Wizard
Administrator
Wizard
  • Threads: 1496
  • Posts: 26619
Joined: Oct 14, 2009
October 10th, 2012 at 4:51:39 PM permalink
I just created a new page on World Poker Tour Multi-Strike Super Video Hold 'Em, but I'm going to just call it "Super Video Hold 'Em Multi-Strike."

At this point I don't have any strategy to the game. Maybe if it takes off I'll take the bother. However, if any ambitions member wishes to calculate it himself, I'd be more than happy to use it on my site, with full credit to the creator of course.

Any comments, questions, corrections, etc.?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
rdw4potus
rdw4potus
  • Threads: 80
  • Posts: 7237
Joined: Mar 11, 2010
October 10th, 2012 at 4:56:35 PM permalink
Looks like the same paytable is listed in each column of that table.
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
Pokeraddict
Pokeraddict
  • Threads: 36
  • Posts: 786
Joined: Feb 21, 2012
October 10th, 2012 at 5:08:08 PM permalink
It has been at Red Rock for probably a year if not longer by the cafe. The game was not too exciting but I think the way to play beyond pairs being superior to almost anything else is that straight and flush draws are far more important than high card. For example, A6 offsuit is crap compared to 97s. I think even 96 and 95 offsuit are better than two cards that cannot make a straight together.

The bad beat jackpot makes the higher pairs more valuable because otherwise you would trash AA in favor of many other pairs because you would have more straight draws. 5's through 10's are basically the same hand.

If I remember correctly the two cards you throw away can show up on your board so analyzing burnt flush and straight cards is pointless. I won't swear on that though, I may be wrong, it has been a while since I played it but I remember thinking several times "I threw that card away and it came back on the board." When I look at your screen shot I do not even see a duplicated card. Maybe I just was not following it well and missing suits. I was playing pennies and just trying the game out.

Any way to confirm the cards there and whether they can come back or if it deals all the cards out first?

I am sure a lot of people just pick the highest two cards but I cannot see how that is the winning strategy. It isn't like you have to beat the dealer, you just have to make a hand.
Wizard
Administrator
Wizard
  • Threads: 1496
  • Posts: 26619
Joined: Oct 14, 2009
October 10th, 2012 at 5:11:13 PM permalink
Potus, thanks for that catch, you were right.

The two cards you don't pick are put back in the deck. I'm 99.54% sure each level is dealt from a separate deck. Agreed that playing high cards, as in regular video poker, is not a priority in this game. Hopefully somebody will feel inspired to work out a strategy.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
tringlomane
tringlomane
  • Threads: 8
  • Posts: 6281
Joined: Aug 25, 2012
October 11th, 2012 at 10:41:28 AM permalink
Quote: Wizard

Each pay table is identified by what a full house, flush, and straight pay respectively for a 2-coin per hand bet.



Looking at the paytables, however, these seem to be the values that Quads 2-K, full houses, and flushes pay for 2 coins bet.

The link to this game on the main video poker page is dead. Also within the MS Video Holdem webpage, you have a link to Super Video Hold 'Em which is also misdirected. I found all data about Super Video Hold 'Em in the Video Hold 'em webpage.
DJTeddyBear
DJTeddyBear 
  • Threads: 207
  • Posts: 11006
Joined: Nov 2, 2009
October 11th, 2012 at 3:00:05 PM permalink
Quote: Wizard

I just created a new page on World Poker Tour Multi-Strike Super Video Hold 'Em, but I'm going to just call it "Super Video Hold 'Em Multi-Strike."


Not for nothing, but I don't think you should rename it. Not only is it not your place, but if anyone who plays it wanted to read about it on your site, what are they gonna look for?

Sure, leave in the comment about it being a mouthful, but don't rename it.

Interestingly, I notice that you used the long name in the html title, so why not in that black bar heading?



Quote:

I got a flush on level four, which pays 2.5x for the flush and 8x for the flush,


That should be "Level 4".



What are all those question marks on the multipliers and free ride tables? Is that info that IGT didn't provide? If so, I wonder why they provided all 5 returns....



