Analyzing Magic Deal
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March 4th, 2017 at 8:08:10 PM
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There is already a Magic Deal thread for discussion about the game itself.
I'd like to create a separate thread for the analysis of the game.
To start, to ensure I'm scoring hands correctly, here is the poker value of each possible hand on the deal, according to the number of Magic Cards. How does that stack up to your scoring?
Please assuming the player is playing Double Double Bonus. The pertinent fact there is a straight flush pays less than all four of a kinds.
Also, if the player has MC-MC-MC-6h-10h, for example, then the hand could be scored as either a straight flush or four 5-K, both of which pay 50. For such hands, please score them as a straight flush.
Table 1 -- One Magic Deal card
Table 2 -- Two Magic Deal cards
Table 3 -- Three Magic Deal cards
The question for the poll is do you agree with my results?
p.s. Sorry, I forgot an option for agreeing with none. If that is the case, please for anarchist.
I'd like to create a separate thread for the analysis of the game.
To start, to ensure I'm scoring hands correctly, here is the poker value of each possible hand on the deal, according to the number of Magic Cards. How does that stack up to your scoring?
Please assuming the player is playing Double Double Bonus. The pertinent fact there is a straight flush pays less than all four of a kinds.
Also, if the player has MC-MC-MC-6h-10h, for example, then the hand could be scored as either a straight flush or four 5-K, both of which pay 50. For such hands, please score them as a straight flush.
Table 1 -- One Magic Deal card
| Hand | Count |
|---|---|
| Royal flush | 20 |
| Straight flush | 144 |
| Four A + 2-4 | 49 |
| Four 2-4 + A-4 | 147 |
| Four A + 5-K | 144 |
| Four 2-4 + 5-K | 432 |
| Four 5-K | 1737 |
| Full house | 2808 |
| Flush | 2696 |
| Straight | 8820 |
| Three of a kind | 82248 |
| Two pair | 0 |
| Jacks or better | 144204 |
| Junk | 27276 |
Table 2 -- Two Magic Deal cards
| Hand | Count |
|---|---|
| Royal flush | 40 |
| Straight flush | 216 |
| Four A + 2-4 | 76 |
| Four 2-4 + A-4 | 228 |
| Four A + 5-K | 216 |
| Four 2-4 + 5-K | 648 |
| Four 5-K | 2628 |
| Full house | 0 |
| Flush | 888 |
| Straight | 3840 |
| Three of a kind | 13320 |
| Two pair | 0 |
| Jacks or better | 0 |
| Junk | 0 |
Table 3 -- Three Magic Deal cards
| Hand | Count |
|---|---|
| Royal flush | 40 |
| Straight flush | 80 |
| Four A + 2-4 | 54 |
| Four 2-4 + A-4 | 66 |
| Four A + 5-K | 128 |
| Four 2-4 + 5-K | 432 |
| Four 5-K | 526 |
| Full house | 0 |
| Flush | 0 |
| Straight | 0 |
| Three of a kind | 0 |
| Two pair | 0 |
| Jacks or better | 0 |
| Junk | 0 |
The question for the poll is do you agree with my results?
p.s. Sorry, I forgot an option for agreeing with none. If that is the case, please for anarchist.
Last edited by: Wizard on Mar 5, 2017
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
March 4th, 2017 at 8:58:32 PM
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Looking at the table for 3 magic cards, shouldn't the Royal Flush count be 40?
* combin(4,1) = 4 suits
* combin(5,2) = 10 rank combinations per suit (AK, AQ, AJ, AT, KQ, KJ, KT, QJ, QT, JT)
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= 40 ?
* combin(4,1) = 4 suits
* combin(5,2) = 10 rank combinations per suit (AK, AQ, AJ, AT, KQ, KJ, KT, QJ, QT, JT)
---------------------------------------------------------------------------------------------
= 40 ?
March 4th, 2017 at 9:52:56 PM
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Quote: JBLooking at the table for 3 magic cards, shouldn't the Royal Flush count be 40?
You're absolutely right. One character in the program was wrong.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
March 5th, 2017 at 7:29:40 PM
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With three wilds I get 80 SFs : K9 Q&9-8 J&9-7 T&9-6 9&8-5 8&7-5 7&6-5 65 perms * 4, and 4(K-5) as 20 less.
This means the average payout is 96 and you should hold any Ace. I've also got you hold any 4 3 2 - I suppose this guarantees you 80 - anyone else agree?
This means the average payout is 96 and you should hold any Ace. I've also got you hold any 4 3 2 - I suppose this guarantees you 80 - anyone else agree?
