Strange idea...

We are planning a trip to Pearl River this weekend. My brother came over for some tune-up games, and I saw something that I don't recall having seen before.

We were playing 2D to tune up his BS play, We were basically trying to tweak his play for higher counts since he doesn't count and hasn't memorized any indices as a result.

Early in the session, the TC hit +16, something I don't recall having seen in 2D games. What happened next was strange to say the least. On one hand, we had 3 20's (push). Next hand I had a BJ, he had a 20, dealer had a BJ. Next hand I got a 19, he got a 20, dealer got a 21.

In short, it seemed that the count that high was not nearly as profitable as more normal good counts such as +8 or so. I've not tried to run any sims to see what happens on such high counts, has anyone given this any serious attention? IE large negative counts reach a point where the house advantage peaks and gets no better, but for this one shuffle, it seemed that a very high positive count was not as good.

Was it a run of bad luck, or an observed condition others have seen?

In thinking about it, it would seem that at such a large count, my only advantage is the 3:2 BJ payoff... IE a deck with nothing but 10's and aces. I should statistically get as many 21's as the house, and pocket the extra payoff. But there will be a significant number of pushes (both 20 and 21) as well.

Thoughts???

I seem to work real hard for maybe two days and get ahead maybe about 60 units. Then I run into a monster count on 6D and dump the whole thing back to them in one shoe. It seems like as if it happens way too often. Then I get flac from my family when they make stupid statements like: "You're to greedy. You can't just stop while you're ahead". "So you gave it all back to them again. Don't you know when to say when?" "I told you to stop while you're ahead."

My brain frys when that start talking like this. :-) And also what seems to be an inevetable azzwhippin' on nearly every monster count.

What made me pay attention was that we were playing and betting with plastic chips. And my chip pile shrank during this ridiculous + count.

I decided to experiment a bit by removing 32 small cards, shuffling thoroughly, then playing. Seemed to me to be worse overall, but it really needs a huge SIM to test thoroughly. I've never considered wonging out at +16 but am now thinking about it. :)

Or maybe the bet should track something other than a linear function, so that above something like +10 it starts to ramp back down as the count stays up?

Strange food for thought...

And maybe the idea is totally wrong. It is human nature to remember the strange things that happened when they were bad, but the good ones tend to fade away...

I reached Table Max best of $1,000 this weekend as I experienced a True Count of OVER (Hi-Opt II) +40 on a 8 decker and then later over + 30 on a 2 decker !!!! Needless to say I blew a 5 figure sum representing 1/3 of my B R !!!!!!

Not the 1st time that I have been clobbered when there were primarily picture cards left and I get the stiffs and must stand in helplessly as there is NO late surrender.

I prefer normal high T.C.'s

There is a trend here. I wonder if anyone has run a sim to determine where the inflection point is? IE where the slope of the bet ramp should reverse (still assuming it should)...

Actually 2.

1. what was the running count?

2. how many decks were left when you reached that point?

I don't do much practice in producing running counts of 100+. :)

I certainly don't practice running counts below -40, I'm long since gone. :)

gorilla player,

Click the link below to see the Win, Loss & Tied Percentages by True Count for 2 Decks, 75% penetration, 1-8 spread, no cover, S17, DAS, High-Low from Norm's excellent BJ Stats site.

If you neglect the TC of +17 and above (since as you can see by dividing the Total Units Bet by the Avg. Bet, these TC's comprised a total of 7 hands out of a grand total of more than 500,000,000 hands), you'll see that the Including Ties Win% increases nearly monotonically with increasing TC. Thus, for any reasonable TC, the rules is "The Higher, The Better!"

Of course, as Meadowlark correctly indicated, at fantastically high TC's your EV may not increase, but how often do you see a TC of +50?

Dog Hand

That was my point. IE that as the count increases, up to a point, your EV increases also. The question is where does it begin to taper off? IE my "impression" was that at the incredibly high TC the other night, all I was winning was the natural bonus...

Of course, with Hi-Lo, a TC of +50 would be a bit hard to get in 2D (or in any number of decks). :) Perhaps in the "good old days" a +50 might happen if the house removed a bunch of 10's :) Otherwise it had better stop at +20... :)

I looked at the chart you gave me a link to after I replied. how did that sim get a TC of +21, which produced a loss (100%)??? Seems fishy as it claims at the top to be using Hi-Lo. 2-6 is 5 cards, 20 per deck. I could see a 2D running count of +40 if all the small cards came out, but a TC of > +20? :)

What am I missing?