All in all, a nice write up.

And nice hit on that demo hand, turning 40 into 330!
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
October 24th, 2012 at 10:01:38 AM permalink
I have come up with a strategy for the 10-6-5 paytable. The strategy tables below represent a power ranking for each starting hand. The strategy changes slightly depending on which level you are on. The reason is that at lower levels, it is sometimes advantageous to choose a hand with a lower return but with a higher win%, which will permit the player to continue to the higher paying hands more frequently. To use the charts, choose the chart for your current level and look up both starting hands and choose the one with the lower power ranking. If you have a free ride, always use the chart for Level 4.

The only problem that I have is that the return I have calculated is significantly lower than the return stated by IGT. I calculate an optimal return of 85.26% while IGT has reported a return of 100.32%.

Some background information: I started by calculating the return for a standard Super Video Hold 'Em paytable, for which the Wizard has posted an analysis here: Super Video Hold 'Em. My results and strategy table are consistent with his. With confidence in these results, I was able to then calculate the optimal strategy at each level and the probability of reaching each level. In my experience in analyzing other Multi-Strike games, I expected the probability of continuing to each successive level to be just over 50% and I expected the overall return to be just slightly higher than the return for Level 4 (the amount in the table below divided by 8, which is the level multiplier). The games are designed to give the player a slight advantage for playing each successive level.

The strategy presented is rather cumbersome, so it should be noted that the player can the strategy for Level 2 always at a return of 85.2436753%. This will cost the player 0.0206481%, which is equivalent to 1 credit per hour if the player wagers 40 credits per game and plays 120 games per hour.

I intented to include detailed hit information, but it made my post too long.

Return Summary:
Free Ride Return No Free Ride Return Average Return p(continue to next level p(playing level) EV for Level
Level 4 6.75344 6.75344 0.12844 0.867413
Level 3 3.37672 3.376205 3.376278 0.508633 0.25252 0.852578
Level 2 1.68836 1.687393 1.68752 0.503053 0.501975 0.847093
Level 1 0.84418 0.843386 0.843489 0.501975 1 0.843489
Overall Return 0.852643




Level 1 Strategy - No Free Ride
Suited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 45
4 43 33
5 40 30 19
6 62 42 32 21
7 101 53 39 27 22
8 88 88 49 35 28 22
9 88 73 73 46 36 28 22
T 81 68 64 64 44 34 26 20
J 97 81 68 64 71 48 38 31 18
Q 104 97 81 68 71 85 51 41 25 15
K 108 104 97 81 85 85 100 61 37 16 17
A 67 63 60 50 95 77 77 95 47 14 7 6

Unsuited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 121
4 117 103
5 113 92 54
6 134 115 94 56
7 164 127 111 76 57
8 156 153 123 107 79 57
9 156 143 141 119 109 79 57
T 148 137 131 130 118 106 75 55
J 160 148 137 131 140 122 110 93 52
Q 165 160 148 137 142 152 126 114 91 102
K 167 165 160 148 154 154 163 133 112 116 120
A 145 136 129 125 158 146 146 158 124 128 135 144

Pairs

2s 3s 4s 5s 6s-9s Ts Js Qs Ks As Red As
13 12 11 9 10 8 3 5 4 2 1


Level 2 Strategy - No Free Ride
Suited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 44
4 43 33
5 40 30 19
6 62 42 32 21
7 101 52 39 27 22
8 88 88 49 35 28 22
9 88 73 73 46 36 28 22
T 79 68 64 64 45 34 26 20
J 97 79 68 64 71 48 38 31 18
Q 104 97 79 68 71 85 51 41 25 15
K 106 104 97 79 85 85 100 61 37 16 17
A 67 63 53 50 91 75 75 91 47 8 7 6

Unsuited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 121
4 117 103
5 113 94 55
6 134 115 96 57
7 164 127 111 78 58
8 156 153 123 108 83 58
9 156 143 141 119 109 83 58
T 148 137 131 130 118 107 77 56
J 160 148 137 131 140 122 110 95 54
Q 165 160 148 137 142 152 126 114 93 102
K 167 165 160 148 154 154 163 133 112 116 120
A 145 136 129 125 158 146 146 158 124 128 135 144

