7-14-21
Quote: CrystalMathConsider this hand: AA779T
You could avoid busting with AA 77 9T, but the best strategy is 9A 77 TA, which is a bust on the 7 hand.
Well I guess there is something wrong with my math, as this isn't true in my case.
I'm assuming you are only counting the regular game and not including the bonus bet.
Quote: CrystalMathConsider this hand: AA779T
You could avoid busting with AA 77 9T, but the best strategy is 9A 77 TA, which is a bust on the 7 hand.
I stand corrected.
The more I get my hands dirty with this, the harder I realize it is.
Quote: Wizard
All things considered, here is my latest strategy to run up the flagpole. The higher the rule, the higher the priority.
1. Never bust more hands than you have to.
2. Make 21 in the 21 hand, if you can.
3. Make 14 in the 14 hand, if you can.
4. Maximize the 7.
5. Maximize the 14.
When this game was first mentioned on this site, I became intrigued and played it a lot. My experience was to clearly switch "4" and "5". It didnt appear to be close. Meaning play 13/5 instead of 11/7 if that is possible. I would say generally you would MINIMIZE the 7 point hand if you can make the others stronger, as the dealer most often busts on the 7 point hand.
Quote: WizardMiplet, CM, SH79 -- How is the strategy progress coming along?
Not too good. I put my spread sheet in Google docs in case someone else want to work on one. 7-14-21 My vacation starts in 4 days and I'll have lots of time to work on one then.
Quote: soulhunt79
I'm assuming you are only counting the regular game and not including the bonus bet.
Correct, I'm just looking at the base game.
Quote: mipletNot too good. I put my spread sheet in Google docs in case someone else want to work on one. 7-14-21 My vacation starts in 4 days and I'll have lots of time to work on one then.
I compared miplet's list to mine, and we only disagree on 7 hands, but they pay an identical amount. One such hand is:
2 2 2 2 3 5. Miplet holds 7 5 4 and I hold 7 4 5. The 4 and the 5 are both worthless in the 14 and 21 hands since the dealer must get 3 3 3 4 4 or higher.
| Total | "7" | "14" | "21" |
|---|---|---|---|
| 21 | 7045408 | ||
| 20 | 8655452 | ||
| 19 | 1936844 | ||
| 18 | 1175056 | ||
| 17 | 720188 | ||
| 16 | 381972 | ||
| 15 | 215948 | ||
| 14 | 7385556 | 105312 | |
| 13 | 5206416 | 62716 | |
| 12 | 3213990 | 30752 | |
| 11 | 1712764 | 17472 | |
| 10 | 859236 | 7084 | |
| 9 | 572462 | 3168 | |
| 8 | 311128 | 896 | |
| 7 | 1600220 | 184544 | 224 |
| 6 | 1613102 | 64418 | 28 |
| 5 | 1834756 | 16112 | |
| 4 | 981694 | 1122 | |
| 3 | 58544 | ||
| 2 | 13180 | ||
| bust | 14257024 | 830772 |
I've added this to the 3rd sheet in my google doc. Sheet 2 is the same but has each 7-14-21 hand combination.
I took the liberty of converting these numbers to player expected values. In other words, ignoring the effect of removal, this is how many units the player can expect to win for each total on each hand.
| Total | "7" | "14" | "21" |
|---|---|---|---|
| 21 | 0.307866 | ||
| 20 | -0.117285 | ||
| 19 | -0.637573 | ||
| 18 | -0.790428 | ||
| 17 | -0.883521 | ||
| 16 | -0.937659 | ||
| 15 | -0.967028 | ||
| 14 | 0.637225 | -0.982809 | |
| 13 | 0.018714 | -0.991062 | |
| 12 | -0.394892 | -0.995653 | |
| 11 | -0.636891 | -0.998022 | |
| 10 | -0.763227 | -0.999228 | |
| 9 | -0.833551 | -0.999732 | |
| 8 | -0.876953 | -0.999931 | |
| 7 | 0.921398 | -0.901300 | -0.999986 |
| 6 | 0.763561 | -0.913529 | -0.999999 |
| 5 | 0.594204 | -0.917484 | |
| 4 | 0.455862 | -0.918331 | |
| 3 | 0.404766 | ||
| 2 | 0.401243 | ||
| bust | -1.000000 | -1.000000 | -1.000000 |
However, nobody wants to sit there adding up numbers to six decimal places at the table, so I converted them to 0 to 10, as follows.
