MATH Recap, and Bayes Rule in a Poker Context

Nineteen runners came out for the Labor Day edition of Mondays at the Hoy on full tilt, creating a $456 prize pool to be paid to the top three finishers in a field that included two first-time MATHers, one of whom complained about what I think was a pretty fatty turnout for a fucking holiday. Maybe it's just me. Anyways, I got no good starting cards over nearly two hours, receiving pocket Queens and pocket Tens once each, and an AQ and a bunch of JackAces but not even an AK on the night. It was pretty sick. But pretty usual for me, while also usual was me getting to watch pocket Aces and pocket Kings flipped up by my opponents again and again throughout, including a couple of times like on my one pocket Queens of the night which naturally ran into Wes's Aces. Not that I haven't sucked out on Wes and knocked him out of tournaments doing it, don't get me wrong, but when you play for two hours, get exactly one hand better than pocket Tens on the entire night, and that hand runs into pocket Aces, I think anyone has the right to act pissay. Anyways I ended up restealing with 65s in my big blind against Wes's button open-raise with my small stack after we sat with 11 players left for probably a good 30 minutes, which ran into Wes's AK and IGH in 11th place.

Another unspectacular performance for me as my good streak of the past couple of months is now officially totally gone and a thing of the past. The past few days have been among my most frustrating on full tilt for some time. The setups are downright silly, the beats are recockulous. And both plentiful. My one QQ in two hours in the big blind, against the button's AA. That is rich. In the Labor Day 100k on Monday evening, I busted in the first hand when I reraised allin on a K♠Q♠T♥ flop with my J♠5♠, giving me 8 oesd outs and 7 more flush outs for 15 outs twice and therefore making me the favorite in the hand. Still, as I am racing here I do not at all like to call allin in this spot on the first hand of a big mtt, but I love the allin raise since I get good fold equity and am the favorite if called. Unsurpisingly my opponent called with top two pair, unsurprisingly for my luck of late my favored hand failed to make one of its copious outs, and IGH very very early in that one. I ran flopped two pair into a flopflush as well in the 28k to round out what was my third or fourth consecutive super-frustrating night on full tilt. I even started thinking about putting some more money into pokerstars for a bit this weekend, taint-hound that that site is.

Btw did KOD really delete his entire blog? Is that really possible?

Anyways, back to the MATH. In the end it was first-timer Wormmsu ending the night in 3rd place for $91.20 and his first entrance onto the 2007 MATH moneyboard (if you have a blog please leave a comment, you know the drill). In second place was host of the biggest regular weekly blogger tournament out there, Mookie himself, who won $136.80. And winning the MATH this week, fresh back from Tunica for some mtt goodness there was perennial blonkament killer Surflexus.

Here are the updated 2007 MATH moneyboard standings, including the Labor Day MATH tournament this week:

1. Bayne_s $1175
2. Columbo $1168
3. Hoyazo $1162
4. VinNay $775
5. cmitch $774
6. Iggy $745
7. NewinNov $677
8. Pirate Wes $672
9. Lucko21 $665
10. Waffles $650
11. Astin $616
12. Tripjax $561
13. IslandBum1 $527
14. RaisingCayne $522
15. Julius Goat $507
16. bartonf $492
16. mtnrider81 $492
18. PokerBrian322 $490
19. Chad $485
20. scots_chris $474
21. Fuel55 $458
22. Mike_Maloney $456
23. RecessRampage $434
24. Otis $429
25. Surflexus $402
25. Miami Don $402
27. jeciimd $382
27. Jordan $382
29. Blinders $379
30. lightning36 $371
31. ChapelncHill $353
32. Zeem $330
33. OMGitsPokerFool $324
34. oossuuu754 $312
35. leftylu $295
36. Emptyman $288
36. Wigginx $288
38. ScottMc $282
39. Fishy McDonk $277
40. Irongirl $252
40. Manik79 $252
42. Wippy1313 $248
43. swimmom95 $245
44. Byron $234
45. wwonka69 $216
46. Omega_man_99 $210
47. katiemother $209
48. Pushmonkey72 $208
49. Buddydank $197
50. Gary Cox 194
51. 23Skidoo $176
52. Santa Clauss $170
53. Iakaris $162
53. Smokkee $162
55. cemfredmd $156
55. NumbBono $156
57. lester000 $147
58. LJ $146
59. Heffmike $145
60. brdweb $143
61. Mookie $137
61. DDionysus $137
63. Patchmaster $135
64. InstantTragedy $129
65. Ganton516 $114
66. Fluxer $110
67. hoops15mt $95
68. Gracie $94
68. Scurvydog $94
70. wormmsu $91
71. Shag0103 $84
72. crazdgamer $82
73. PhinCity $80
74. maf212 $78
75. Alceste $71
76. dbirider $71
77. Easycure $67
78. Rake Feeder $53