Pairs

2s 3s 4s 5s 6s-9s Ts Js Qs Ks As Red As
14 13 12 10 11 9 3 5 4 2 1


Level 3 Strategy - No Free Ride
Suited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 44
4 43 33
5 40 30 19
6 55 42 32 21
7 97 52 39 27 22
8 84 84 49 35 28 22
9 84 73 73 47 37 28 22
T 77 68 65 65 46 34 26 20
J 93 77 68 65 71 48 38 31 18
Q 102 93 77 68 71 81 51 41 25 9
K 106 102 93 77 81 81 96 54 36 10 15
A 64 56 53 50 88 75 75 88 45 8 7 6

Unsuited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 121
4 117 105
5 113 99 58
6 134 115 101 60
7 164 127 111 90 61
8 156 153 123 108 91 61
9 156 143 141 119 109 91 61
T 148 137 131 130 118 107 87 59
J 160 148 137 131 140 122 110 100 57
Q 165 160 148 137 142 152 126 114 98 104
K 167 165 160 148 154 154 163 133 112 116 120
A 145 136 129 125 158 146 146 158 124 128 135 144

Pairs

2s 3s 4s 5s 6s-9s Ts Js Qs Ks As Red As
17 16 14 12 13 11 3 5 4 2 1


Level 4 Strategy (to be used with free ride games as well)
Suited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 45
4 43 33
5 40 30 19
6 56 42 32 21
7 93 53 39 27 22
8 86 86 50 36 28 22
9 86 75 75 47 37 28 22
T 79 70 58 58 46 35 26 20
J 89 79 70 58 73 49 38 31 18
Q 98 89 79 70 73 83 52 41 25 9
K 104 98 89 79 83 83 92 55 34 10 11
A 57 54 51 48 77 68 68 77 44 8 7 6

Unsuited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 125
4 119 106
5 115 103 64
6 136 114 102 63
7 164 129 111 95 65
8 158 155 124 108 96 65
9 158 147 145 118 109 96 65
T 151 142 133 131 117 107 94 62
J 161 151 142 133 141 123 110 101 61
Q 165 161 151 142 146 150 128 113 100 105
K 167 165 161 151 156 156 160 135 112 116 122
A 138 132 127 121 148 139 139 148 120 126 130 137

Pairs

2s 3s 4s 5s 6s-9s Ts Js Qs Ks As Red As
17 16 15 13 14 12 3 5 4 2 1
I heart Crystal Math.
miplet
miplet
  • Threads: 5
  • Posts: 2116
Joined: Dec 1, 2009
October 24th, 2012 at 10:48:33 AM permalink
I want to be just like CrystalMath when I grow up. I just barely got started with my analysis. I think I'll continue to get some practice.
溺an Babes #AxelFabulous
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
October 24th, 2012 at 11:31:17 AM permalink
Quote: miplet

I want to be just like CrystalMath when I grow up. I just barely got started with my analysis. I think I'll continue to get some practice.



Thanks, miplet! Truth is, there are times that I envy the skills of many on this board, including you.
I heart Crystal Math.
JB
Administrator
JB
  • Threads: 334
  • Posts: 2089
Joined: Oct 14, 2009
October 25th, 2012 at 5:30:36 PM permalink
Here are my results for the same paytable that CrystalMath analyzed:

Level NFR Return NFR Proceed FR Prob NFR Prob Local Return Level Prob Global Return
8x 0.844180 0.000000 0.000 1.000 6.753440 0.128440 0.216853
4x 0.844051 0.427311 0.142 0.858 3.376278 0.252520 0.213145
2x 0.843696 0.427481 0.132 0.868 1.687520 0.501975 0.211773
1x 0.843386 0.427557 0.130 0.870 0.843490 1.000000 0.210872
Total  0.852643


