Good morning!
Does anyone have some ideas on what the EV and variation for the
following AA paytable would be, or how to compute them?
The first difference is that the AA paytable has SF = 500, rather
than the standard 1,000, i.e.,
4000, 500, 200, 40, 40, 40, 15, 5, 5
Of course, for this situation, WP gives EV=99.3653%, Var.=21.81403
Now, for the "interesting" part. There are additional payouts on
hands that have 4 or 5 (4s and/or 5s), namely:
With a combination of 5 (4s and/or 5s), the payout is 100.
With a combination of 4 (4s and/or 5s), the payout is 20.
Question: If you get 55554 or 44445 is the payout reduced from
200 to 100? I've assumed that the answer is "NO". If the quad
payoffs are reduced, the loss is too big for the other bonuses
to compensate.
Any comments and/or suggestions are appreciated.
Or, are the answers obvious and I am simply overlooking the obvious?
I don't think the exact answer is the least bit obvious. In fact, I
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
···
On Thursday 14 October 2004 04:09 am, bornloser1537 wrote:
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Final Hand Payoff % Hit Cycle % Return
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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
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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
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Rank Return Cards to keep
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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)
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