Last edited by: charliepatrick on Mar 5, 2017
March 5th, 2017 at 7:45:33 PM
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Quote: charliepatrickI get 80 SFs : K9 Q&9-8 J&9-7 T&9-6 9&8-5 8&7-5 7&6-5 65 perms * 4, and 4(K-5) as 20 less.
I assume you're referring to the case with three Magic Cards. This is based on 9-6 double double bonus, where those two hands pay the same. I scored them as straight flushes, as mentioned in the OP. Does that explain our difference?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
March 5th, 2017 at 8:03:08 PM
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I've just realised all Straight Flushes can be four of a kind (unless they're one of the higher paying ones using A234), however my spreadsheet just worked its way along the possible payouts putting SF before 4(K-5).Quote: WizardI assume you're referring to the case with three Magic Cards. This is based on 9-6 double double bonus, where those two hands pay the same. I scored them as straight flushes, as mentioned in the OP. Does that explain our difference?
Thus this part covers all hands using suited cards King thru 5 (and not being Royal Flush, so excludes KQ KJ KT QJ QT JT).
King can be with a 9 (1 perm)
Queen can be with a 9 or 8 (2 perms)
Jack can be with a 9 8 or 7 (3 perms)
Ten can be with a 9 8 7 or 6 (4 perms)
Nine can be with a 8 7 6 or 5 (4 perms)
Eight can be with a 7 6 or 5 (3 perms)
Seven can be with a 6 or 5 (2 perms)
Six can be with a 5 (1 perms)
20 perms, four suits = 80.
March 5th, 2017 at 9:58:05 PM
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You're right. I had a bug in my code for scoring a straight flush with three Magic Cards. Thank you.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
March 6th, 2017 at 2:21:36 PM
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I just got the Magic Card probabilities from the mathematician at VideoPoker.com. Here they are:
| Game | Pay table | 1 MC | 2 MC | 3 MC | Base Return | Feature Return |
|---|---|---|---|---|---|---|
| Double Double Bonus | 9-6 | 8.40% | 1.00% | 0.10% | 98.981% | 99.398% |
| Double Double Bonus | 9-5 | 8.40% | 1.00% | 0.10% | 97.873% | 98.778% |
| Double Double Bonus | 8-5 | 8.30% | 1.00% | 0.10% | 96.786% | 97.898% |
| Double Double Bonus | 7-5 | 8.00% | 1.00% | 0.10% | 96.497% | 96.497% |
| Double Double Bonus | 7-5 | 7.80% | 1.00% | 0.10% | 95.712% | 95.966% |
| Triple Double Bonus | 9-6 | 2.96% | 1.00% | 0.10% | 98.154% | 99.045% |
| Triple Double Bonus | 9-6 | 2.71% | 1.00% | 0.10% | 98.154% | 98.232% |
| Triple Double Bonus | 9-5 | 2.71% | 1.00% | 0.10% | 97.020% | 97.645% |
| Triple Double Bonus | 8-5 | 2.61% | 1.00% | 0.10% | 95.969% | 96.770% |
| Triple Double Bonus | 7-5 | 2.46% | 1.00% | 0.10% | 94.918% | 95.739% |
| Bonus Poker | 7-5 | 10.80% | 2.00% | 0.20% | 98.015% | 99.079% |
| Bonus Poker | 7-5 | 10.60% | 2.00% | 0.20% | 98.015% | 98.739% |
| Bonus Poker | 6-5 | 10.10% | 2.00% | 0.20% | 96.869% | 97.229% |
| Bonus Poker | 6-5 | 9.92% | 2.00% | 0.20% | 96.869% | 96.926% |
| Double Bonus | 10-6-5 | 9.60% | 1.00% | 0.15% | 98.885% | 99.317% |
| Double Bonus | 9-6-5 | 9.63% | 1.00% | 0.15% | 97.806% | 98.766% |
| Double Bonus | 9-6-4 | 9.64% | 1.00% | 0.15% | 96.375% | 97.793% |
| Double Bonus | 9-5-4 | 9.65% | 1.00% | 0.13% | 95.274% | 96.091% |
| Double Bonus | 8-5-4 | 9.64% | 1.00% | 0.13% | 94.190% | 95.443% |
| Jacks or Better | 8-6 | 10.85% | 2.60% | 0.20% | 98.393% | 99.055% |
| Jacks or Better | 8-5 | 10.90% | 2.60% | 0.20% | 97.298% | 98.428% |
| Jacks or Better | 7-5 | 10.90% | 2.60% | 0.20% | 96.147% | 97.747% |
| Jacks or Better | 7-5 | 10.90% | 2.50% | 0.20% | 96.147% | 96.849% |
| Jacks or Better | 6-5 | 10.95% | 2.40% | 0.20% | 94.996% | 95.344% |
| Bonus Poker Deluxe | 8-6 | 9.30% | 1.00% | 0.11% | 98.493% | 99.134% |
| Bonus Poker Deluxe | 8-5 | 9.30% | 1.00% | 0.11% | 97.401% | 98.520% |
| Bonus Poker Deluxe | 7-5 | 9.30% | 1.00% | 0.10% | 96.253% | 97.172% |
| Bonus Poker Deluxe | 7-5 | 9.12% | 1.00% | 0.10% | 96.253% | 96.697% |
| Bonus Poker Deluxe | 6-5 | 9.02% | 1.00% | 0.10% | 95.361% | 95.921% |
| Deuces Wild | 25-15-9 | 12.00% | 2.40% | 0.20% | 98.913% | 99.229% |
| Deuces Wild | 20-12-10 | 12.10% | 2.40% | 0.20% | 97.579% | 98.203% |
| Deuces Wild | 25-16-13 | 12.00% | 2.30% | 0.20% | 96.765% | 97.747% |
| Deuces Wild | 25-16-13 | 12.00% | 2.22% | 0.20% | 96.765% | 96.988% |
| Deuces Wild | 25-15-10 | 12.00% | 2.20% | 0.20% | 94.818% | 95.411% |
| Deuces Wild Bonus | 13-4-3-3 | 11.60% | 2.00% | 0.20% | 98.803% | 99.464% |
| Deuces Wild Bonus | 10-4-3-3 | 11.60% | 2.00% | 0.20% | 97.364% | 98.429% |
| Deuces Wild Bonus | 10-4-3-3 | 11.60% | 1.90% | 0.20% | 97.364% | 97.401% |
| Deuces Wild Bonus | 12-4-3-2 | 11.60% | 1.85% | 0.20% | 96.218% | 96.478% |
| Deuces Wild Bonus | 10-4-3-2 | 11.60% | 1.85% | 0.20% | 95.337% | 95.826% |
Last edited by: Wizard on Mar 6, 2017
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
March 6th, 2017 at 5:37:44 PM
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He only gave Magic card percentages to the nearest tenth of a percent? :( On videopoker.com, the help screens say the overall magic card percentage is 13.65%. So I wouldn't count on 3 magic cards being exactly 1 in 500 or 1 in 1000...
March 6th, 2017 at 5:53:13 PM
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Quote: tringlomaneHe only gave Magic card percentages to the nearest tenth of a percent? :( On videopoker.com, the help screens say the overall magic card percentage is 13.65%. So I wouldn't count on 3 magic cards being exactly 1 in 500 or 1 in 1000...
Sorry, he gave them to five decimal places. It was my fault on the rounding in the table. I just reposted it.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
March 6th, 2017 at 7:54:54 PM
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Are the percentages for 1 MC under Triple Double Bonus correct? If so, any thoughts on why so low compared to the others?
March 6th, 2017 at 8:23:42 PM
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Quote: rsactuaryAre the percentages for 1 MC under Triple Double Bonus correct? If so, any thoughts on why so low compared to the others?
You'll hit much bigger when you get magic cards, especially 2 or 3. Magic cards create a lot more quads and royals. Strategy gets interesting when the magic cards show up. A videopoker.com member worked on a DDB strategy that looks pretty accurate. Would like to see even more.
Playing DDB on videopoker.com, got this for 8000 credits.
Same deal in TDB, I would get 20000 credits instead.
March 7th, 2017 at 5:45:06 AM
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I certainly understand that there are more hands to give a potential big payoff in TDB. Was just surprised that it resulted in that kind of difference in getting magic cards... especially on the 1 card line. I'm still thinking the chart is wrong.
Last edited by: rsactuary on Mar 7, 2017
March 7th, 2017 at 7:55:12 PM
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The next step in my analysis is done, hopefully correctly. It was to determine the expected value of the average hand on the draw with ONE Magic Card. The following table shows my results:
As a reminder, the player will get one Magic Card in 9-6 Double Double Bonus 8.4% of the time. The product of 8.4% and 6.345418 units won is 0.533015154. However, the player has to bet twice as much to invoke the feature, which implies the return from getting one Magic Card is 26.65%. That passes my smell test at least. I hope to do the two and three magic card cases later this week.
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal flush | 800 | 143,426,496 | 0.000681 | 0.544544 |
| Straight flush | 50 | 523,794,192 | 0.002486 | 0.124292 |
| Four A + 2-4 | 400 | 253,219,560 | 0.001202 | 0.480696 |
| Four 2-4 + A-4 | 160 | 727,804,620 | 0.003454 | 0.552648 |
| Four A + 5-K | 160 | 604,322,040 | 0.002868 | 0.458883 |
| Four 2-4 + 5-K | 80 | 1,544,961,420 | 0.007332 | 0.586572 |
| Four 5-K | 50 | 5,345,057,340 | 0.025367 | 1.268340 |
| Full house | 9 | 6,135,845,580 | 0.029120 | 0.262078 |
| Flush | 6 | 4,969,881,612 | 0.023586 | 0.141518 |
| Straight | 4 | 11,185,328,112 | 0.053084 | 0.212335 |
| Three of a kind | 3 | 96,146,990,820 | 0.456299 | 1.368896 |
| Two pair | 1 | - | 0.000000 | 0.000000 |
| Jacks or better | 1 | 72,614,497,812 | 0.344617 | 0.344617 |
| Junk | 0 | 10,515,552,396 | 0.049905 | 0.000000 |
| Total | 210,710,682,000 | 1.000000 | 6.345418 |
As a reminder, the player will get one Magic Card in 9-6 Double Double Bonus 8.4% of the time. The product of 8.4% and 6.345418 units won is 0.533015154. However, the player has to bet twice as much to invoke the feature, which implies the return from getting one Magic Card is 26.65%. That passes my smell test at least. I hope to do the two and three magic card cases later this week.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
March 8th, 2017 at 10:50:55 AM
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Please see my question above regarding TDB 1MC percentage?
March 8th, 2017 at 11:30:06 AM
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Quote: WizardI'm proud to say I finished my analysis and my return matches VideoPoker.com's. My analysis can be found here. As usual, I welcome questions, comments, and especially corrections.
Great analysis. Thank you.
With over 9.5% of the return coming from the royal, what is the volatility and n-play bankroll requirements for different ROR's?
At my age, a "Life In Prison" sentence is not much of a deterrent.
March 8th, 2017 at 11:34:20 AM
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Quote: WizardI'm proud to say I finished my analysis and my return matches VideoPoker.com's. My analysis can be found here. As usual, I welcome questions, comments, and especially corrections.
Strategy changes? Split low pairs to try to catch aces?
Simplicity is the ultimate sophistication - Leonardo da Vinci
March 8th, 2017 at 12:00:57 PM
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Quote: AyecarumbaQuote: WizardI'm proud to say I finished my analysis and my return matches VideoPoker.com's. My analysis can be found here. As usual, I welcome questions, comments, and especially corrections.
Strategy changes? Split low pairs to try to catch aces?
Here is the 9/6 DDB strategy worked on by videopoker.com member "alpax". Since his return numbers for 1, 2, and 3 magic cards match the Wizard's, I assume the strategy should be correct. I've been referring to it regularly during this week's contest. The biggest change is with 1 or 2 magic cards, a single 2-4 is better than a face card. And with 2 magic cards, there is no good reason to hold a single face card at all! I expect a lot of casual players to not play that way because we're trained to try to improve to at least a high pair. With "magic cards" that goal is too low. You'll luck into a winning hand a lot with magic cards.
http://forum.videopoker.com/forum/forum_posts.asp?TID=8761
I'm "Vman96" at videopoker.com, fyi.
March 8th, 2017 at 12:06:10 PM
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Quote: rsactuaryI certainly understand that there are more hands to give a potential big payoff in TDB. Was just surprised that it resulted in that kind of difference in getting magic cards... especially on the 1 card line. I'm still thinking the chart is wrong.
Triple Double Bonus pumps up the top wins at the expense of the small ones. The Magic Cards help the player achieve those larger awards. Because they are more valuable, they had to cut the frequency they occur.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
March 8th, 2017 at 12:10:59 PM
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Quote: DRichGreat analysis. Thank you.
With over 9.5% of the return coming from the royal, what is the volatility and n-play bankroll requirements for different ROR's?
You're welcome. To answer your first question, the standard deviation of 9-6 Double Double Bonus is 8.431228274, relative to the total amount bet, assuming it were played as a single line game, which it can't.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
March 8th, 2017 at 1:17:17 PM
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Quote: WizardYou're welcome. To answer your first question, the standard deviation of 9-6 Double Double Bonus is 8.431228274, relative to the total amount bet, assuming it were played as a single line game, which it can't.
Just as a comparison, the single line SD for 9/6 DDB single line Dream Card is 6.33. While playing it, the swings even seem bigger than what I would expect from an 8.43 SD game. Some of that is probably due to the magic cards being correlated with 10 lines.
