charliepatrick
charliepatrick
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November 20th, 2015 at 7:28:42 AM permalink
Quote: ThatDonGuy

I'll have to go over my code again...

I am beginning to look at this and so far have only managed to work out the chances of the dealer making various totals given a deck missing the 5-player cards. My next bit will be, rather than analysing each player hand, adding up the dealer values, average over all player hands and see how those results compare.

However since it's single deck, there will be some hands (e.g. AAAAT Lo21 is winner, AT999 where you have 9's), where the specific hand play might be different (as you have hinted, some plays will be card dependent.)
Paradigm
Paradigm
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November 20th, 2015 at 7:33:03 AM permalink
PGD, what is the push/win/loss percentage breakdown if you count winning one side and losing the other side a push?

From a hands per hour count, are you expecting about the same pace as PGP?
charliepatrick
charliepatrick
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November 20th, 2015 at 8:10:37 AM permalink
Here's my first stab at a simple strategy - I have a few differences (e.g. 17/21 over 20/18) but I haven't yet checked my code. Some of the numbers are close so I can visualise some of the decisions flipping based on cards you hold. Note I have not added the bonus for 21-21 since this doesn't affect the strategy.

HLnn - means make two valid hands with firstly a High nn, if not a Low nn (e.g. HL21 means make H21/L19 before L21/H19 or 20/20.)
Lownn or Highnn - means make one valid hand and sacrifice the other.

Note my idea if you can make two valid hands, is to make either hand 21 before anything else, and just Low 21 only if you can't make a 20+-17+ or 19-19.
HL21 LH20 (except HL20-18) 19-19 Low 21 18-18 LH19 Low 20 High 21 LH18 Low 19 17-17 Low18 High20 Low17 High19>17
HiLoEV (High)EV (low)Net EV
2121
0.625 865
0.966 620
1.592 485
2120
0.625 865
0.668 592
1.294 457
2021
0.079 010
0.966 620
1.045 630
2119
0.625 865
0.326 657
0.952 522
1921
-0.212 066
0.966 620
0.754 554
2020
0.079 010
0.668 592
0.747 602
2118
0.625 865
0.164 282
0.790 147
1821
-0.426 753
0.966 620
0.539 867
2117
0.625 865
-0.082 425
0.543 440
1920
-0.212 066
0.668 592
0.456 526
2019
0.079 010
0.326 657
0.405 667
1721
-0.618 637
0.966 620
0.347 983
2018
0.079 010
0.164 282
0.243 291
1820
-0.426 753
0.668 592
0.241 840
1919
-0.212 066
0.326 657
0.114 591
1720
-0.618 637
0.668 592
0.049 955
2017
0.079 010
-0.082 425
-0.003 415
021
-1.000 000
0.966 620
-0.033 380
1818
-0.426 753
0.164 282
-0.262 471
1719
-0.618 637
0.326 657
-0.291 979
1917
-0.212 066
-0.082 425
-0.294 491
020
-1.000 000
0.668 592
-0.331 408
210
0.625 865
-1.000 000
-0.374 135
1718
-0.618 637
0.164 282
-0.454 355
1817
-0.426 753
-0.082 425
-0.509 177
019
-1.000 000
0.326 657
-0.673 343
1717
-0.618 637
-0.082 425
-0.701 062
018
-1.000 000
0.164 282
-0.835 718
200
0.079 010
-1.000 000
-0.920 990
017
-1.000 000
-0.082 425
-1.082 425
190
-0.212 066
-1.000 000
-1.212 066
180
-0.426 753
-1.000 000
-1.426 753
170
-0.618 637
-1.000 000
-1.618 637
00
-1.000 000
-1.000 000
-2.000 000
Paigowdan
Paigowdan
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November 20th, 2015 at 10:37:14 AM permalink
Quote: Paradigm

PGD, what is the push/win/loss percentage breakdown if you count winning one side and losing the other side a push?

From a hands per hour count, are you expecting about the same pace as PGP?



