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Mathematics of Poker - Outs & Odds

Strategy: No-Limit. Mathematics of Poker - Outs & Odds. Outs All cards that improve your hand and could make your hand the best hand. Example 1 (OESD): Your outs: Example 2 (OESD + flush draw): Your outs:. Outs – which cards can help you?. Odds

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Mathematics of Poker - Outs & Odds

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  1. Strategy: No-Limit Mathematics of Poker - Outs & Odds

  2. Outs All cards that improve your hand and could make your hand the best hand. Example 1 (OESD): Your outs: Example 2 (OESD + flush draw): Your outs: Outs – which cards can help you?

  3. Odds Odds = Number of non-helpful cards : Number of helpful cards Example: Your outs: Odds = (47 – 8) : 8 = 39 : 8 = 5 : 1 (rounded) Odds – what are your chances of completing a draw?

  4. Pot odds Pot odds = possible winnings : cost of staying in the hand Example: Pot size before the bet: $10 The amount of the bet: $2 Possible winnings: $12 Amount required to play: $2 Odds of a straight on the turn: 5:1 Total profit: $12 - $10 = $2 Pot Odds: $12 : $2 = 6:1 Pot odds – can you play your hand profitably? • If the pot odds are higher than the odds against you , it is profitable in the long run. If they are lower, you will lose money in the long run.

  5. Discounted / modified outs Example: Your outs: Opponent’s hand: Your discounted outs: Discounted / modified outs

  6. Real examples- #1 Flop: Amount to pay: $0.75 Pot after your opponent’s bet: $2.60 Pot odds: ~ 3.5:1 Hero (BU) $25 BB $25 UTG $25 MP1 $25 Outs: 9 (flush draw) + 3 (gutshot) = 12 Odds: (47 – 12) : 12 = 35 : 12 = 3:1 Preflop: UTG1 calls $0.25, 2 folds, MP1 calls $0.25, 3 folds, Hero calls $0.25, 1 fold, BB checks. • Turn: • Due to the possible full house, there are only about 8 discounted outs. • Required pot odds: ~ 5:1 • Actual pot odds: ~ 2:1 Flop: ($ 1.10) BB bets $0.75, UTG calls $0.75, 1 fold, Hero calls $0.75. Turn: ($ 3.35) BB bets $3, 1 fold, Hero folds.

  7. Real examples- #2 Outs: 9 (flush draw) Odds: (47 – 9) : 9 = 38 : 9 = ~4:1 Hero (SB) $25 BB $25 UTG $25 MP1 $25 Flop: Pot after opponent‘s bet: $1.75 Amount to pay: $0.75 Pot odds: 2,3:1 Preflop: UTG1 calls $0.25, 2 folds, MP1 calls $0.25, 4 folds, Hero calls $0.15, BB checks. Flop: ($ 1.00) 3 checks, MP1 bets $0.75, Hero ? 3 checks, MP1 bets $0.75, Hero folds.

  8. Real examples- #3 Flop: Pot after opponent‘s bet: $6.60 Amount to pay: $1.50 Pot odds: ~ 4,5:1 Hero (CO) $25 BB $25 Preflop: Outs: 8 (straight) + 3 (overcards) = 11 Odds: (47 – 11) : 11 = 36 : 11 = ~3,3:1 6 folds, Hero raises to $1, 2 folds, BB calls $0.75. Flop: ($ 2.10) • Turn: • Only 9 discounted outs. • Required pot odds: ~ 4:1 • Actual pot odds: ~ 2,5:1 BB checks, Hero bets $1.5, BB raises to $3, Hero calls $1.5. Turn: ($ 8.10) BB bets $6, Hero folds.

  9. Odds are the ratio between the non-helpful cards and helpful cards. Pot odds are the ratio between possible winnings and the cost of staying in the hand. If the pot odds are higher than the odds, you can play the draw profitably. Summary

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