Pure Theory Question - Page 12

M.B.E. · #**111** 05-01-2005, 02:12 PM

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The list of ev's vs all possible hands would be more meaningful, although I have never seen one.

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http://www.jazbo.com/poker/huholdem.html

http://www.gocee.com/poker/HE_Value.htm

M.B.E. · #**112** 05-01-2005, 02:21 PM

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If you look down at KK, there is really only one hand you don't want to see, and you will crack it anyway about 17% of the time. So, you would be willing to pay (6/1326)*.83*$1000=$3.76 to see his cards.

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You should be using 1225, not 1326, because the two cards you are holding are not available for the other player to hold.

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By this same reasoning, there must be some justification to paying a tiny amount even with AA, if you think it is unwise to gamble against the other AA.

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It might reduce your variance by a minuscule amount, but it would also reduce your EV (by the amount you pay). If you are seeking to maximize EV, then you would not pay anything when you hold AA.

M.B.E. · #**113** 05-01-2005, 04:27 PM

If you code this, it would be good to make your code general enough to answer Pure Theory Questions #2 and #3.

jediael · #**114** 05-02-2005, 10:24 AM

That's easy, for #2 you just split the hands into the < 40% and > 40% vs a random hand (of course taking dead cards into account)

For #3 you do the same with hand < 22.22% and > 22.22% vs a random hand

well · #**115** 06-06-2005, 09:28 AM

Here's what I found.

Without the dealmaking, EVI[x] denotes the expectation value of your winnings when you have hand x.
Clearly, for all hands that have an equity lower than .5 against a random hand, this value will be 0. For hands with EQ>.5, it is 1000*(2*EQ-1).

Let EVII[x] denote the same, but now under the assumption that you get to see your opponent's hand before making your decision.
This means that EVII[x] equals
Sum{y=1..169}:
P(opponent has hand y given you have hand x)*
{ 1000(2*EQ[x,y]-1), if EQ[x,y]>.5
{ 0, if EQ[x,y]<.5

Here EQ[x,y] denotes the equity of hand x versus hand y.
Note that for all x, EVI[x]<=EVII[x].

Since it shouldn't matter for both whether the first game is played, or the second one (where you pay to see your opponent's hand), the amount that should be payed when you hold x would be

EVII[x]-EVI[x]

So, here's a sorted table:
AAo 0
32o 0
32s 0.24645061119224881
42o 0.49362920679162253
42s 1.2115147968194
43o 1.5270018808409391
KKo 3.129409025404243
43s 3.350338229088077
52o 3.527280393277474
52s 4.898684307631056
AKs 5.180016670700013
53o 5.577367436756899
QQo 6.218631595267539
62o 7.801543822754339
53s 7.842160299210643
54o 7.991409021209468
AKo 8.612611893634153
JJo 9.271872570405549
AQs 10.403735289423992
62s 10.886796565401026
54s 11.326334194710027
63o 12.00972133309915
TTo 12.287896236621066
AQo 14.706253285941273
72o 15.037341738478267
99o 15.328348141880099
AJs 15.451208740160098
63s 15.501353850765788
64o 15.992477780504743
88o 18.317801092348247
64s 19.82958776536152
ATs 20.231383193256818
72s 20.413498003692286
AJo 20.59982339584593
65o 21.225719312477604
77o 21.3849667358312
73o 21.83522151607259
66o 24.547986043294316
65s 25.55751925416258
ATo 26.187359730705623
A9s 26.627246811600315
73s 27.384889789739766
82o 27.532403649094572
55o 27.885729236330064
74o 28.235451133891708
KQs 29.578990932565944
A8s 30.592463459187087
44o 32.08376502284227
83o 32.8375154059045
A9o 33.72238927247432
74s 33.92100124887223
A7s 34.436049501796504
KJs 34.99541040871836
75o 35.30181175152761
82s 35.663389735677306
33o 36.868416079463714
A5s 37.132510896882735
A6s 38.196752588849165
A8o 38.49263701219604
A4s 39.92909660710663
KTs 40.13759715755259
83s 41.039884010678236
75s 41.108788902828785
84o 42.07177830905857
A3s 42.380391732843265
92o 42.640624466645356
22o 42.80234808581603
KQo 42.9525760350387
76o 42.954186944870166
A7o 43.13894338045273
A2s 45.01100987026729
QJs 46.27455958135147
A5o 47.08036537856785
A6o 47.724989135059246
76s 48.9960575377517
KJo 49.1476599329778
93o 49.87199726693582
84s 50.138481989942264
A4o 50.63148142109452
K9s 51.67411575400203
QTs 51.74431213911842
85o 51.90216366309929
A3o 53.805121100944916
92s 54.022055686850194
KTo 55.02402110172642
94o 56.14166738654646
JTs 56.63731702419395
A2o 57.1809054123716
85s 59.89297246664765
T2o 59.954161296172614
K8s 61.07861259044009
86o 61.07891579809116
93s 61.18028726922605
K7s 64.70417183216134
94s 67.39790626535704
Q9s 67.81813443006848
QJo 67.83067511757838
K9o 68.25273540021789
K6s 68.50272534097024
T3o 68.66742287417588
86s 69.20063402817468
95o 69.27160178118285
87o 71.99892170587292
K5s 73.21627038952255
QTo 74.07158198687222
T2s 75.1875272577004
J9s 76.80402545342506
T4o 77.25945240316851
K4s 77.57919297565135
J2o 78.0379561630387
K8o 78.96263080120625
T9s 79.07159914956912
87s 80.07425917694187
95s 80.13169938734896
Q8s 80.97832713664697
96o 81.1433507610989
K3s 81.59441361833392
K7o 83.3215225371956
T3s 83.7048375541173
JTo 85.20727341759478
K2s 85.73284574110565
T5o 85.92617160675837
K6o 87.97846834750511
J3o 88.25879383233686
96s 91.91253660660293
T4s 92.10019258453244
Q9o 92.29328103287388
J8s 93.30496482505136
K5o 93.51652844020992
97o 93.7318635580827
Q7s 93.75806241539058
Q6s 96.5461020558811
Q2o 97.56498702976825
J2s 97.85897020765522
J4o 98.34612240321235
T8s 98.65421331821494
K4o 98.76625712657241
T5s 100.51456483695156
98s 101.08971018116
T6o 101.17919505424462
Q5s 102.1512968992159
K3o 103.64825214137984
97s 104.46927982080614
98o 106.50722473274342
Q8o 107.12012658061255
J3s 107.75741662123318
J9o 107.7688460240992
Q4s 108.03805675551456
K2o 108.67439760362949
Q3o 109.3191281502369
J7s 109.5276220263004
J5o 109.78468824246538
Q3s 113.59733232569201
T6s 115.37911826070946
T9o 115.39549719475704
T7o 116.77052958934807
J4s 117.5250432356948
T7s 117.93065450327212
J6o 118.5506879285788
Q2s 119.30003703328696
Q4o 120.92699827667448
Q7o 121.454421787777
Q6o 124.9702994757174
J6s 125.0165682004588
J8o 126.28830642508485
J5s 128.53511611804197
Q5o 131.47232724839463
T8o 131.5444739833533
J7o 138.04610272331956

According to this, the K2 feeling is quite off.

Regards,

Daan.

abscr · #**116** 06-06-2005, 01:17 PM

And, it's in the dark.

pzhon · #**117** 06-06-2005, 02:53 PM

Thanks for doing that calculation.

Your numbers are slightly off, since you didn't consider the combinations of suits. That can make 32o a favorite over 32o, for example. It also determines whether A7s is a favorite over 22 or not.

The differences shouldn't matter enough to affect the calculation of the best hand.

TheActionKid · #**118** 06-06-2005, 03:49 PM

I think the biggest factor we have to put into consideration here is that he moves all in "in the dark". Everyone is talking about tight players and loose players and what he could have and what he couldnt have...but he himself doesnt even know what he has. Therefore, if you have any huge hands, AA, KK, QQ, AK, etc.. you dont pay him anything and take your chances because more often than not you will be the favorite by a lot with these hands. For example, let us say that you see KK, the only hand that true dominates you is AA, but what are the odds that he has AA. In this situation you take your chances and call with KK without paying anything, since he probably might not even have an ace, not even one over, and if he does, he is drawing to 3 outs. If he has a smaller pocket pair, then he is drawing to two outs. I feel that the best hand to pay him off with in this situation would be a middle pocket pair such as 88 or 99 or two face cards suited such as KQs or QJs. The reason for this is that if you have 88 or 99 and he shows 7 4 you know you are a tremendoes favorite, however if you have 88 or 99 and he shows 10s or better you know you are a severe underdog. Also if he shows two cards above 8s or 9s then you know its a coinflip - and you should not call his all in, never put all your money in on a coinflip - if you want to do that, you are playing the wrong game and should go to the casino and bet red/black on roulette. I hope some of you find this enlightening.

-TheActionKid

kyro · #**119** 06-06-2005, 04:14 PM

[ QUOTE ]
I think the biggest factor we have to put into consideration here is that he moves all in "in the dark". Everyone is talking about tight players and loose players and what he could have and what he couldnt have...but he himself doesnt even know what he has. Therefore, if you have any huge hands, AA, KK, QQ, AK, etc.. you dont pay him anything and take your chances because more often than not you will be the favorite by a lot with these hands. For example, let us say that you see KK, the only hand that true dominates you is AA, but what are the odds that he has AA. In this situation you take your chances and call with KK without paying anything, since he probably might not even have an ace, not even one over, and if he does, he is drawing to 3 outs. If he has a smaller pocket pair, then he is drawing to two outs. I feel that the best hand to pay him off with in this situation would be a middle pocket pair such as 88 or 99 or two face cards suited such as KQs or QJs. The reason for this is that if you have 88 or 99 and he shows 7 4 you know you are a tremendoes favorite, however if you have 88 or 99 and he shows 10s or better you know you are a severe underdog. Also if he shows two cards above 8s or 9s then you know its a coinflip - and you should not call his all in, never put all your money in on a coinflip - if you want to do that, you are playing the wrong game and should go to the casino and bet red/black on roulette. I hope some of you find this enlightening.

-TheActionKid

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If you had KK, refusing to pay ANY sort of money to see your opponent's hand is very bad.

wrestler_118 · #**120** 06-06-2005, 09:47 PM

Clearly with AA you call and 32o you fold.

Consider you hold KK:
If you call you will win 82.4% of the time with an EV of $648
If you know your opponents cards:
He will hold AA (6 of 1225 times), you would fold.
And he will not hold AA (1219 of 1225 times), you would call. You would win 82.7% of the time.
If you knew his cards your EV would be $654
Then it would be worth paying to see his cards if it was less than $6

Consider you hold 32s:
If you call you will win 36.0% of the time with an EV of -$280
So you would fold for an EV of $0.
If you know your opponents cards:
He will hold a hand better than 32o (1219 of 1225 times), you would fold.
And he will hold 32o (6 of 1225 times), you would call. You would win 7.2% of the time, lose 0.4% and split 92.4%.
If you knew his cards your EV would be $0.34
Then it would be worth paying to see his cards if it was less than $0.34

Notice that it would be valuable to know your opponents card the closer you got the middle holdings of J5s.

Matt