NFR Return = Return from Non-Free-Ride hands
NFR Proceed = Probability of proceeding to the next level on Non-Free-Ride hands
FR Prob = Probability of a Free Ride hand
NFR Prob = Probability of a Non-Free-Ride hand
Local Return = the multiplied return for the level
Level Prob = the probability of reaching the level
Global Return = the contribution towards the game's overall return from the level

So both CrystalMath and I have calculated a return which is about 15% lower than what IGT claims.
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
October 26th, 2012 at 9:03:28 AM permalink
I just realized that I had used 0.130, 0.133, and 0.143 for the free ride probabilities, when they should have been 0.130, 0.132, and 0.142.

My updated return is 85.2643234%, which is still slightly higher than JB.
I heart Crystal Math.
JB
Administrator
JB
  • Threads: 334
  • Posts: 2089
Joined: Oct 14, 2009
October 26th, 2012 at 3:43:11 PM permalink
After recalculating my figures from a glitch that CrystalMath helped me find, I now agree with his figures. My prior post has been updated accordingly.

We both agree that the overall return is 85.2643234335895%.
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
October 26th, 2012 at 3:50:28 PM permalink
I corrected my strategy table post to reflect the correct chance of free rides.
I heart Crystal Math.
tringlomane
tringlomane
  • Threads: 8
  • Posts: 6281
Joined: Aug 25, 2012
October 27th, 2012 at 4:51:11 PM permalink
The fact the math is that off on a published game saddens me. It would also be illegal in Kansas...haha Great work, guys!
Wizard
Administrator
Wizard
  • Threads: 1496
  • Posts: 26619
Joined: Oct 14, 2009
October 27th, 2012 at 5:13:12 PM permalink
This bothers me that too separate good minds agree with each other, but not IGT, on the game. I've never known IGT to make a math error before. It would seem there is some rule to the game that I'm not aware of, that works in the player's favor.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Wizard
Administrator
Wizard
  • Threads: 1496
  • Posts: 26619
Joined: Oct 14, 2009
October 31st, 2012 at 9:07:15 AM permalink
I played the Multi-Strike game at the Red Rock for about half an hour, so see if there was anything I was missing, but nothing jumped out at me. It was probably just luck, but the Free Ride cards seems to come up more often than the stated probabilities.

I added some pictures of the rule screens to my Super Video Hold 'Em Multi-Strike, should that help.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
October 31st, 2012 at 9:32:01 AM permalink
Thanks for the screen shots.

Here is the return that I get for this game: 0.961585867

Matching up the multipliers, free ride probabilities, and return, this is the paytable you have listed as 8-5-4.

But, the pays are different:

win categoryactual payspays listed on woo
royal on the board 1000 1000
royal 100 100
straight flush 50 50
4 aces 25 25
quads 10 4
full house 4 2.5
flush 2.5 2
straight 2 2
trips 1.5 1.5
two pair 1 1


I'm thinking it's just a clerical error.
I heart Crystal Math.
Wizard
Administrator
Wizard
  • Threads: 1496
  • Posts: 26619
Joined: Oct 14, 2009
October 31st, 2012 at 10:10:24 AM permalink
Quote: CrystalMath

I'm thinking it's just a clerical error.



You're right -- it was. I hope I didn't put you and Miplet to too much wasted work.

That said, can I trouble you for the strategy based on the corrected pay table?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
October 31st, 2012 at 10:19:50 AM permalink
Quote: Wizard

You're right -- it was. I hope I didn't put you and Miplet to too much wasted work.

That said, can I trouble you for the strategy based on the corrected pay table?



Yes. The strategy is below. If the player chooses to use a single strategy table, they should use the table for level 2. This will give a return of 96.1425658%, which will cost the player 0.0160209% over the optimal strategy. This is equivalent to 0.77 credits per hour with 40 credits wagered and 120 games per hour.