Michael, the split decisions occur 57.8% of the time, so it is a pushy game, but the game is considerably faster than PGP. By how much in live play that is still being pinned down, but it is faster. Quicker to set, quicker to deal.
Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.
Paradigm
Paradigm
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November 20th, 2015 at 10:56:03 AM permalink
Dan, good info to have...sounds like It will provide plenty of time on device for the players, I bet the game ends up being quite popular as players will feel like they aren't getting fleeced quickly.

Yet there are errors to be made, so it may hold OK as well...very interesting, will be fun to watch and I look forward to giving it a spin when I am in towm next.
charliepatrick
charliepatrick
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November 20th, 2015 at 11:07:56 AM permalink
Quote: Paigowdan

...house edge....
1. It is actually 3.12% (or 1.56% of the two main bets) with no bonus payout; very close, Don.


I got 3.122785% although I've yet to analyse what strategy is used. Also I got player busting at 0.974% and 21-21 as yours. Thus I'm happy with my average figures, but will see what exceptions there are.
ThatDonGuy
ThatDonGuy
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November 20th, 2015 at 1:36:12 PM permalink
Quote: Paigowdan

We have three house edge options, which were checked by both Steve How and GLI lab math:

1. It is actually 3.12% (or 1.56% of the two main bets) with no bonus payout; very close, Don.
2. It is 2.03% (or 1% on the two main bets) with the extra half-unit bonus on the two-card bet when holding a double-21 hand. This pays 3:2 if the player's two-card side 21 wins, and pays 1:2 on a two-card side tie.

We launched the game with a 2% HE (or 1% EoR), with the half-unit bonus.


I think I see the real problem; I'm apparently using the term "house edge" incorrectly.
When I say 3%, I mean, assuming you bet 50 on the 2-card hand and 50 on the 3-card hand (you have to bet both, right?), for a total bet of 100, you are expected to lose 3 per deal.
My value of 3.03626% most likely translates to 1.51813%.
That's also close to what I get when I run a Monte Carlo simulation on it using this strategy:
These are listed as 3-card hand / 2-card hand

21/21
21/20
21/19
21/18
21/17
20/21
20/20
20/19
20/18
20/17
19/21
18/21
17/21
19/20
18/20
17/20
19/19
19/18
18/19
Fold/21
18/18
19/17
17/19
Fold/20
21/Fold
17/18
18/17
17/17
Fold/19
20/Fold
Fold/18
19/Fold
Fold/17
18/Fold
17/Fold
Fold/Fold

At least, I think I am playing the game right:
1 deck
Dealer must make 2 hands if possible, and make the best possible 3-card hand if there is a choice
Dealer's 3-card hand is compared to the player's 3-card hand; if both are fouled (less than 17 or greater than 21), the player loses
Dealer's 2-card hand is compared to the player's 2-card hand; again, if both are fouled (less than 17), the player loses
If both of the player's hands are 21, the player gets a bonus equal to half of his 2-card bet
Paigowdan
Paigowdan
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November 20th, 2015 at 3:02:14 PM permalink
Yes. Your description is pretty straightforward (could have said pretty and straightforward)..

I'd have the EV table look like this grid (set your hand to the highest or least negative value):

Three card Two Card ======>
x ---0 17 18 19 20 21
0 2.000 -1.082 -0.835 -0.673 -0.331 -0.033
17 -1.618 -0.701 -0.454 -0.291 0.049 0.347
18 -1.426 -0.509 -0.262 -0.885 0.241 0.539
19 -1.212 -0.294 -0.249 0.114 0.456 0.754
20 -0.920 -0.003 0.243 0.405 0.747 1.045
21 -0.374 0.543 0.790 0.952 1.294 1.592
Beware of all enterprises that require new clothes - Henry David Thoreau. Like Dealers' uniforms - Dan.
charliepatrick
charliepatrick
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November 20th, 2015 at 3:28:28 PM permalink
I'm now using this order, this leaves 27 exceptions to this. I think some of the places can be reversed which means your list will have other exceptions (usually more) and also using your original ten-rule strategy changes some of these round.