| Total | "7" | "14" | "21" |
|---|---|---|---|
| 21 | 7 | ||
| 20 | 4 | ||
| 19 | 2 | ||
| 18 | 1 | ||
| 17 | 1 | ||
| 16 | 0 | ||
| 15 | 0 | ||
| 14 | 8 | 0 | |
| 13 | 5 | 0 | |
| 12 | 3 | 0 | |
| 11 | 2 | 0 | |
| 10 | 1 | 0 | |
| 9 | 1 | 0 | |
| 8 | 1 | 0 | |
| 7 | 10 | 0 | 0 |
| 6 | 9 | 0 | 0 |
| 5 | 8 | 0 | |
| 4 | 7 | 0 | |
| 3 | 7 | 0 | |
| 2 | 7 | 0 | |
| bust | 0 | 0 | 0 |
To use this chart, add up any viable way to play a hand and go with the one with the greatest sum of the above power ratings.
Again, this ignors the effect of removal. One hand where it gives bad advice is the AA779T hand mentioned earlier. This method would tell the player to play 2-14-19, while CrystalMath's spreadsheet says bust-14-21 is the best play. Why the disparity? I'm pretty sure it is that the game is played with a single deck, so the two aces already removed significantly lowers the chances of the dealer making 21, increasing the value of the player's 21.
However, maybe that is just an unusual case and it is overall a good, yet cumbersome strategy. What do the rest of you think?
A 3 6 7 8 K
The consensus here seems to be to play it as
A 6
3 7
K 8
But is that really better than
3 7
8 6
A K
for two perfect hands and one bust?
edit -- just saw miplet's spreadsheet, and it appears my intuition to set the two perfect hands and one bust is correct. I wonder how many exceptions there are like this.
Quote: mipletUsing the Wiz's power rating I get a player ev of -0.006911823 If there is more than one way to get the same number of points, set the best "21" then "14".
My intuition for strategy was sure wrong [yet again][g].
That HE is mighty low for a new game.
Quote: ecofinaThe consensus here seems to be to play it as
A 6
3 7
K 8
Miplet's spreadsheet aside, I think the consensus here would have said:
A 3
6 8
K 7
Once the 21 hand isn't at least a 20, it should be played as a lost cause and maximize the other hands.
Quote: ecofinaA 3 6 7 8 K
The power rating shows three viable ways to play the hand as follows:
7,10,18 --> 10+1+1 = 12 points
Bust,14,21 --> 0+8+7 = 15 points
4,14,17 --> 7+8+1 = 16 points
Yet according to CrystalMath's spreadsheet the best play is Bust,14,21.
Quote: DJTeddyBearOnce the 21 hand isn't at least a 20, it should be played as a lost cause and maximize the other hands.
I agree. The dealer will make 20 or 21 in the "21" hand 77% of the time, including 35% for a 21. However, the "7" hand is much less sensitive to getting a top score. As a general rule of thumb you should try to just not bust the "7," and spend your ammo getting the "21" or "14" to the highest possible score, preferable the 14. Of course, there are some sticky hands like the one above, where this advice doesn't help much.
Quote: Wizard
The power rating table says 7-10-18 = 12 points, and bust-14-21 = 15 points, so is correct on that hand. The rack card strategy would incorrectly have the player play the 7 in the "7" hand.
Yes, but if you play A3 68 7K, you get a power ranking of 16 (right?). I also calculate that this will cost the player 4.45 cents per dollar wagered.
Quote: mipletUsing the Wiz's power rating I get a player ev of -0.006911823 If there is more than one way to get the same number of points, set the best "21" then "14". Of course I might have a braino or typo in my program somewhere.