Free Ride Return No Free Ride Return Average Return p(continue to next level p(playing level) EV for Level
Level 4 7.598442 7.598442 0.128451 0.976025
Level 3 3.799221 3.798359 3.798477 0.505841 0.253935 0.964565
Level 2 1.899611 1.898769 1.898882 0.504202 0.503637 0.956346
Level 1 0.949805 0.949347 0.949408 0.503637 1 0.949408
Overall Return 0.961586



Level 1 Strategy - No Free Ride
Suited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 46
4 43 33
5 40 30 19
6 62 42 32 21
7 101 56 39 27 22
8 88 88 49 35 28 22
9 88 73 73 45 36 28 22
T 81 68 64 64 44 34 25 20
J 97 81 68 64 71 48 37 31 18
Q 104 97 81 68 71 85 54 41 26 15
K 109 104 97 81 85 85 100 61 38 16 17
A 67 63 60 50 95 79 79 95 47 7 8 6

Unsuited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 121
4 117 103
5 113 92 52
6 134 115 94 55
7 164 127 111 76 57
8 156 153 123 107 77 57
9 156 143 141 119 108 77 57
T 148 137 131 130 118 106 75 53
J 160 148 137 131 140 122 110 93 51
Q 165 160 148 137 142 152 126 114 91 102
K 167 165 160 148 154 154 163 133 112 116 120
A 145 136 129 125 158 146 146 158 124 128 135 144

Pairs

2s 3s 4s 5s 6s-9s Ts Js Qs Ks As Red As
14 13 12 10 11 9 3 5 4 2 1


Level 2 Strategy - No Free Ride
Suited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 44
4 43 33
5 40 30 19
6 62 42 32 21
7 101 52 39 27 22
8 88 88 49 35 28 22
9 88 73 73 46 36 28 22
T 81 68 64 64 45 34 26 20
J 97 81 68 64 71 48 38 31 18
Q 104 97 81 68 71 85 51 41 25 15
K 106 104 97 81 85 85 100 61 37 16 17
A 67 63 57 50 92 75 75 92 47 7 8 6

Unsuited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 121
4 117 103
5 113 94 54
6 134 115 96 56
7 164 127 111 78 58
8 156 153 123 108 79 58
9 156 143 141 119 109 79 58
T 148 137 131 130 118 107 77 55
J 160 148 137 131 140 122 110 95 53
Q 165 160 148 137 142 152 126 114 91 102
K 167 165 160 148 154 154 163 133 112 116 120
A 145 136 129 125 158 146 146 158 124 128 135 144

Pairs

2s 3s 4s 5s 6s-9s Ts Js Qs Ks As Red As
14 13 12 10 11 9 3 5 4 2 1


Level 3 Strategy - No Free Ride
Suited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 44
4 43 33
5 40 30 19
6 55 42 32 21
7 97 52 39 27 22
8 84 84 49 35 28 22
9 84 73 73 47 36 28 22
T 77 68 64 64 46 34 26 20
J 93 77 68 64 71 48 38 31 18
Q 102 93 77 68 71 81 51 41 25 9
K 106 102 93 77 81 81 96 54 37 16 17
A 67 57 53 50 91 75 75 91 45 7 8 6

Unsuited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 121
4 117 105
5 113 99 58
6 134 115 101 60
7 164 127 111 88 61
8 156 153 123 108 89 61
9 156 143 141 119 109 89 61
T 148 137 131 130 118 107 87 59
J 160 148 137 131 140 122 110 100 56
Q 165 160 148 137 142 152 126 114 98 104
K 167 165 160 148 154 154 163 133 112 116 120
A 145 136 129 125 158 146 146 158 124 128 135 144

Pairs

2s 3s 4s 5s 6s-9s Ts Js Qs Ks As Red As
15 14 13 11 12 10 3 5 4 2 1


Level 4 Strategy (to be used with free ride games as well)
Suited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 45
4 43 33
5 40 30 19
6 56 42 32 21
7 93 53 39 27 22
8 84 84 50 36 28 22
9 84 73 73 47 37 28 22
T 77 68 58 58 46 35 26 20
J 89 77 68 58 71 49 38 31 18
Q 98 89 77 68 71 81 52 41 25 9
K 104 98 89 77 81 81 92 55 34 10 11
A 57 54 51 48 87 75 75 87 44 7 8 6

