vpFREE2 Forums

An AA variation

#1

Steve,

I really do appreciate your coments with respect to this AA
variation. I am also extremely embarrassed because of a "fat-
fingering" on my part.

Namely, the standard AA paytable remains as I stated it before:

4000, 500, 200, 40, 40, 40, 15, 5, 5

However:

With a combination of 5 (4s and/or 5s), the payout is 225 (not 100)
With a combination of 4 (4s and/or 5s), the payout is 45 (not 20)

Sorry for the mis-representation.

.....bl

I don't think the exact answer is the least bit obvious. In fact,

I

···

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:

doubt that any commercially available VP programs can compute
the exact solution.

If all quads are left intact and the 4/5 bonuses are applied to
full house, 3oK and two pair payoffs, then according to my
computations the max-EV strategy for this game gives a
return of 100.2444%.

NOTE: The numbers listed below are in terms of whole bets.
Multiply by 5 to get number of coins.

  All American w/ bonus for 4+5 patterns
  Distribution of Final Hands
-------------------------------------------------------------------

-------

Final Hand Payoff % Hit Cycle %

Return

-------------------------------------------------------------------

-------

Royal Flush 4000 0.002198 45492.0252 1.758549
Straight Flush 500 0.012620 7923.6965

1.262037

4/Kind 200 0.222476 449.4857

8.899059

5/4 4/5 Boat 100 0.030200 3311.1942

0.604011

5/x 4/x Boat 40 0.123761 808.0042

0.990093

Full House 40 0.909961 109.8948

7.279688

Flush 40 1.567958 63.7771

12.543671

Straight 40 1.893901 52.8010

15.151208

Trip (4,5)'s + (5,4) + X 20 0.054768 1825.8613

0.219074

Trip (4,5)'s + X + (5,4) 20 0.270704 369.4070 1.082816
Trip (4,5)'s + X + Y 15 0.703898 142.0659

2.111695

3/Kind 15 5.845547 17.1070

17.536643

2P 5's + 4's 20 0.329437 303.5474

1.317751

2P 5's + X's 5 0.329437 303.5474

0.329437

Two Pair 5 10.971511 9.1145

10.971511

High Pair 5 18.187210 5.4983

18.187210

-------------------------------------------------------------------

-------

                                   41.455595 2.4122

100.244460

I'm not sure how much confidence I have in the strategy,
but here is what my program produces:

            Recommended Strategy
              High cards: AKQJ
------------------------------------------------------------
Rank Return Cards to keep
------------------------------------------------------------
    1 800.0000 Royal Flush
    2 100.0000 Straight Flush
    3 40.0000 4/Kind
    4 21.5009 suited KQJT
    5 20.0000 5/4 4/5 Boat
    6 19.1037 suited AKQJ
    7 19.0412 suited AQJT/AKJT/AKQT
    8 8.0000 5/x 4/x Boat
    9 8.0000 Full House
   10 8.0000 Flush
   11 8.0000 Straight
   12 6.4913 4/str-flush (0 holes)
   13 5.7872 quads + kicker
   14 5.1018 trips (54)
   15 4.8797 trips (AKQJT987632)
   16 4.0421 4/str-flush (1 hole)
   17 1.7895 suited QJT
   18 1.7185 4/flush (3 high)
   19 1.7099 suited KQJ
   20 1.6619 two pair
   21 1.6563 4/flush (2 high)
   22 1.6150 suited KJT/KQT
   23 1.5941 4/flush (1 high)
   24 1.5507 unsuited KQJT
   25 1.5319 4/flush (0 high)
   26 1.5241 suited AQJ/AKJ/AKQ
   27 1.4875 unsuited QJT9
   28 1.4376 suited AJT/AQT/AKT
   29 1.4255 unsuited JT98
   30 1.4081 pair (AKQJ)
   31 1.3617 4/straight (0 holes, 0 high)
   32 1.1488 trips (54) + kicker
   33 1.0774 3/str-flush (0 holes, 1 high)
   34 0.9834 3/str-flush (1 hole, 2 high)
   35 0.9808 3/str-flush (0 holes, 0 high)
   36 0.9362 unsuited AKQJ
   37 0.8831 3/str-flush (1 hole, 1 high)
   38 0.8723 4/straight (1 hole, 3 high)
   39 0.8085 4/straight (1 hole, 2 high)
   40 0.7992 3/str-flush (2 holes, 2 high)
   41 0.7880 pair (4)
   42 0.7810 3/str-flush (1 hole, 0 high)
   43 0.7714 pair (5)
   44 0.7447 4/straight (1 hole, 1 high)
   45 0.6988 3/str-flush (2 holes, 1 high)
   46 0.6820 pair (T987632)
   47 0.6809 4/straight (1 hole, 0 high)
   48 0.6323 suited QJ
   49 0.6272 unsuited QJT
   50 0.6087 unsuited KQJ
   51 0.6082 suited KJ/KQ
   52 0.6042 3/flush (2 high)
   53 0.5963 3/str-flush (2 holes, 0 high)
   54 0.5730 suited AJ/AQ/AK
   55 0.5384 suited JT
   56 0.5265 unsuited JT9
   57 0.5147 suited QT
   58 0.5088 unsuited KJT/KQT
   59 0.5083 unsuited QJ9
   60 0.5076 unsuited QJ
   61 0.5032 3/flush (1 high)
   62 0.4903 unsuited AQJ/AKJ/AKQ
   63 0.4824 suited KT
   64 0.4796 unsuited KJ/KQ
   65 0.4735 2/str-flush (1 hole, 1 high)
   66 0.4569 Jack
   67 0.4538 2/str-flush (0 holes, 0 high)
   68 0.4532 suited AT
   69 0.4490 Queen
   70 0.4487 unsuited AJ/AQ/AK
   71 0.4467 2/str-flush (2 holes, 1 high)
   72 0.4421 3/straight (0 holes, 0 high)
   73 0.4405 King
   74 0.4388 Ace
   75 0.4035 3/flush (0 high)
   76 0.3855 2/straight (0 holes, 0 high)
   77 0.3448 2/str-flush (1 hole, 0 high)
   78 0.3363 (draw 5 cards)
------------------------------------------------------------