So that's 78 different bloggers and non-bloggers alike now who have cashed at least once in Mondays at the Hoy during 2007, through by my calculation approximately 32 MATH tournaments, give or take probably 1 tourney. This week Mookie and wormmsu enter the moneyboard for the first time, while Surf jumps into the top 25 with his win in addition to previous cashes this year in the Hoy. No movement in the top few spots or even in the top 25 at all this week, so that virtual tie for the top spot between myself, Bayne and Columbo will persist for at least one more week. Congratulations again to all three cashers and I look forward to another fun time next Monday in Mondays at the Hoy on full tilt.

I kinda want to get this post up for today, but I know I talked a lot about Bayes Theorem last week and a number of you have been asking about the promised discussion about how this relates to poker. I'm thinking I will write some more about this later in the week, but I will start that discussion here today with a quick example poker problem for you all to chew on. I'm going to try to give a hypothetical that applies somewhat to my own style of play to illustrate a point from The Mathematics of Poker that I've been reading for the past week or two.

So we're talking about a typical aggressive player here. What percentage of the time is such an aggressive player dealt what most of us would consider a "strong" preflop raising hand? Let's assign a 0.45% chance to being dealt each of AA, KK, QQ, JJ and TT, and 1.2% chance of being dealt AK. That totals to 3.95%, so I'm going to go ahead and use 4% just to make that calculation easier. So let's say that this aggressive player is dealt a "strong" raising hand 4% of the time in nlh, and he will put in a preflop raise 90% of the time when he does receive such a strong raising hand preflop. Now, of this aggressive player's 96% of hands that are not the strong raising hands, assume he will also raise with those hands about 20% of the time (probably somewhat typical of an aggressive preflop player).

The question is, then, if this aggressive player puts in a preflop raise, what are the chances that he actually has one of those six "strong" raising hands? I suggest that you re-read the assumptions above, and make an estimate based on the percentages you see as to what you think the correct answer is, and then read on below where I will use Bayes rule to come up with the mathematically correct answer.







OK if everyone has come up with their estimates or answers to the question, here is how to solve it by using Bayesian mathematics. The chances that a preflop raise from the aggressive player we described above actually indicates one of the six strong raising hands TT-AA and AK are:

90% x 4%
(90% x 4%) + (20% x 96%)

This equals:

.036
.228

Which equals 15.79%. So there you have it, even though an aggressive player raises 90% of the time with his strongest raising hands, those strong hands occur so infrequently that a preflop raise from such an aggressive player only generally means a 15.79% chance, or less than one-sixth of the time, that he actually has TT-AA or AK. In other words, if you understand the theory of conditional probability sufficiently, then there is a more than 5 in 6 chance that when such a player raises preflop, he still does not have a "strong" hand.

That's the lesson for today on Bayes theorem in a poker context. I plan to write more about this later in the week, but it is my contention that without a doubt most players do not appreciate the significance of Bayes' rules on conditional probability, and that most players I play with with some regularity do not properly make this calculation, even if it is only being estimated subconsciously. In other words, most people do not respond to the aggressive preflop players by treating their preflop raises as a more than 5 in 6 chance of not really being among the top hands. Most players fold far too often for that. It's just something to think about -- later in the week I will write some more about the implications of Bayes rule in this context, as well as some other areas where it can be used to make useful conclusions based on conditional probabilities in the world of poker.