Real Life Stats Applicaions of the Week 1

# Real Life Stats Applicaions of the Week 1 - count Need 3...

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Real Life Stats Application of the Week 1 Texas Hold’em – the perils of the inside straight draw Rules: Each player gets two cards face down Five cards are dealt face up, shared between all players First three are called the ﬂop, fourth is the turn, ﬁfth is the river Each player tries to make the best poker hand from the 7 cards (5 shared, 2 own) Inside Straight Draw river if not on turn? In next two cards? IMPORTANT: treat the cards other players have in their hands (and any cards the dealer has burned) as being still in the deck, because we dont know what they are so they dont aﬀect the probabilities. If we thought we knew what someone was holding (bad poker face or they showed their cards), we would use that information. 1. Prob. of 8 on turn: 4 / 47 8 . 5% 2. Prob. of 8 on river given it didnt occur on turn: 4 / 46 8 . 7% 3. Prob. of 8 in next two cards? CANNOT just add up above probabilities! That will double-

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Unformatted text preview: count. Need 3 cases: Turn River Probability 8 not 8 (4 / 47) × (43 / 46) not 8 8 (43 / 47) × (4 / 46) 8 8 (4 / 47) × (3 / 46) Now add up these three cases ≈ 16 . 5% Open-ended Straight Draw Now, what if you have 7 & 5 and ﬂop is 6, 8, & K. A 9 or a 4 would give you a straight! 1. Prob. of 4 or 9 on turn: 8 / 47 ≈ 17% 2. Prob. of 4 or 9 on river given it didnt occur on turn: 8 / 46 ≈ 17 . 4% 3. Prob. of 4 or 9 in next two cards? Again need 3 cases: Turn River Probability 4 or 9 not (4 or 9) (8 / 47) × (39 / 46) not (4 or 9) 4 or 9 (39 / 47) × (8 / 46) 4 or 9 4 or 9 (8 / 47) × (7 / 46) Now add up these three cases ≈ 31 . 5% 1 What if you need two runners to make the straight? You have 7 & 5. Flop is 2, 9, & K. You need 6 and 8 to complete your straight. Prob. you make it? Only two ways this can happen: Turn River Probability 6 8 (4 / 47) × (4 / 46) 8 6 (4 / 47) × (4 / 46) Now add up these two cases ≈ 1 . 48% 2...
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Real Life Stats Applicaions of the Week 1 - count Need 3...

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