#2

These changes will make the EV enormous. Just to be sure, here
are all the bonuses I've put in place:

payoff hand

···

On Saturday 16 October 2004 10:44 am, bornloser1537 wrote:

Steve,

I really do appreciate your coments with respect to this AA
variation. I am also extremely embarrassed because of a "fat-
fingering" on my part.

Namely, the standard AA paytable remains as I stated it before:

4000, 500, 200, 40, 40, 40, 15, 5, 5

However:

With a combination of 5 (4s and/or 5s), the payout is 225 (not 100)
With a combination of 4 (4s and/or 5s), the payout is 45 (not 20)

------------------------------
225 Four 5's with kicker 4
225 Four 4's with kicker 5
225 5's full of 4's
225 4's full of 5's
45 Three 5's with 4 as one of the kickers
45 Three 4's with 5 as one of the kickers
45 Two pair, 5's and 4's.
--------------------------------

I have *NOT* reduced the payoff for "Four 5's, non-4 kicker"
or "Four 4's, non-5 kicker", but left those at 200.

The number I get now is 109.1570% for the max-EV strategy.
Using a convential AA strategy would still give a large EV.
There must be some other "catch".

The overall result shown below the strategy doesn't agree
with the overall result shown with the distribution. This means
at least one of the numbers must be wrong, so there is a
bug in my program. Still, I don't think either number is
off by much, but if someone else has numbers it would be
interesting to see how they compare.

  All American w/ bonus for 4+5 patterns
  Distribution of Final Hands
--------------------------------------------------------------------------
Final Hand Payoff % Hit Cycle % Return
--------------------------------------------------------------------------
Royal Flush 4000 0.0021813066358 45844.08187231016
1.74504530864
Straight Flush 500 0.0124582626075 8026.80142088519
1.24582626075
Quad 5/4 + 4/5 225 0.0055637605507 17973.45501992604
0.25036922478
5/4 4/5 Boat 225 0.0340656231219 2935.51066546743
1.53295304048
4/Kind 200 0.1911399442008 523.17688182920
7.64559776803
Quad 5/4 + X 200 0.1404208719497 712.14484436335
5.61683487799
5/x 4/x Boat 40 0.1404208719497 712.14484436335
1.12336697560
Full House 40 0.9282166097480 107.73347400792
7.42573287798
Flush 40 1.5243055751240 65.60364380473
12.19444460099
Straight 40 1.8503441624765 54.04400004492
14.80275329981
Trip (4,5)'s + (5,4) + X 45 0.0601023013388 1663.82979973325
0.54092071205
Trip (4,5)'s + X + (5,4) 45 0.3108248359168 321.72461285164
2.79742352325
Trip (4,5)'s + X + Y 15 0.6804398266049 146.96376680205
2.04131947981
3/Kind 15 5.8469651344789 17.10288973853
17.54089540344
2P 5's + 4's 45 0.4011228738814 249.30016838073
3.61010586493
2P 5's + X's 5 0.4011228738814 249.30016838073
0.40112287388
Two Pair 5 10.9427174850251 9.13849783080
10.94271748503
High Pair 5 17.6996247515407 5.64983729338
17.69962475154
--------------------------------------------------------------------------
                                   41.1720370710328 2.42883294376
109.15705432900