I get nearly the same result. I think the difference is just the order that we run through the hands, because there are often many hands with identical power rankings, and I use the first one I find.
My ev is -0.006940896.
I also evaluated every Power Ranking hold against every optimal hold, and it is different in only 323 out of 4915 hands. Considering the frequency of the hands affected, it is different 4.9% of the time.
Quote: CrystalMathYes, but if you play A3 68 7K, you get a power ranking of 16 (right?). I also calculate that this will cost the player 4.45 cents per dollar wagered.
Right, good catch. I just amended my post to include that. However, I see your spreadsheet says bust-14-21 is the best play.
If anyone can come up with something better, weighing both power and simplicity, I'm all ears.
When I make this change, my new player ev is -0.006057435, compared to the previous power ranking ev of -0.006940896 and an optimal ev of -0.005401715.
Quote: CrystalMathI think you should change the power ranking of 21 to 8. If you have a 21, then you have used an ace, which makes the 21 more valuable because that ace is not available to the dealer. You are also removing a 10, but that doesn't have as much effect.
When I make this change, my new player ev is -0.006057435, compared to the previous power ranking ev of -0.006940896 and an optimal ev of -0.005401715.
Wow! Ask and ye shall receive. Great work!
The asterist should indicate that ANY hand that includes an ace (including a total of 21) should be rated at +1.
Of course, you'll have to run the math first....
Changing the Power rating of 21 to 8 gives me a player ev of -0.005986828
Quote: mipletI just did a "Rack Card" strategy. I get a player ev of -0.077824706
Ouch!
Quote: mipletChanging the Power rating of 21 to 8 gives me a player ev of -0.005986828
Thanks for that confirmation. I assume CrystalMath got a slightly higher figure was due to how to handle ties.
Outstanding work by both of you guys! The least I could do is buy you dinner your next trip to Vegas.
Quote: miplet-0.005912303 is the best I can come up with. Change the "21" hand of 17 from 1 to 0. Only 231 hands get played incorrectly. Weighted its 3.0507129 %.
Yet another good find, thanks. This has been an outstanding thread.
Quote: DJTeddyBearIn that case, maybe the rating of a 21 should stay at 7 with an asterisk.
The asterist should indicate that ANY hand that includes an ace (including a total of 21) should be rated at +1.
Of course, you'll have to run the math first....
The 21 rating will only affect you if you have and ace and a ten, so leaving it at 8 or a 7 with a condition is identical. I also tried to see what would happen if I conditionally increased the value of a 20 based on having an ace, and it is a slightly worse strategy.
I must say that I enjoyed this thread a lot and it was great building off the ideas of miplet and the Wizard and seeing the evolution of this beast. I'm amazed at the poor rack card strategy and I realize that most people will never come close to 99.4%. If I go to G2E, I'll probably make a special visit to the Palms just for this.
I disagree.Quote: CrystalMathThe 21 rating will only affect you if you have and ace and a ten....
You specified earlier that the Ace is important enough to give it extra value because of card removal. I.E. Having an ace reduces the chance of the dealer having an ace.
That being the case, it shouldn't matter how the ace is played. Whichever hand it is played on should rank higher than the same total with different cards. I.E. A-9 should rank higher than T-T.
Similarly, A-6 should rank higher than 2-5, and A-3 higher than 5-9.
Then again, maybe the math will prove me wrong. Maybe only A-T gets the extra value out of the ace - although I don't see how....
Edit after re-reading...
Are you saying that A-9 is worse than T-T?Quote: CrystalMathI also tried to see what would happen if I conditionally increased the value of a 20 based on having an ace, and it is a slightly worse strategy..
Yes it has. I'm kinda glad I re-started with some "gut feel" strategy that seemed counter-intuitive, back on page 2.Quote: WizardYet another good find, thanks. This has been an outstanding thread.
Quote: DJTeddyBearI disagree.
You specified earlier that the Ace is important enough to give it extra value because of card removal. I.E. Having an ace reduces the chance of the dealer having an ace.
That being the case, it shouldn't matter how the ace is played. Whichever hand it is played on should rank higher than the same total with different cards. I.E. A-9 should rank higher than T-T.
