Playing European No Hole Card (ENCH)

bdk

New Member
#1
Hi

I recently played some blackjack in Estonia, and in the casinos in Tallinn they practiced the rule European No Hole Card (ENHC). I played all my hands alone at the table. Just the dealer and me. The thing is that I feel that ENHC gave me a huge advantage. After the dealer has dealt two face up cards for me and one face down card for the dealer I am to act. I can decide to hit, but if I don't hit, the card I would have hit, will be dealt to the dealer. So I get to choose if I want the card or if the dealer will have the card. This must give me a huge advantage, or? You say that the strategy should not change playing ENHC, but I do not understand that.
Let's say that I have hard 14 after my first two cards and the dealer has 7. Normal strategy dictates that I should hit. Let's look closer at this scenario. I assume, for simplicity, that the second card from the top of the deck is a 10.
I have made a table of this scenario:

First card hit Second card hit My total after one card My total after two cards
Ace 10 15 Bust
2 10 16 Bust
3 10 17 17
4 10 18 18
5 10 19 19
6 10 20 20
7 10 21 21
8 10 Bust Bust
9 10 Bust Bust
10 10 Bust Bust

So if I follow the normal strategy, I will bust quite often.

Let's see what happens if I don't hit, but let the dealer have a go at the next two cards:

First card hit Second card hit Dealer total after one card Dealer total after two cards
Ace 10 18 18
2 10 9 19
3 10 10 20
4 10 11 21
5 10 12 Bust
6 10 13 Bust
7 10 14 Bust
8 10 15 Bust
9 10 16 Bust
10 10 17 17


I would say that this looks much better for me as a player.
Let's look at one case in particular. Let's say the next card is a 7, which will give me 21, the best hand I can get. But if I do not hit, and the dealer gets the 7 instead, the dealer will have 14, and will be forced to hit again, and he will most likely bust, and I win anyway. Almost every card that is good for me (3, 4, 5, 6, 7) when I start with 14 I just as well can let the dealer hit in the scenario above, since the dealer will have to hit a second card that most likely will cause him to bust.

So why risk hitting in this scenario. If the first card I hit is a 10 (which is most likely) I am screwed anyway.
I played this scenario (or similar once) time and time again when I was in Tallinn, and the bank busted time and time again. I doubled my money several times during my visit :)

So you get this advantage when you play alone or if you are the player sitting next to the dealer on the dealers right hand side.

So my point is; if you get to choose if you or the dealer gets the next card, even if you of course don't know what the card is, you will have an atvantage as opposed to american rules where the dealer already has a hole card.

Did I manage to get my point across?
Hope some of you have some comments regarding this.
I hope you can read them anyway.
 

Mikeaber

Well-Known Member
#2
bdK, I must be missing your point. Your logic is flawed if you think that you as the player immediately before the dealer (3rd base) can control the dealer's "bust" card. You do NOT know what that next card is going to be.

You stated that the dealer has a 7 showing. You can go through all the scenarios (dealer has roughly a 38.5% chance of having either 17 or 18 (face or Ace either down or drawing the down card of face or Ace). So in 38% of the cases, you are beat with a stiff hand to start with if you stand on it.

If you hit the stiff, you have 5 ranks that will give you 17 or better (with a 14 you can hit a 3,4,5,6 or 7) plus in the case of a 14, two additional cards that will not help you but will not hurt you either (the Ace and deuce). That's 28 cards out of a deck of 52 or 27 out of 52 if you want to get picky since your hand is made up of one card that could help you). That gives you around a 38% chance of busting and around a 51% chance of drawing a card that will not bust you but that might not help you. Seems to me, you are better off hitting unless you can SEE the card that you would be hitting or that the dealer will be drawing.

Note that for simplicity, I've pretty much ignored cards in play or that have been played already. The assumption for percentages I gave is based on a 52 card deck with all cards present. Of course, cards in play will skew the figures somewhat but the concept is still valid.
 

bdk

New Member
#3
Hi

Thanks for the reply, Mikeaber.

I'm still a bit puzzled by this. I have a hard time accepting the fact that 3rd base players should automatically use the same strategy as other players when playing ENCH. I do know of course that the player at 3rd base doesn't know what the next card is. But even if the card to be hit is unknown, I still feel that the 3rd base player has some sort of advantage because he gets to choose if the unknown card is dealt to himself or to the dealer. That there is a difference between this scenario and the scenario other players face; the fact that the dealer will get a different card. Is there really no difference between one unknown card to be dealt to either the player or the dealer, or two different cards to be dealt to the player and the dealer?
Is one "shared" unknown card the same as two unknown cards?