Sorry I'm using the term Hi and Lo (just habit) for 3-card and 2-card.

My understanding is the dealer makes two hands if possible and within that makes best Hi. Otherwise he makes Best Hi, else makes Best Lo, else busts. Remember if the player busts both hands, it's an immediate total loss for the player.

I can only guess to get a lower House Edge (ignoring the bonus) sometimes you're giving the dealer a worse hand that he should get. Alternatively If you're including a bonus then perhaps the player isn't playing optimally or you're giving the dealer a better option that "House Way" - it's possible you need to factor in some of the exceptions or check the order in your play table.

Obviously when calculating the House Edge in this case one doesn't use any rules, but the computer needs to choose the best of the ten ways to play the hand. I've noted when it's different and listed the exceptions. With your order you'll get a different set of exceptions.

OrderHiLoNotes
12121
22120
32021
42119
52020
61921
72118
81821
92117
101920
112019
122018A - Flipping these leaves 27 exceptions
131721A
141820
151919
161720B - Technically there are less exceptions leaving these two in this order
172017B
181918
19021
201819
211818C - Technically there are less exceptions leaving these two in this order
221917C
231719
24020
25210
261718D - Technically there are less exceptions leaving these two in this order
271817D
281717
29019
30018E - Technically there are far fewer exceptions leaving these two in this order
31200E
32017F - Technically there are far fewer exceptions leaving these two in this order
33190F
34180
35170
3600


Exceptions
H(2 6 1) L(2 2) make 19-0 not 0-17
H(9 9 1) L(9 8) make 19-17 not 18-18
H(1 1 7) L(1 6) make 19-17 not 18-18
H(9 8 2) L(9 8) make 19-17 not 18-18
H(9 7 3) L(9 8) make 19-17 not 18-18
H(8 8 3) L(10 7) make 19-17 not 18-18
H(7 8 4) L(7 10) make 19-17 not 18-18
H(1 1 7) L(9 8) make 19-17 not 18-18
H(8 7 4) L(6 1) make 19-17 not 18-18
H(10 8 1) L(10 8) make 19-18 not 17-20
H(2 7 1) L(2 2) make 20-0 not 0-18
H(7 2 1) L(7 2) make 20-0 not 0-18
H(2 1 7) L(2 1) make 20-0 not 0-18
H(2 7 1) L(2 6) make 20-0 not 0-18
H(2 7 1) L(2 5) make 20-0 not 0-18
H(2 7 1) L(2 4) make 20-0 not 0-18
H(8 1 1) L(8 9) make 20-17 not 17-20
H(10 9 1) L(10 7) make 20-17 not 17-20
H(10 8 2) L(10 7) make 20-17 not 17-20
H(9 9 2) L(6 1) make 20-17 not 17-20
H(1 10 9) L(1 6) make 20-17 not 17-20
H(7 2 1) L(9 8) make 20-17 not 17-20
H(8 1 1) L(8 10) make 20-18 not 17-21
H(10 5 5) L(10 9) make 20-19 not 19-20
H(10 7 3) L(10 9) make 20-19 not 19-20
H(10 6 4) L(10 9) make 20-19 not 19-20
charliepatrick
charliepatrick
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November 20th, 2015 at 3:52:21 PM permalink
Quote: Paigowdan

...the EV table...

I started with exactly the same table - so this is a good check. Also this method generated my initial order for the player's action. However when I analysed all the hands (i.e. card dependent) then there were five flips in the order.
20 20 > 19 21 20 18 >17 21 19 18 > 0 21 19 17 > 17 19 17 17 > 0 19
As I've just said comparing it with Don's list, there are some decisions where it's nearly 50-50 which way round you put them - I played around and listed them in the order which gives the fewest exceptions. However, like Pai Gow Tiles, this might be a perfect strategy, but in practice a simpler one might be easier to play.

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