1 / 7

Stat 35b: Introduction to Probability with Applications to Poker Outline for the day:

Stat 35b: Introduction to Probability with Applications to Poker Outline for the day: Project A and teams. P(4 of a kind), etc. Expected value and pot odds, continued Yang / Kravchenko Violette / Elezra example. Reminders: HW2 is due Fri Jan 31. Read up through chapter 4.

khuyen
Download Presentation

Stat 35b: Introduction to Probability with Applications to Poker Outline for the day:

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Stat 35b: Introduction to Probability with Applications to Poker Outline for the day: • Project A and teams. • P(4 of a kind), etc. • Expected value and pot odds, continued • Yang / Kravchenko • Violette / Elezra example. • Reminders: • HW2 is due Fri Jan 31. Read up through chapter 4. • Luck vs. skill. pp 71-79. Any thoughts? • Project A is due by email by Feb 6, 8pm. • You may email me for your teammates’ email addresses.  u   u 

  2. Teams: team a HUANG, RIHAN. ZHANG, HO KWAN. MCELROY, DAVID. team b LI, JESSE. THOMA, TREVOR. DITTMAR, MICHAEL. team c WANG, ERIC. LU, SIAO. GU, JIAQI. team d CHIANG, NICOLE. ZHANG, TONY. ALCORN, KIMBERLY. team e CHEN, ZHAOYUAN. LI, GAN. REITZ, CLAIRE. team f BARBER, THOMAS. MENG, QINGYI. SUEZAKI, PATRICK. team g LAM, SUI YUEN. ZHUANG, YUAN. LAHOZ GONZALEZ, LAURA. team h XIE, ZITONG. GU, YINGQIAN. LUAN, PEIYAO. team i CHEN, YIMING. TUZMEN, MEHMET. WANG, ZHAOXIN. team j POWER, JUSTIN. ALEXANDER, AREN. MAULEON, KIMBERLY. team k KIM, SO YOUNG. CHEN, XINYUAN. DUTTA, ANJALI. team l ZHOU, MENGRUI. YU, BRANDON. SANGHVI, ANAV. team m GAO, YANG. LA, CASEY. TSAI, PEI-CHEN. team n LIU, YIHAO. LI, RUOYU. SHI, BO. team o ZHOU, CAROL. YUN, XINYAO. DUONG, MINDY. team p MAVRODIEV, TEODOR. WONG, LAP KAN. YUZAWA, KATSUHIRO. team q LEE, FIONA. YANG, YIK. HUSSEIN, MARYAM. MOUTOUX, ALEX. team r LI, JIANJUN. MUSTAFA, JAMAL. YANG, YI-LONG. HSUEH, JESSICA. Just submit one email per team.

  3. Winning code last time. legendary = function(numattable1, crds1, board1, round1, currentbet, mychips1, pot1, roundbets, blinds1, chips1, ind1, dealer1, tablesleft){ ## all in if pair of 9s or better, ## or same suit with the lower card is 10 or above, ## or different suit with lower card is Jack or above, ## or you have less than 4 times big blind and at least one card is Jack or higher. a1 = 0 if((crds1[1,1] == crds1[2,1]) && (crds1[2,1] > 8.5)) a1 = mychips1 if((crds1[2,1] == crds1[2,2]) && (crds1[2,1] > 9.5)) a1 = mychips1 if((crds1[2,1] > 10.5)) a1 = mychips1 if((mychips1 < 4 * blinds1) && (crds1[1,1] > 10.5)) a1 = mychips1 a1 } ## end of legendary

  4. Suppose you’re all in next hand, no matter what cards you get. P(eventually make 4-of-a-kind)? [including case where all 4 are on board] Trick: just forget card order, and consider all collections of 7 cards. Out of choose(52,7) different combinations, each equally likely, how many of them involve 4-of-a-kind? 13 choices for the 4-of-a-kind. For each such choice, there are choose(48,3) possibilities for the other 3 cards. So, P(4-of-a-kind) = 13 * choose(48,3) / choose(52,7) ~ 0.168%, or 1 in 595. P(flop 4-of-a-kind) = 13*48 / choose(52,5) = 0.024% = 1 in 4165. P(flop 4-of-a-kind | pocket pair)? No matter which pocket pair you have, there are choose(50,3) possible flops, each equally likely, and how many of them give you 4-of-a-kind? 48. (e.g. if you have 7 7, then need to flop 7u 7 x, & there are 48 choices for x) So P(flop 4-of-a-kind | pp) = 48/choose(50,3) = 0.245% = 1 in 408.

  5. P(flop an ace high flush)? [where the ace might be on the board] -- 4 suits -- one of the cards must be an ace. choose(12,4) possibilities for the others. So P(flop ace high flush) = 4 * choose(12,4) / choose(52,5) = 0.0762%, or 1 in 1313. P(flop a straight flush)? -- 4 suits -- 10 different straight-flushes in each suit. (5 high, 6 high, …, Ace high) So P(flop straight flush) = 4 * 10 / choose(52,5) = 0.00154%, or 1 in 64974.

  6. 3) Pot odds and expected value, continued. From previous lecture: to call an all-in, need P(win) > B ÷ (B+pot). Expressed as an odds ratio, this is sometimes referred to as pot odds or express odds. If the bet is not all-in & another betting round is still to come, need P(win) > wager ÷ (wager + winnings), where winnings = pot + amount you’ll win on later betting rounds, wager = total amount you will wager including the current round & later rounds, assuming no folding. The terms Implied-odds / Reverse-implied-odds describe the cases where winnings > pot or where wager > B, respectively. See p66.

  7. 4. Yang / Kravchenko. Yang A 10u. Pot is 19million. Bet is 8.55 million. Needs P(win) > 8.55 ÷ (8.55 + 19) = 31%. vs. AA: 8.5%. AJ-AK: 25-27%. KK-TT: 29%. 99-22: 44-48%. KQs: 56%. Bayesian method: average these probabilities, weighting each by its likelihood. See p49-53.

More Related