Another example. Let's say I, as a 3rd base player, have 16 and the dealer has 9. Normal strategy dictates that I should hit hoping to get either A, 2, 3, 4 or 5. If the card I'm to hit is a 3, I will get 19 against the dealers 9. If I didn't hit the card but let the dealer have it, I would be faced with the situation where I have 16 and the dealer has 12. Which is a better scenario for me? 19 against 9 or 16 against 12?

If the first card in the above situation is a 4, the scenarios would be. Am I better off with 20 against the dealers 9 or would I be better off with 16 against 13?

So playing ENCH as a 3rd base player I would actually consider standing if I get 16 and the bank has 9. Am I really way off?
 

KenSmith

Administrator
Staff member
#4
I wish I could figure out a good concise way of illustrating this, because it IS confusing.

If you look at every possible combination of the dealer's hand, your hand, and the next card to be dealt, you'll find that the good situations and the bad situations balance out.

Since I can't think of a good way to explain this, I'll instead talk more about your example of 16v9.

If you stand, you'll win the hand if the dealer busts, and lose otherwise.
We'll use an infinite deck to approximate here, since the math is easier.
With a 9 up, the dealer will bust 22.84% of the time.
(Refer to Blackjack Dealer Outcome charts on this site.)

You'll win 22.84% of the time, and lose 77.16% of the time, for a net loss of 0.5432 of your bet.

Now, if you hit instead...
If you draw a 6 or higher, you immediately lose (probability 8/13).
If you draw an Ace, you'll win if the dealer busts, push with 17, and lose against dealer 18-21. (probability 1/13, W: 22.84%, P: 12.00%, L:65.16%)
If you draw a 2, you win with dealer bust or 17, push 18, lose to 19-21.
(probability 1/13, W: 34.84%, P: 12.00%, L:53.16%)
If you draw a 3: (probability 1/13, W: 46.84%, P: 35.08%, L: 18.08%)
If you draw a 4: (probability 1/13, W: 81.92%, P: 12.00%, L: 6.08%)
If you draw a 5: (probability 1/13, W: 93.92%, P: 6.08%, L:0%)

If you add up the win percentages for all thirteen card values, and divide by 13, you get an overall win percentage of 21.57%.
You'll push 5.93% of the time.
You'll lose 72.50% of the time.

The average net loss per bet is (72.50% - 21.57%) = 0.5093 of a bet.

Hitting is quite a bit better than standing (-0.5093 is better than -0.5432).

Now, that's all fine and dandy, except I haven't once mentioned the idea that the card you choose to take or not ends up on the dealer's hand. So, my illustration may leave you feeling like you I haven't addressed the issue you're asking about.

Consider this... What if the casino required the dealer to burn a card after you played your hand, and before completing his hand? Would that change any of the above? No. An unseen random card is still an unseen random card, whether it could have been your card, or whether it is after a burned card, or whether it is randomly chosen from the remaining deck instead of dealt from the top of the deck.
 

Mikeaber

Well-Known Member
#5
Consider also that if there are more than just you playing, the person playing before you has just as much "control" of the card the dealer will receive as do you! His decision to take or not take a hit impacts the card you either may or may not take which in turn determines which card the dealer will get!

All this simply boils down to the fact that you cannot know which decision to make to force the dealer to bust. Heck, you can't even know whether it's going to take a face to make the dealer bust. It might only take a "6". The only play you can make with any logic associated with it will be the play that gives you the best chance to win.

Hitting any stiff hand against what will probably be a dealer "made hand" (7 thru Ace) gives you a very slight advantage in losing fewer times than if you stand on that hand (aproximately 1% though Ken broke it down even finer.)
 

bdk

New Member
#6
Still do not agree :)

Hi, thanks for the replies. I still feel that you have missed my point. I agree with all your statistics, but I feel that the "standard" probability analysis is not apropriate in the case of a 3rd base player playing ENHC.
So I'll try to explain once again why I mean that the 3rd base player has an advantage, and I'll use the example og the player having 16 after two cards and the dealer showing 9 after his one card. I also assume an infinite deck, because this does not affect the point I'm trying to make.
First we establish some basic facts.
1. The next card in the deck is either going to be dealt to the player if he choses to hit or to the dealer if the player stands.
2. The player does of course not know what this card is going to be.
3. The next card in the deck can either be a A, 2, 3, 4, 5, 6, 7, 8, 9 or 10.
4. Based on the first point in this list, the player knows that there will be 10 different scenarios to "choose" from, based on the first card in the deck. Let's put these different scenarios in a table. P is player, D is dealer