You're probably right, but the goal with writing about strategy is to balance the power of the strategy with the simplicity of using it. As someone who has written about gambling for 14 years, I can tell you that readers hate or are confused by exceptions and asterisks. There was a thread recently about how my soft 18 exception was a stumbling block to some friends of a member learning my Wizard's Simple Blackjack Strategy. So I tend to concur with keeping the 21 at 8 points and leaving the asterisk out of it, even at the cost of a higher house edge.
Quote: AlanCan't you have a simple strategy, then a complicated one, too?
The power rating strategy is pretty simple and comes within 0.05% of optimal. I think that is good enough. Maybe if the game gets really huge I'll put more thought into it. However, between me, miplet, and CrystalMath, I think we've done an outstanding job on cracking this nut, and can get it off our desks.
Quote: WizardThe power rating strategy is pretty simple and comes within 0.05% of optimal. I think that is good enough. Maybe if the game gets really huge I'll put more thought into it. However, between me, miplet, and CrystalMath, I think we've done an outstanding job on cracking this nut, and can get it off our desks.
Oh, I agree that all you folks that participated in crunching the numbers did a fantastic job. I assume that the complicated strategy, well, would be pretty damn complicated. Probably so complicated nobody but the grinder would possibly use it.
Quote: DJTeddyBear
Are you saying that A-9 is worse than T-T?
No, an A9 is worth more than a TT, but it does not have enough effect on the strategy to justify adding another point to the 20 on the 21 hand. If you make a decision by adding an extra point, you are losing more money by taking that point away from another hand.
Quote: AlanOh, I agree that all you folks that participated in crunching the numbers did a fantastic job. I assume that the complicated strategy, well, would be pretty damn complicated. Probably so complicated nobody but the grinder would possibly use it.
Agreed, the power strategy IS the simple strategy. If you look at the data that's been posted, there really is no simple "always make 21" or "minimize busts"-style rule that will work often enough. I believe I am on to the method of comprising the optimal strategy, and it will be much more complex than the power strategy, while only providing an extra .05% advantage.
See if my thinking makes sense: When you are dealt your 6 cards, they will add up to a certain total in blackjack numbering. Let's say, hypothetically, that total is 23. Now, imagine that instead of being given 6 specific cards, you are just given that total: 23. You can pick any 6 cards that make up that total, and arrange them as you please. Using the same theory as the power table, there will always be an optimal set of values to play for each total. In this case, assuming you have no aces, that would be 5-14-4. That is, I feel that 5-14-4 will always be preferable to 6-13-4, no matter what cards make the total 23. The composition of the cards will only affect whether or not you will be able to play the optimal total.
So, the way I envision the optimal strategy table looking is a column of totals on one side, which then gives you an ordered list of totals. The first on the list is the one you should make, unless you can't, and then you move on to the second, and so on. I imagine having aces will greatly affect this, so there will probably need to be 5 different tables, one each for the possible number of aces in your hand. I have filtered miplet's data by totals and started to make a chart to give you guys an example:
No Aces (Value to play for 21/value to play for 14)
14 4/4
15 4/4 4/5
16 4/5 4/6
17 4/6 4/9
18 4/7 5/6 4/8 4/10
19 4/8 4/11 4/9 5/7 6/6
20 4/9 5/8 5/9 4/10 4/11 4/12 6/7 6/8
21 4/10 4/11 4/12 4/13 5/9 6/8 5/10
22 4/14 4/13 4/12 4/11 5/10 5/11 6/9 6/10 7/8
23 4/14 4/13 4/12 5/12 5/11 6/10 6/11 7/9 8/8 8/11 9/10
You should play the left-most values, unless you can't, then move to the right. Note that the options aren't necessarily listed highest EV to lowest EV. For example, with total 21, if you can make 4/13, you can't make any other total on the list. So really, it could go anywhere. In that case, I put it after 4/12, as it seemed like that would be the easiest, rather than having someone look for 4/13 first, then 4/10 up to 4/12.