cost: 0.865307758998571

            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 40.0000 528 0.8126 4/Kind
    6 40.0000 528 0.8126 Quad 5/4 + X
    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 3168 0.9752 Full House
   12 8.0000 4952 1.5243 Flush
   13 8.0000 10128 3.1176 Straight
   14 6.7021 6.8104 7128 1.8385 trips (54)
   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 4.8797 46464 8.7240 trips (AKQJT987632)
   19 4.1702 4.1915 144 0.0232 4/str-flush (1 hole, 3 high)
   20 4.1064 4.1277 576 0.0914 4/str-flush (1 hole, 2 high)
   21 4.0426 4.0638 1152 0.1801 4/str-flush (1 hole, 1 high)
   22 4.0000 2160 0.3324 4/str-flush (1 hole, 0 high)
   23 2.3256 2.3367 42024 3.7723 trips (54) + kicker
   24 1.5957 12.9787 123192 10.1496 two pair
   25 1.7123 1.8409 3756 0.2586 suited QJT
   26 1.7021 1.7234 4836 0.3198 4/flush (3 high)
   27 1.6263 1.7447 2856 0.1879 suited KQJ
   28 1.6383 1.6596 31836 2.0289 4/flush (2 high)
   29 1.5412 1.6448 5616 0.3490 suited KJT/KQT
   30 1.5745 1.5957 50388 3.0906 4/flush (1 high)
   31 1.5319 1.5532 6744 0.4024 unsuited KQJT
   32 1.5319 16044 0.9457 4/flush (0 high)
   33 1.4773 1.5486 8352 0.4898 suited AQJ/AKJ/AKQ
   34 1.4681 1.4894 7800 0.4464 unsuited QJT9
   35 1.4107 1.4487 6048 0.3346 suited AJT/AQT/AKT
   36 1.4255 7764 0.4259 unsuited JT98
   37 1.4131 1.4279 319332 17.4979 pair (AKQJ)
   38 1.3617 47016 2.4634 4/straight (0 holes, 0 high)
   39 1.1710 61260 2.7602 pair (4)
   40 1.1407 1.1555 60888 2.7018 pair (5)
   41 1.0315 1.0934 1632 0.0676 3/str-flush (0 holes, 1 high)
   42 0.9260 1.0934 10032 0.3860 3/str-flush (0 holes, 0 high)
   43 0.9352 0.9972 1680 0.0636 3/str-flush (1 hole, 2 high)
   44 0.9362 6492 0.2338 unsuited AKQJ
   45 0.8353 0.8973 5772 0.1961 3/str-flush (1 hole, 1 high)
   46 0.8723 25992 0.8724 4/straight (1 hole, 3 high)
   47 0.8085 25476 0.7925 4/straight (1 hole, 2 high)
   48 0.7928 0.8011 4020 0.1236 3/str-flush (2 holes, 2 high)
   49 0.7216 0.8973 25860 0.7859 3/str-flush (1 hole, 0 high)
   50 0.7447 55668 1.5951 4/straight (1 hole, 1 high)
   51 0.6873 0.8094 13572 0.3704 3/str-flush (2 holes, 1 high)
   52 0.6924 0.6998 531180 14.2661 pair (T987632)
   53 0.6809 77856 2.0396 4/straight (1 hole, 0 high)
   54 0.3692 0.7304 23004 0.5979 2/str-flush (0 holes, 0 high)
   55 0.6096 0.6542 18348 0.4463 suited QJ
   56 0.6272 11892 0.2870 unsuited QJT
   57 0.6087 15636 0.3662 unsuited KQJ
   58 0.5950 0.6175 21192 0.4959 suited KJ/KQ
   59 0.6022 0.6050 50412 1.1718 3/flush (2 high)
   60 0.5791 0.7012 12756 0.2961 3/str-flush (2 holes, 0 high)
   61 0.5817 0.6205 68184 1.5760 2/straight (0 holes, 0 high)
   62 0.5661 0.5807 40236 0.8869 suited AJ/AQ/AK
   63 0.5098 0.5635 11856 0.2453 suited JT
   64 0.5245 0.5273 10260 0.2078 unsuited JT9
   65 0.4953 0.5267 7008 0.1387 suited QT
   66 0.5088 25440 0.4980 unsuited KJT/KQT
   67 0.5060 0.5088 12444 0.2434 unsuited QJ9
   68 0.4916 0.5141 28932 0.5646 unsuited QJ
   69 0.4912 0.5051 128736 2.4884 3/flush (1 high)
   70 0.4903 16848 0.3178 unsuited AQJ/AKJ/AKQ
   71 0.4664 0.4900 7332 0.1360 suited KT
   72 0.4746 0.4825 51192 0.9442 unsuited KJ/KQ
   73 0.4600 0.4836 4164 0.0758 2/str-flush (1 hole, 1 high)
   74 0.4439 0.4769 64296 1.1374 Jack
   75 0.4433 0.4678 60192 1.0505 Queen
   76 0.4532 4548 0.0793 suited AT
   77 0.4430 0.4509 77688 1.3414 unsuited AJ/AQ/AK
   78 0.4368 0.4558 59328 1.0170 King
   79 0.4368 0.4530 51624 0.8823 Ace
   80 0.4378 0.4457 2304 0.0392 2/str-flush (3 holes, 1 high)
   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 0.3765 0.3946 7824 0.1158 Five
   84 0.3827 360 0.0053 2/str-flush (1 hole, 0 high)
   85 0.3735 0.3909 10104 0.1482 Four
   86 0.3558 0.3582 3624 0.0497 (draw 5 cards)
------------------------------------------------------------
                            2598960 108.9945