Code:
[FONT=Fixedsys][SIZE=1] Scenario | Next card | Player hits | Player stands | Prob. for this scenario |
 ------------------------------------------------------------------------
           |              | P   |   D  |  P   |   D     |                     |
 ------------------------------------------------------------------------
     1     |        A     | S17 |  9   |  16  |  S20    |   1/13                      |    
     2     |        2     | 18  |  9   |  16  |   11    |   1/13                      |
     3     |        3     | 19  |  9   |  16  |   12    |   1/13                      |
     4     |        4     | 20  |  9   |  16  |   13    |   1/13                      |
     5     |        5     | 21  |  9   |  16  |   14    |   1/13                      |
     6     |        6     | BUST|  9   |  16  |   15    |   1/13                      |
     7     |        7     | BUST|  9   |  16  |   16    |   1/13                      |
     8     |        8     | BUST|  9   |  16  |   17    |   1/13                      |
     9     |        9     | BUST|  9   |  16  |   18    |   1/13                      |
    10     |        10    | BUST|  9   |  16  |   19    |   4/13                      |
 -----------------------------------------------------------------------
[/SIZE][/FONT]
Since we know that the first card in the deck is going either to the player or to the dealer, we KNOW that one of the 10 scenarios listed above is going to take place. That's why I mean a 3rd base player has a huge advantage. No other player knows this. I'll repeat my point, since this is the key to my whole logic. The player KNOWS that one of the ten scenarios listed above will take place. We do not know of course which one, but we know that one of them will happen.

The player will be garanteed to loose scenarios 6, 7, 8, 9 and 10 if he hits. The probability of one of these scenarios occuring is 8/13. If he stands he will be garanteed to loose scenarios 1, 8, 9 and 10. The probability of one of these scenarios occuring is 7/13. So the probability of a garanteed loss is somewhat higher (1/13) if the player chooses to hit. So far it seems that it would be wice for the player to stand.

What we need to figure out next is how the other scenarios play out. Will the other scenarios be able to "even out" the 1/13 probability advantage for not hitting. Unfortunately I'm not able to calculate this accurately. The Dealer outcome charts (http://www.blackjackinfo.com/bjtourn-dealercharts.php#IDS17, Infinite deck, dealer stands on S17) unfortunately only looks at the dealer starting with Ace through 10. I need to know the probability of the dealer busting when he has 11, 12, 13, 14, 15, 16 after two cards to be able to see the whole picture. Maybe this can be found somewhere else on the internet?

Let's make another table where we look at the probabilities for winning (W), pushing(P) and loosing for the different scenarios. This table will not be complete, since I do not have all the information i need. Hopefully someone can help me geting hold of the missing data. All data in this table is taken from the Dealer Outcome Chart mentioned above.
Code:
[FONT=Fixedsys][SIZE=1] Scenario|   Player hits              |    Player stands            | Scenario prob.
 ------------------------------------------------------------------------
            W    |    P    |    L    |   W   |    P    |   L    |  
 ------------------------------------------------------------------------
  1    |     *   |    *    |   *     |   0%  |   0%    |  100%  |      1/13
  2    | 34.84%  |  12.0%  |  53.16% |   ??  |   0%    |   ??    |     1/13
  3    | 46.84%  |  35.08% |  18.08% |   ??  |   0%    |   ??    |     1/13
  4    | 81.92%  |  12.0%  |   6.08% |   ??  |   0%    |   ??    |     1/13
  5    | 93.92%  |   6.08% |    0%   |   ??  |   0%    |   ??    |     1/13
  6    |  0%     |   0%    |  100%   |   ??  |   0%    |   ??    |     1/13
  7    |  0%     |   0%    |  100%   |   ??  |   0%    |   ??    |     1/13
  8    |  0%     |   0%    |  100%   |   0%  |   0%    | 100%   |     1/13
  9    |  0%     |   0%    |  100%   |   0%  |   0%    | 100%   |     1/13
  10   |  0%     |   0%    |  100%   |   0%  |   0%    | 100%   |     4/13
 -----------------------------------------------------------------------
 * Scenario 1 is a bit tricky, since the player, if he hits will have to hit again.
[/SIZE][/FONT]
Does anybody know where I can get the missing data? What is the probability of the dealer busting when he has 11, 12, 13, 14, 15 or 16 after two cards? What is the probability of the dealer of the dealer hitting S17 to 21 when he has 11, 12, 13, 14, 15 or 16 after two cards. And finally I need to figure out how S17 plays against dealer 9.
But I am convinced that when the missing data is filled in it will show that standing is far better that hitting. The data replacing the ?? can't be so bad that hitting all together is a beter alternative.