Unsuited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 125
4 119 106
5 115 103 64
6 135 114 102 63
7 164 128 111 95 65
8 158 153 123 108 96 65
9 158 144 141 118 109 96 65
T 149 138 131 130 117 107 94 62
J 161 149 138 131 137 121 110 101 61
Q 165 161 149 138 142 148 126 113 100 105
K 167 165 161 149 154 154 160 133 112 116 120
A 145 136 129 124 156 146 146 156 122 127 134 143

Pairs

2s 3s 4s 5s 6s-9s Ts Js Qs Ks As Red As
17 16 15 13 14 12 3 5 4 2 1
I heart Crystal Math.
Wizard
Administrator
Wizard
  • Threads: 1496
  • Posts: 26619
Joined: Oct 14, 2009
October 31st, 2012 at 10:26:46 AM permalink
Thanks, this is great! I hate to push my luck, but I think any player with the dedication to use such a strategy will be too smart to play the 96.16% pay table. Chances are nobody is going to offer the 100.3%. So, can I trouble you for the same stuff, but for the 99.51% pay table?

Also, I plan to give you full credit on my site. To whom, exactly, should I give the credit?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
October 31st, 2012 at 10:58:14 AM permalink
Here it is:

The best single table strategy to use is the 3rd level strategy. This will give a return of 99.4985899%.

I would prefer that you credit Daniel Dale.

Free Ride Return No Free Ride Return Average Return p(continue to next level p(playing level) EV for Level
Level 4 7.773979 7.773979 0.133008 1.034005
Level 3 3.886989 3.886004 3.886163 0.519588 0.255988 0.994812
Level 2 1.943495 1.942557 1.942688 0.507068 0.50484 0.980747
Level 1 0.971747 0.970963 0.971069 0.50484 1 0.971069
Overall Return 0.995158



Level 1 Strategy - No Free Ride
Suited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 46
4 43 33
5 40 30 19
6 62 42 32 21
7 101 56 38 26 22
8 88 88 49 35 28 22
9 88 73 73 45 36 28 22
T 81 68 64 64 44 34 25 20
J 97 81 68 64 71 48 37 31 18
Q 104 97 81 68 71 85 55 41 27 15
K 109 104 97 81 85 85 100 61 39 16 17
A 67 63 60 50 95 79 79 95 47 14 7 6

Unsuited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 121
4 117 103
5 113 92 52
6 134 115 94 54
7 164 127 111 76 57
8 156 153 123 107 77 57
9 156 143 141 119 108 77 57
T 148 137 132 130 118 106 75 53
J 160 148 137 132 140 122 110 93 51
Q 165 160 148 137 142 152 126 114 91 102
K 167 165 160 148 154 154 163 131 112 116 120
A 145 136 129 125 158 146 146 158 124 128 135 144

Pairs

2s 3s 4s 5s 6s-9s Ts Js Qs Ks As Red As
13 12 11 9 10 8 3 5 4 2 1


Level 2 Strategy - No Free Ride
Suited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 44
4 43 33
5 40 30 19
6 62 42 32 21
7 101 52 39 27 22
8 88 88 49 35 28 22
9 88 73 73 46 36 28 22
T 81 68 64 64 45 34 26 20
J 97 81 68 64 71 48 38 31 18
Q 104 97 81 68 71 85 51 41 25 15
K 106 104 97 81 85 85 100 61 37 16 17
A 67 63 60 50 94 77 77 94 47 8 7 6

Unsuited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 121
4 117 103
5 113 92 54
6 134 115 96 56
7 164 127 111 76 57
8 156 153 123 108 79 57
9 156 143 141 119 109 79 57
T 148 137 132 130 118 107 75 55
J 160 148 137 132 140 122 110 93 53
Q 165 160 148 137 142 152 126 114 91 102
K 167 165 160 148 154 154 163 131 112 116 120
A 145 136 129 125 158 146 146 158 124 128 135 144