I've basically been doing this by sight using miplet's spreadsheet, and I'll keep plugging away at it, but if someone has a faster method to figure this out, all the better
Quote: mipletI just did a "Rack Card" strategy. I get a player ev of -0.077824706 Yep 7.78%
They may rate it pretty decently, as they may expect players to play at a considerably higher HE than optimal.
Quote: hoguaAnyone know how Palms rates play on this game? .
Not me. However, in general, novelty games rate pretty well.
Quote: jc2286Although I'm an infrequent poster, I just wanted to drop in to say outstanding work guys! I'm a big prob & stats guy, especially in the gaming area, and I'm enjoying this thread immensely. It looks like it'd be a really fun game to play with a lot of decision-making hands, not mechanical like BJ or even PGP for the most part.
Agreed! Not to get too off-topic, but I stopped lurking on this site, and actually created an account, specifically because of this thread.
Btw, I haven't had too much extra time to get too much more done on the optimal strategy. It's probably not worth the time from an EV standpoint, but as a math/prob/stats nerd, I can't help myself. :)
Quote: sodawaterLooks like they have changed the rules of the game on the official site.
Player perfect hand now pays 3-1 on all wagers, instead of 4-1. (I assume it still actually pays 3:1 as opposed to the 3-2 implied by the way the paytable lists everything in terms of "for one" -- but in the previous version, the website paytable listed a perfect hand aware of 375 for a 25 base bet, but it was confirmed that they actually were paying 4-1)..... anyway....
They added a "perfect pair" category that pays 2-1 on only the 7 and 21 if the player sets a 7 and 21. They also added a "Dealer perfect hand" whereby all wagers push, unless, (I can only hope) the player himself has a perfect hand as well, where the 3-1 on all wagers would apply.
Can any of the more mathematically inclined members -- or dare I suggest, the Wizard Himself -- crunch the numbers on these new rules?
Any changes to the "power rating table" that previously produced a house edge of 0.59 percent?
I do love this game -- hopefully these rule changes don't bump up the house edge too much.
This is how I interpret the new rules:
"Perfect Hands" pay 2 to 1 on all wagers regardless of the dealers hand.
"Perfect Pairs" pay 1 to 1 on the "7" and "21" hands regardless of the dealers hand, with the "14" hand still compared to the dealers "14" hand.
If the dealer gets a "Perfect Hand", wagers push (including busted ones) except ones that were a "Perfect Hands" or "Perfect Pairs".
I'm not going to reanalyze the game until it is confirmed that this is how it is now played. The How To Play section of their website lists a suggested player strategy, which looks pretty good to me.
For example:
If you are dealt 2, 3, 4, 5, 10, 11; you get equivalent power ratings from 2/5, 3/4, 10/11 and 2/4, 3/5, 10/11, but it is best to go with the perfect pair.
I would love to hear the WOO memebers thoughts on this?
Quote: ShiftyRickyI have looked at putting this game in my pit.
I would love to hear the WOO memebers thoughts on this?
I've played the demo game. I really like the game. It's fun and interesting, but it moves pretty slow for a casino game. Would it be a net-add for your pit, or would it replace another game? I'm not sure if the game would show enough hands/hour to net a larger hold than an existing table in the pit.
I studied the online version prior to playing it at the Palms in October.Quote: ShiftyRickyI have looked at putting this game in my pit.
I would love to hear the WOO memebers thoughts on this?
Then again, I had a specific reason for going to the Palms (John Huxley's AAA event at GhostBar while G2E was going on), so I made the effort to learn it, and try the game.
It was an empty table when I stepped up (around 6:00pm). While I was seated, some other people stopped by to try it. I think I was alone when I finally left (around 7:00pm).
I had no reason or desire to stop by Palms last week to play it again - even though the thought DID cross my mind.
Will I play it again this coming October? Undecided.
Does that give you an idea about how popular it may be?
rdw...i would not replace a game I would add it.
As far as slow goes, i feel the same way.
I think someone in a different post said something about drinking and being able to play this game. I was thinking along those lines too. Maybe too much going on for the casual player.