This was a looooooooooong post, but I hope you stuck with me during my attempt to explain.

So the bottom line is; when sitting at 3rd base playing ENCH, the normal strategy should not automatically be followed, in this case illustrated with the 16 vs. 9 example.

The two tables did not look very good in the preview, but I hope they are understandable anyway.

regards,
BDK
 

KenSmith

Administrator
Staff member
#7
I'll come back and respond more, but first I'll just post the information you requested. In an infinite deck game, here are the dealer outcome probabilities when starting with hard 11,12,13,14,15,16.

Code:
DlrHand  p(17)     p(18)     p(19)     p(20)     p(21)   p(Bust)
  11  0.111424  0.111424  0.111424  0.111424  0.342194  0.212109
  12  0.103465  0.103465  0.103465  0.103465  0.103465  0.482673
  13  0.096075  0.096075  0.096075  0.096075  0.096075  0.519625
  14  0.089213  0.089213  0.089213  0.089213  0.089213  0.553937
  15  0.082840  0.082840  0.082840  0.082840  0.082840  0.585799
  16  0.076923  0.076923  0.076923  0.076923  0.076923  0.615385
 

KenSmith

Administrator
Staff member
#8
I also took the liberty of editing your post to clean up the table alignment.
The trick is using both {code} and changing the font to Fixedsys.
(Use square brackets, not curly brackets.)
 

Mikeaber

Well-Known Member
#9
BDK,
Do you accept the fact that there is a strong chance that with a dealer showing a 9 that you are beat over 70% of the time if you do not hit? Let's break it down.

With a dealer 9 showing, he needs a 7, 8, 9, 10 or Ace to make at least 17. A 17 is going to beat your 16 no matter how you look at it! In addition, he could have a deuce down which gives him at least two draws to make a hand (17-21) so Let's add the 2's into the mix. That's 36 cards out of 49 remaining besides the three that are showing.

This means that there is a 75% chance that you are beat if you do not draw a card. Your only chance, 75% of the time, is to make that miracle draw for a card that will beat him. Chances are, that is going to have to be either a 4 or a 5 but it could be anything deuce or larger since there is a chance that he has a 17 or 18.

Your whole premise of standing on all 16's is based on the dealer busting. Well, 70% or 75% of the time, he's not even going to be drawing and you're beat. Why take that laying down? 25% of the time, you might win. I say "might" because the dealer would still have to draw a card and if so, his chances of making a hand are the same as are yours. He would have to have an 11 thru 16 total value. With a 1 card hit, he needs any of 5 cards (5 thru 9 to beat you....didn't count the eleven because he either makes 21, makes a hand or has another draw). He has a LOT of outs is what I'm getting at.

You on the other hand, have a small shot of making a hand that will beat him. In fact, the only way you can be guaranted that you will not lose is to draw a 5 for 21 and a guaranteed win or at least a push. Not good odds, but it's better than laying down and giving up.

But all of the above is proven Basic Strategy...all forms of the game. What I still do not understand is how you think that you as the final person to play, have an advantage that the other players do not have? You still haven't convinced me (or pounded it into my 2x4 brain), how you know something that they do not know?

I could let the rest go without debate and wish you well on standing on hard 16's.....I've done that so many times and MEANT it. In fact, for the so slight advantage you gain by hitting it, I joke around about it at the table. If the server drops a napkin, I'll stand....or maybe if the person 3 seats to my right has a black duece, I'll hit. Or, I'll pull a coin out and toss it...heads I hit and tails I stand.

But I get the impression that you believe YOU have an advantage the other's do not have and I'd really like to comprehend that.
 

KenSmith

Administrator
Staff member
#10
First correction... Drawing an Ace on your 16 makes hard 17, not soft 17. Therefore, the line in your table for player drawing an Ace can be filled in easily. I've also updated your table with the results from the data I just shared when the dealer has 11-16.

Here is the completed table:

Code:
[FONT=Fixedsys][SIZE=1] Scenario|   Player hits              |    Player stands            | Scenario prob.
 ------------------------------------------------------------------------
            W    |    P    |    L    |   W   |    P    |   L    |  
 ------------------------------------------------------------------------
  1    | 22.84%  |  12.00% |  65.16% |   0%  |   0%    |  100%  |   1/13
  2    | 34.84%  |  12.00% |  53.16% | 21.21%|   0%    | 78.79% |   1/13
  3    | 46.84%  |  35.08% |  18.08% | 48.27%|   0%    | 51.73% |   1/13
  4    | 81.92%  |  12.00% |   6.08% | 51.96%|   0%    | 48.04% |   1/13
  5    | 93.92%  |   6.08% |    0%   | 55.39%|   0%    | 44.61% |   1/13
  6    |  0%     |   0%    |  100%   | 58.58%|   0%    | 41.42% |   1/13
  7    |  0%     |   0%    |  100%   | 61.54%|   0%    | 38.46% |   1/13
  8    |  0%     |   0%    |  100%   |   0%  |   0%    |  100%  |   1/13
  9    |  0%     |   0%    |  100%   |   0%  |   0%    |  100%  |   1/13
  10   |  0%     |   0%    |  100%   |   0%  |   0%    |  100%  |   4/13
 -----------------------------------------------------------------------
[FONT=Arial][SIZE=2]
So, where does that get us...

If the players hits, his weighted average results:
Win: 21.57%
Push: 5.94%
Lose: 72.50%
Net EV = -0.5093

(Note this EV matches what I posted near the beginning of this thread.)

If the player stands, his weighted average results:
Win: 22.84%
Push: 0%
Lose: 77.16%
Net EV = -0.5432

Again, this matches the stand EV I quoted earlier in this thread.

So, when we take into account the fact that our possible hit card is also the dealer's second card if we stand, the math is identical.
That's no coincidence. I still wish I could come up with a satisfactory one sentence explanation of why ENHC doesn't affect the strategy.




[/SIZE]

[/FONT][/SIZE][/FONT]
 

bdk

New Member
#11
Thanks

Hi Ken and all

Thanks for very good replies! For fixing my tables and everything. 16 plus an Ace is definitely not S17, but H17. And last but not least understanding what I was trying to say.
I can see now that there is no difference between ENHC and other forms of blackjack. You completed my table and it spells out very nicely that I was wrong :) It is actually a quite nice table that says it all.

I discussed this problem with my brother yesterday, and what I have been doing is looking at what I think in English is called conditional probabilities. That is I have been looking at a collection of "what if..."-scenarios. There is a theorem in probability which states that "the sum of all conditional probabilities equals the unconditional probability", which was the probability that you guys where talking about all along. And it does look like the theorem is right :)

I was very caught up in the fact that I thought that the "shared unknown card" would give the player more information and thereby changing the odds, but that is clearly wrong. I still find that somewhat unlogical, but the fact is that "one shared unknown card" is the same as "two unknown cards", to put it that way. :)

One other thing that surprised me is how "bad", 16 vs dealers 15 or 16 plays. In my head I reckoned that the odds of winning would be somewhat higher than they actually are. So thanks for that information, Ken.

Thanks for a great discussion and the conclusion is that basic strategy also applies to ENHC, and that I was very lucky when winning a lot of money playing faulty strategies in Tallinn. :)

regards,
BDK
 

Mikeaber

Well-Known Member
#13
I had surgery on my shoulder last Monday and this discussion gave me something to look forward to. Some day, when I quit taking the Lortab painkillers, I'll go back and readread it <LOL>

I have enjoyed it...and enjoyed "meeting" you BDK.
 
#14
I had a similiar question to the origional poster regarding this. It is interesting that the odds add up like that. I had some example cases that interested me.

First one: 15 vs 10 showing

Odds normally say hit, that doesn't change, but it does seem more clear when you and the dealer "share" the card. This is because, you want to improve your hand, but at the risk of busting. However, all your bust cards, 7-K, had you stayed, would have given the dealer a hand that would beat you anyhow. So, basically, there is no risk to improving your hand, whereas vegas style, staying could reveal the dealer actually had a 15, and your hit was a mistake.

The other case was very similiar to the one the OP stated: 16 vs 7

The one hand that kills you immediately is a 17 to ur 16 if you stay, however, if you had hit, you would have busted anyhow. So no matter which action, a 10=lose. Take the 10's out of the equation for the first card and the dealer is always drawing instead of you. Your remaining bust cards, 6-9 give the dealer 13-16 which leaves you in good shape. The lower cards that would have helped you, somewhat hurt you, but you still have a chance to win. I'm not sure if it will even out again, I feel like it might, though in this case the dealer is drawing in all the cases except the ones that didn't matter(and the ace).

I'm just wondering if it would be better to stay 16 vs 17 instead of the normal hit against 17 in vegas rules. Mainly for the reason that you can take the case of dealer having a 17 of the bat out of the equation.

Sorry if this is a bit reduntant, but the choice between hit and stay is a bit different between 16v7 and 16v9.

Insights into the first situation would be nice, as it seems to me that 2 unknowns verse 1 unknown changes the situation. In vegas, if the card on the top of the deck is a 10, there is a chance you can win. In ENCH rules, if there is a 10 on the top, you can never win.
 
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