Pairs

2s 3s 4s 5s 6s-9s Ts Js Qs Ks As Red As
14 13 12 10 11 9 3 5 4 2 1


Level 3 Strategy - No Free Ride
Suited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 44
4 43 33
5 40 30 19
6 56 42 32 21
7 98 52 39 27 22
8 84 84 49 35 28 22
9 84 73 73 47 36 28 22
T 77 68 64 64 46 34 26 20
J 93 77 68 64 71 48 38 31 18
Q 102 93 77 68 71 81 51 41 25 9
K 106 102 93 77 81 81 96 54 37 16 17
A 67 63 53 50 91 75 75 91 45 8 7 6

Unsuited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 121
4 117 105
5 113 99 57
6 134 115 101 59
7 164 127 111 88 60
8 156 153 123 108 89 60
9 156 143 141 119 109 89 60
T 148 137 132 130 118 107 87 58
J 160 148 137 132 140 122 110 100 55
Q 165 160 148 137 142 152 126 114 97 104
K 167 165 160 148 154 154 163 131 112 116 120
A 145 136 129 125 158 146 146 158 124 128 135 144

Pairs

2s 3s 4s 5s 6s-9s Ts Js Qs Ks As Red As
15 14 13 11 12 10 3 5 4 2 1


Level 4 Strategy (to be used with free ride games as well)
Suited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 45
4 43 33
5 40 30 19
6 55 42 32 21
7 94 52 39 27 22
8 84 84 49 36 28 22
9 84 73 73 47 37 28 22
T 77 68 62 62 46 35 26 20
J 89 77 68 62 71 48 38 31 18
Q 98 89 77 68 71 81 51 41 25 9
K 104 98 89 77 81 81 92 54 34 10 11
A 57 56 53 50 87 75 75 87 44 8 7 6

Unsuited

Higher Lower Card
Card 2 3 4 5 6 7 8 9 T J Q K
3 121
4 117 106
5 114 102 60
6 134 115 103 61
7 164 127 111 95 65
8 156 153 123 108 96 65
9 156 143 141 119 109 96 65
T 148 137 132 130 118 107 93 59
J 160 148 137 132 140 122 110 101 58
Q 165 160 148 137 142 152 126 113 100 105
K 167 165 160 148 154 154 163 131 112 116 120
A 145 136 129 125 158 146 146 158 124 128 135 144

Pairs

2s 3s 4s 5s 6s-9s Ts Js Qs Ks As Red As
17 16 15 13 14 12 3 5 4 2 1
I heart Crystal Math.
Wizard
Administrator
Wizard
  • Threads: 1496
  • Posts: 26619
Joined: Oct 14, 2009
November 1st, 2012 at 7:48:27 AM permalink
I just posted your tables on my Odds site. Many thanks again!
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
November 1st, 2012 at 10:01:16 AM permalink
Quote: WOO


The expected return following this strategy is 99.50%, just 0.01% less than optimal. The reason it is not exactly optimal is there are some obscure penalty card situations. If the user wishes to use just a single level strategy for all levels, the best one to use is for level 3.



You are welcome.

Actually, using all 4 tables is optimal. Using just the level 3 table will result in a 99.50% return.
I heart Crystal Math.
Wizard
Administrator
Wizard
  • Threads: 1496
  • Posts: 26619
Joined: Oct 14, 2009
November 1st, 2012 at 10:10:35 AM permalink
Quote: CrystalMath

Actually, using all 4 tables is optimal. Using just the level 3 table will result in a 99.50% return.



Do they put the unchosen two cards back in the deck? I thought they didn't, thus there could be some obscure penalty card situations.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
CrystalMath
CrystalMath
  • Threads: 8
  • Posts: 1911
Joined: May 10, 2011
November 1st, 2012 at 10:26:49 AM permalink
Quote: Wizard

Do they put the unchosen two cards back in the deck? I thought they didn't, thus there could be some obscure penalty card situations.



They do put the unchosen cards back in the deck. I just verified on the help screens.
I heart Crystal Math.
  • Jump to: