Yeah, my strategy generator is confusing with this kind of game.
I believe line 5 means you are dealt either 4444 or 5555 and
draw hoping to hit the kicker. Line 10 means you are dealt
4445 or 5554 and draw hoping to hit quads but usually
settling for trips + kicker.
I found some more corrections, but the new changes only
bring the EV up to 104.9861%. This doesn't have much
impact on the strategy, but you can see a slight problem
by looking at lines 42 and 44 (on the old table). The numbers
show a different value for a pair of 4's as opposed to a pair
of 5's, and that doesn't make sense -- both pairs should have
the same value. New numbers are given below.
All American w/ bonus for 4+5 patterns
Distribution of Final Hands
···
--------------------------------------------------------------------------
Final Hand Payoff % Hit Cycle % Return
--------------------------------------------------------------------------
Royal Flush 4000 0.0021812026687 45846.26703186488
1.74496213496
Straight Flush 500 0.0124755696667 8015.66603141247
1.24755696667
Quad 5/4 + 4/5 225 0.0059265275590 16873.28692974909
0.26669374015
5/4 4/5 Boat 225 0.0347447785447 2878.13030298725
1.56351503451
4/Kind 200 0.1913325339969 522.65026710839
7.65330135988
Quad 5/4 + X 200 0.0256767750896 3894.57007941647
1.02707100359
5/x 4/x Boat 40 0.1347845824630 741.92461906712
1.07827665970
Full House 40 0.9238327389687 108.24470251144
7.39066191175
Flush 40 1.5248269182546 65.58121371209
12.19861534604
Straight 40 1.8563973068425 53.86777907478
14.85117845474
Trip (4,5)'s + (5,4) + X 45 0.0685301234851 1459.21231298805
0.61677111137
Trip (4,5)'s + X + (5,4) 45 0.3066250034447 326.13126417149
2.75962503100
Trip (4,5)'s + X + Y 15 0.6746946709313 148.21519171326
2.02408401279
3/Kind 15 5.8568252207018 17.07409667042
17.57047566211
2P 5's + 4's 45 0.4086720398568 244.69498827236
3.67804835871
2P 5's + X's 5 0.2694086009072 371.18339824064
0.26940860091
Two Pair 5 11.3111100474481 8.84086527145
11.31111004745
High Pair 5 17.7347645427851 5.63864266474
17.73476454279
--------------------------------------------------------------------------
41.3428091836144 2.41880031799
104.98611997911
cost: 0.921655238912207
Recommended Strategy
High cards: AKQJ
------------------------------------------------------------
Expected Value
Rank min max Ways Gain Cards to keep
------------------------------------------------------------
1 800.0000 4 0.1231 Royal Flush
2 100.0000 36 0.1385 Straight Flush
3 45.0000 8 0.0139 Quad 5/4 + 4/5
4 45.0000 48 0.0831 5/4 4/5 Boat
5 40.4255 88 0.1369 quads (54)
6 40.0000 528 0.8126 4/Kind
7 21.3830 21.5532 184 0.1522 suited KQJT
8 18.9787 19.1489 188 0.1382 suited AKQJ
9 18.9149 19.0851 564 0.4132 suited AQJT/AKJT/AKQT
10 12.0638 1408 0.6536 quads (54) + kicker
11 8.0000 528 0.1625 5/x 4/x Boat
12 8.0000 3168 0.9752 Full House
13 8.0000 4952 1.5243 Flush
14 8.0000 10128 3.1176 Straight
15 6.5745 6.5957 132 0.0335 4/str-flush (0 holes, 2 high)
16 6.5106 6.5319 132 0.0332 4/str-flush (0 holes, 1 high)
17 6.4681 792 0.1971 4/str-flush (0 holes, 0 high)
18 6.0361 7040 1.6350 trips (54)
19 4.8797 46464 8.7240 trips (AKQJT987632)
20 4.1702 4.1915 144 0.0232 4/str-flush (1 hole, 3 high)
21 4.1064 4.1277 576 0.0914 4/str-flush (1 hole, 2 high)
22 4.0426 4.0638 1152 0.1801 4/str-flush (1 hole, 1 high)
23 4.0000 2160 0.3324 4/str-flush (1 hole, 0 high)
24 2.2202 2.2211 45192 3.8606 trips (54) + kicker
25 1.7123 1.8409 3756 0.2586 suited QJT
26 1.5957 12.0638 120024 8.0074 two pair
27 1.7021 1.7234 4836 0.3198 4/flush (3 high)
28 1.6263 1.7447 2856 0.1879 suited KQJ
29 1.6383 1.6596 31836 2.0289 4/flush (2 high)
30 1.5412 1.6448 5616 0.3490 suited KJT/KQT
31 1.5745 1.5957 50388 3.0906 4/flush (1 high)
32 1.5319 1.5532 6744 0.4024 unsuited KQJT
33 1.5319 16044 0.9457 4/flush (0 high)
34 1.4773 1.5486 8352 0.4898 suited AQJ/AKJ/AKQ
35 1.4681 1.4894 7800 0.4464 unsuited QJT9
36 1.4107 1.4487 6048 0.3346 suited AJT/AQT/AKT
37 1.4255 7764 0.4259 unsuited JT98
38 1.4081 319332 17.3017 pair (AKQJ)
39 1.3617 47016 2.4634 4/straight (0 holes, 0 high)
40 1.0315 1.0934 1656 0.0687 3/str-flush (0 holes, 1 high)
41 0.9315 1.0934 10284 0.3963 3/str-flush (0 holes, 0 high)
42 0.9352 0.9972 1704 0.0645 3/str-flush (1 hole, 2 high)
43 0.9758 60636 2.2765 pair (5)
44 0.9758 61212 2.2982 pair (4)
45 0.9362 6492 0.2338 unsuited AKQJ
46 0.8353 0.8973 5772 0.1961 3/str-flush (1 hole, 1 high)
47 0.8723 25992 0.8724 4/straight (1 hole, 3 high)
48 0.8085 25476 0.7925 4/straight (1 hole, 2 high)
49 0.7928 0.8011 4020 0.1236 3/str-flush (2 holes, 2 high)
50 0.7382 0.8973 25932 0.7920 3/str-flush (1 hole, 0 high)
51 0.7447 55620 1.5937 4/straight (1 hole, 1 high)
52 0.6957 0.8011 12936 0.3536 3/str-flush (2 holes, 1 high)
53 0.6953 376320 10.0674 pair (T9876)
54 0.6953 157068 4.2019 pair (32)
55 0.6809 80388 2.1059 4/straight (1 hole, 0 high)
56 0.3613 0.7084 20436 0.4972 2/str-flush (0 holes, 0 high)
57 0.6096 0.6542 18348 0.4463 suited QJ
58 0.6272 11892 0.2870 unsuited QJT
59 0.6087 15636 0.3662 unsuited KQJ
60 0.5950 0.6175 21480 0.5026 suited KJ/KQ
61 0.5957 0.7012 13464 0.3137 3/str-flush (2 holes, 0 high)
62 0.6022 0.6050 51396 1.1947 3/flush (2 high)
63 0.5606 0.5988 65592 1.4618 2/straight (0 holes, 0 high)
64 0.5661 0.5807 40704 0.8974 suited AJ/AQ/AK
65 0.5109 0.5635 11964 0.2476 suited JT
66 0.5245 0.5273 10152 0.2057 unsuited JT9
67 0.4964 0.5267 6996 0.1385 suited QT
68 0.5088 25440 0.4980 unsuited KJT/KQT
69 0.5060 0.5088 12444 0.2434 unsuited QJ9
70 0.4916 0.5141 28860 0.5632 unsuited QJ
71 0.4995 0.5051 128820 2.4961 3/flush (1 high)
72 0.4903 16848 0.3178 unsuited AQJ/AKJ/AKQ
73 0.4675 0.4900 7332 0.1360 suited KT
74 0.4746 0.4825 51192 0.9442 unsuited KJ/KQ
75 0.4611 0.4836 4164 0.0758 2/str-flush (1 hole, 1 high)
76 0.4439 0.4719 55272 0.9731 Jack
77 0.4532 4548 0.0793 suited AT
78 0.4402 0.4628 56952 0.9867 Queen
79 0.4430 0.4509 89952 1.5528 unsuited AJ/AQ/AK
80 0.4338 0.4509 59328 1.0086 King
81 0.4338 0.4480 53928 0.9134 Ace
82 0.4274 8916 0.1466 3/straight (0 holes, 0 high)
83 0.4052 10872 0.1695 3/flush (0 high)
84 0.3492 0.3674 6552 0.0902 Five
85 0.3472 0.3630 2544 0.0347 2/str-flush (1 hole, 0 high)
86 0.3449 0.3597 7560 0.1021 Four
87 0.3433 0.3496 3840 0.0514 (draw 5 cards)
------------------------------------------------------------
2598960 104.9861
On Thursday 21 October 2004 01:41 pm, bornloser1537 wrote:
Dear Steve,
I find your posting very interesting and I thank you for having taken the
trouble to do the analysis. With the crush of other things (like a job!
LOL) I am only slowly making my way through the post. My first question
(perhaps there will be others) concerns lines 5 and 10 of the strategy (see
below). I don't seem to be able to understand the difference between
keeping "quads (54)" on line 5 and keeping "quads (54) + kicker" on line
10. I seem to be missing something crucial here. Can you explain?
Thanks!
.....bl
--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:
> Recommended Strategy
> High cards: AKQJ
> ------------------------------------------------------------
> Expected Value
> Rank min max Ways Gain Cards to keep
> ------------------------------------------------------------
> 1 800.0000 4 0.1231 Royal Flush
> 2 100.0000 36 0.1385 Straight Flush
> 3 45.0000 8 0.0139 Quad 5/4 + 4/5
> 4 45.0000 48 0.0831 5/4 4/5 Boat
> 5 40.4255 88 0.1369 quads (54)
> 6 40.0000 528 0.8126 4/Kind
> 7 21.3830 21.5532 184 0.1522 suited KQJT
> 8 18.9787 19.1489 188 0.1382 suited AKQJ
> 9 18.9149 19.0851 564 0.4132 suited AQJT/AKJT/AKQT
> 10 12.0638 1408 0.6536 quads (54) + kicker
> 11 8.0000 528 0.1625 5/x 4/x Boat
> 12 8.0000 3168 0.9752 Full House
> 13 8.0000 4952 1.5243 Flush
> 14 8.0000 10128 3.1176 Straight
> 15 6.5745 6.5957 132 0.0335 4/str-flush (0 holes, 2
> high) 16 6.5106 6.5319 132 0.0332 4/str-flush (0 holes,
> 1 high) 17 6.4681 792 0.1971 4/str-flush (0
> holes, 0 high) 18 6.0361 7040 1.6350 trips (54)
> 19 4.8797 46464 8.7240 trips (AKQJT987632)
> 20 4.1702 4.1915 144 0.0232 4/str-flush (1 hole, 3
> high) 21 4.1064 4.1277 576 0.0914 4/str-flush (1 hole, 2
> high) 22 4.0426 4.0638 1152 0.1801 4/str-flush (1 hole, 1
> high) 23 4.0000 2160 0.3324 4/str-flush (1 hole, 0
> high) 24 2.3256 2.3377 45192 4.0567 trips (54) + kicker 25
> 1.7123 1.8409 3756 0.2586 suited QJT
> 26 1.5957 12.9787 109944 7.4443 two pair
> 27 1.7021 1.7234 4836 0.3198 4/flush (3 high)
> 28 1.6263 1.7447 2856 0.1879 suited KQJ
> 29 1.6383 1.6596 31836 2.0289 4/flush (2 high)
> 30 1.5412 1.6448 5616 0.3490 suited KJT/KQT
> 31 1.5745 1.5957 50388 3.0906 4/flush (1 high)
> 32 1.5319 1.5532 6744 0.4024 unsuited KQJT
> 33 1.5319 16044 0.9457 4/flush (0 high)
> 34 1.4773 1.5486 8352 0.4898 suited AQJ/AKJ/AKQ
> 35 1.4681 1.4894 7800 0.4464 unsuited QJT9
> 36 1.4107 1.4487 6048 0.3346 suited AJT/AQT/AKT
> 37 1.4255 7764 0.4259 unsuited JT98
> 38 1.4081 319332 17.3017 pair (AKQJ)
> 39 1.3617 47016 2.4634 4/straight (0 holes, 0
> high) 40 1.0315 1.0934 1656 0.0687 3/str-flush (0 holes,
> 1 high) 41 0.9260 1.0934 10104 0.3888 3/str-flush (0
> holes, 0 high) 42 0.9909 61212 2.3339 pair (4)
> 43 0.9352 0.9972 1704 0.0645 3/str-flush (1 hole, 2
> high) 44 0.9606 0.9844 70896 2.6578 pair (5)
> 45 0.9362 6492 0.2338 unsuited AKQJ
> 46 0.8353 0.8973 5772 0.1961 3/str-flush (1 hole, 1
> high) 47 0.8723 25992 0.8724 4/straight (1 hole, 3
> high) 48 0.8085 25476 0.7925 4/straight (1 hole, 2
> high) 49 0.7928 0.8011 4020 0.1236 3/str-flush (2 holes,
> 2 high) 50 0.7216 0.8973 25860 0.7859 3/str-flush (1 hole,
> 0 high) 51 0.7447 55668 1.5951 4/straight (1 hole,
> 1 high) 52 0.6873 0.8094 17508 0.4752 3/str-flush (2
> holes, 1 high) 53 0.6801 0.6875 520080 13.6465 pair (T987632)
> 54 0.6809 84420 2.2116 4/straight (1 hole, 0
> high) 55 0.3539 0.7304 24900 0.6305 2/str-flush (0 holes,
> 0 high) 56 0.6096 0.6542 18348 0.4463 suited QJ
> 57 0.6272 11892 0.2870 unsuited QJT
> 58 0.6087 15636 0.3662 unsuited KQJ
> 59 0.5950 0.6175 21192 0.4959 suited KJ/KQ
> 60 0.5791 0.7012 12900 0.2999 3/str-flush (2 holes, 0
> high) 61 0.6022 0.6050 50412 1.1718 3/flush (2 high) 62
> 0.5817 0.6205 68184 1.5760 2/straight (0 holes, 0 high) 63
> 0.5661 0.5807 40236 0.8869 suited AJ/AQ/AK
> 64 0.5098 0.5635 11856 0.2453 suited JT
> 65 0.5245 0.5273 10260 0.2078 unsuited JT9
> 66 0.4953 0.5267 7008 0.1387 suited QT
> 67 0.5088 25440 0.4980 unsuited KJT/KQT
> 68 0.5060 0.5088 12444 0.2434 unsuited QJ9
> 69 0.4916 0.5141 28932 0.5646 unsuited QJ
> 70 0.4912 0.5051 128736 2.4884 3/flush (1 high)
> 71 0.4903 16848 0.3178 unsuited AQJ/AKJ/AKQ
> 72 0.4664 0.4900 7332 0.1360 suited KT
> 73 0.4746 0.4825 51192 0.9442 unsuited KJ/KQ
> 74 0.4600 0.4836 4164 0.0758 2/str-flush (1 hole, 1
> high) 75 0.4438 0.4719 55272 0.9730 Jack
> 76 0.4532 4548 0.0793 suited AT
> 77 0.4401 0.4628 56952 0.9866 Queen
> 78 0.4430 0.4509 89952 1.5528 unsuited AJ/AQ/AK
> 79 0.4337 0.4509 59328 1.0085 King
> 80 0.4337 0.4480 53928 0.9133 Ace
> 81 0.4191 0.4274 8916 0.1463 3/straight (0 holes, 0
> high) 82 0.3885 0.4052 10872 0.1689 3/flush (0 high) 83
> 0.3491 0.3673 7056 0.0970 Five
> 84 0.3472 0.3630 1368 0.0188 2/str-flush (1 hole, 0
> high) 85 0.3466 0.3636 8472 0.1154 Four
> 86 0.3472 0.3496 3576 0.0479 (draw 5 cards)
> ------------------------------------------------------------
> 2598960 104.8151
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