a 3bet pot with an unmade hade.

  33. Reverse Implied Odds Answer (cont.): Let’s look further with the flop Your opponent’s range could be something like « AJ+, 99+ », plus possibly sometimes a few weaker hands like suited aces, suited connectors, middle/low pocket pairs, or random trash. Go ahead and look at what’s going to happen against this range. Try also with other flops, or try with other « trouble hands » like More information on Implied Odds and Reverse Implied Odds : The Theory of Poker – D.Sklansky (Ch.7)

  34. Putting It Together Exercise: NL $200 (blinds $1/$2). Your stack = $200, everyone has you covered. 2 players limp, you are on the button with You limp behind, the small blind completes, the big blind checks. Pot = $10 Flop : BB bets $10, one of the limpers calls. Calculate: Your pot odds, outs, and probability to hit one of your outs on the turn. Should you call or fold? (for this exercise, do not consider raising)

  35. Putting It Together Answer: Pot odds: You must call $10 on a pot containing $10 (pre-flop) + 2 x $10 Pot odds = 3-to-1 Number of outs: 8 outs - Open-ended straight draw to the nut straight Probability to hit one of your outs:Using the Rule of 2 and 4: 16% or about 5-to-1

  36. Putting It Together Answer (cont.): The odds against making your hand are too low to call. But you have excellent implied odds. If one of your out comes on the turn, you can hope to win much more. Let’s say, you expect to win $50 more on average. Implied odds: 30+50 to 10 = 8-to-1. Implied odds are good enough: You are 5-to-1 against hitting one of your out on the turn, and the implied odds are 8-to-1. => Call

  37. Putting It Together Exercise (cont.): You call and the SB folds. Pot = $40 Turn = The BB bets $40, the player in mid-position folds. You know the player in the BB well, and know that if you raise, he’ll go all-in with a very very wide range. What should you do? (Again, for this exercise, do not consider raising or pushing)

  38. Putting It Together Exercise (cont.): Calculating the outs: The nines and four of heart, spade and diamond give you the nut straight => 6 outs The nine remaining clubs give you a flush (but it’s not the nuts). You think there is a small chance (but higher than zero) that the villain may have a hand like AcQc, KcQc, QcJc or QcTc (draw to a better flush). Instead of counting 9 outs for the flush, you elect to discount 1 and keep 8 outs. Total = 14 outs That’s about 28% probability (about 2.6-to-1)

  39. Putting It Together Exercise (cont.): Calculating pot odds: Pot = $40+$40. You must call 40$. Pot odds = 80 to 40, or 2-to-1. The pot-odds are not good enough to justify a call (you would need 2.6 to 1) But effective stacks are still $148 Once again, the decision to fold or call depends on the amount you expect the villain to call if you hit one of your outs. (implied odds)

  40. Putting It Together Exercise (cont.) : If you think he’ll call a $60 bet on the river: Implied odds = 80 + 60 to 40 = 3.5-to-1 • The implied odds can justify your call. • On the long-term (in these conditions, and if your hypothesis are correct), you will win money by calling and by betting $60 on the river when you hit one of your outs.

  41. Conclusion • Calculating pot odds and estimating implied odds help you decide if it is profitable to call a bet. • Calculating outs help you define the probability of hitting your hand (Rule of 2 and 4). • Be careful when calculating your outs, don’t over-estimate. • Comparing the pot-odds (or implied odds) with the odds against hitting your hand helps you make profitable decisions.

  42. Conclusion I hope this presentation will be helpful to you in your future games. Please feel free to post any comments or remarks. Good luck … may the odds be with you. http://www.grinderschool.com http://mykq.blogspot.com

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