#3

I made an error when configuring my program for the previous
post. The number I get now if 104.8151%, which is still quite
high, but only about half as massive as the erroneous EV.

Both of my numbers now agree, and it was likely that the
configuration error caused them to disagree.

If this game is real, it won't last long (if my numbers are correct).

  All American w/ bonus for 4+5 patterns
  Distribution of Final Hands

···

On Saturday 16 October 2004 07:33 pm, you wrote:

On Saturday 16 October 2004 10:44 am, bornloser1537 wrote:
> Steve,
>
> I really do appreciate your coments with respect to this AA
> variation. I am also extremely embarrassed because of a "fat-
> fingering" on my part.
>
> Namely, the standard AA paytable remains as I stated it before:
>
> 4000, 500, 200, 40, 40, 40, 15, 5, 5
>
> However:
>
> With a combination of 5 (4s and/or 5s), the payout is 225 (not 100)
> With a combination of 4 (4s and/or 5s), the payout is 45 (not 20)

These changes will make the EV enormous. Just to be sure, here
are all the bonuses I've put in place:

payoff hand
------------------------------
225 Four 5's with kicker 4
225 Four 4's with kicker 5
225 5's full of 4's
225 4's full of 5's
45 Three 5's with 4 as one of the kickers
45 Three 4's with 5 as one of the kickers
45 Two pair, 5's and 4's.
--------------------------------

I have *NOT* reduced the payoff for "Four 5's, non-4 kicker"
or "Four 4's, non-5 kicker", but left those at 200.

--------------------------------------------------------------------------
Final Hand Payoff % Hit Cycle % Return
--------------------------------------------------------------------------
Royal Flush 4000 0.0021791544508 45889.35858316995
1.74332356062
Straight Flush 500 0.0126269144474 7919.59115720335
1.26269144474
Quad 5/4 + 4/5 225 0.0060587924820 16504.93894563062
0.27264566169
5/4 4/5 Boat 225 0.0354437169725 2821.37452111695
1.59496726376
4/Kind 200 0.1899050247141 526.57901048468
7.59620098856
Quad 5/4 + X 200 0.0266843591831 3747.51363950407
1.06737436732
5/x 4/x Boat 40 0.1209364765796 826.88038239765
0.96749181264
Full House 40 0.9031676406925 110.72141593040
7.22534112554
Flush 40 1.5299394458558 65.36206401559
12.23951556685
Straight 40 1.8748030639265 53.33893565896
14.99842451141
Trip (4,5)'s + (5,4) + X 45 0.0625927994824 1597.62785539066
0.56333519534
Trip (4,5)'s + X + (5,4) 45 0.3248696090687 307.81580427500
2.92382648162
Trip (4,5)'s + X + Y 15 0.7120102109366 140.44742401721
2.13603063281
3/Kind 15 5.7987640767943 17.24505406250
17.39629223038
2P 5's + 4's 45 0.4210874577283 237.48035749980
3.78978711955
2P 5's + X's 5 0.4210874577283 237.48035749980
0.42108745773
Two Pair 5 10.8633509823684 9.20526273728
10.86335098237
High Pair 5 17.7534052688068 5.63272220095
17.75340526881
--------------------------------------------------------------------------
                                   41.0589124522183 2.43552481124
104.81509167175

cost: 0.924476470662268

            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)
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                            2598960 104.8151