Early in the session, the TC hit +16, something I don't recall having seen in 2D games. What happened next was strange to say the least. On one hand, we had 3 20's (push). Next hand I had a BJ, he had a 20, dealer had a BJ. Next hand I got a 19, he got a 20, dealer got a 21.

To analyze above: The first hand 3 20's that�s equal. Second hand BJ, 20 and BJ, everybody has 1/3 chance of getting 20. If the dealer gets 20, both players have blackjack and gain 3 bets in total.If one of the players gets 20, the players lose 1 bet. But this "20" happens twice, one for player A and another one for player B. So the player wins 1 bet overall (3-1-1) for a total of 6 bets (2 bets x 3 games). That�s 16.67% advantage. For the third hand, 19,20,21 (no blackjack), every one has the same chance to win or lose. Tha's means dealer may have 19,20 or 21 by chance. So it is an equal game again. So your example shows that you just had a poor luck. Theoretically, on the above cards the players should win one bet out of the total 18 bets (2 bets x 3 games x 3. I use x3 to make every game equal weight.). That�s 5.56% gain on your money overall. Not bad at all for average play. Of course, if you got a poor luck you would lose but you could also potentially have a good luck and gain a lot. The advantage play for counters usually points to about 1.5 % advantage. This is exceptionally good if the luck is not that bad.
I am not convinced that the high count in anyway hurts you. More proof is needed if you think otherwise.

At 75% penetration, there will only be 26 cards left to be played. If 10 of them are Tens and 16 are neutral, the TC prior to dealing the hand will be 20. You could conceivably have even higher TCs by replacing one of more of the 16 neutral cards with Ten cards. Theoretically, the TC could go as high as 52 "at the cut-card", using Norm's criteria. The odds of that, though, would obviously be astronomical (and not worth the time and space it would've taken Norm to report the results).

Note that the 8-unit loss represents the play of just one hand (a max bet in a 1-to-8 betting ramp). Similarly, only one hand appears at the other end of the scale, too (TC = -20).

Late at night it didn't make much sense. Clearly it does when the morning comes. :)

As I said, this was based on one particularly obvious case.

What I thought about, looking at a "boundary condition" was to remove all low cards. Now on every hand there is a probility for getting a pat hand that is pretty high. Yes there are still neutral cards, but for a SD game, we have 20 big cards, 12 neutral cards. Your "advantage" comes where the dealer gets a stiff hand, which means he has to draw 2 of the neutrals. It seems that this becomes a matter of more luck than anything else. Everyone has an equal chance of getting a 21/20 hand, so the edge to the player is that extra .5 payoff on 21. After that, everyone has an equal chance of getting a stiff but the dealer has to hit and will bust.

But take this to the edge where there are only 10/A cards left, and
now it becomes pure luck as to who gets what, with, as you said, that extra .5 payoff being the only edge we see, which appears to be worse than the previous case where the dealer could get a stiff and break.

Probability theory is strange, of course, and the above is probably all wrong, for obvious reasons. It just struck me as strange, since the negative counts don't seem to get progressively worse for the player...

I understand your point. Itlooks like the dealer has a chance to bust while the player has the option of not hitting and therefore avoids busting. When the dealer busts, the player will win a lot. Hmmm, I don't have the tool to really find out the whole picture to validate or invalidate your point. But I do have a limited tool to find part of the picture. Let's see if you have 1 deck with 2,3,4,5,6 removed. When the dealer's open card is 10 or ace, there is zero chance that the dealer will bust. So the player doesn't have any advantage except that blackjack favors the player for .5 extra payoff. So we can exclude them and study only for dealer's open cards of 7,8 or 9. For a head-to-head comparison between the dealer and the player, let's assume the dealer's first card and the player's first card are both 8. Dealer must hit to soft 17 or higher and the player always stays on stiff hands.The dealer will bust 23.32% of the time. But overall the player will win 52.29% and lose 47.71% with a net gain of 4.58%. What happens here? The reason is that although the dealer will bust over 20% of the time but dealer will also gain some advantage by hitting. If dealer hits on 16 he may get an ace and get to 17 which will win over the player's stiff hands. A similar situation happens when both dealer and the player have 9 as the first cards. The dealer will bust 10.898% of the time. But overall the player will win only 50.34% and lose 49.66% with net gain of 0.68%. For dealer's open card of 7, don't forget the dealer has a chance of getting three 7s and reach 21 which will most likely win over the player. I don't have the tool to find out the figures for 7 vs 7 or where dealer's first card is different from the player's first card.
From the observation of this limited picture I would think the player's advantage in the situation above is smaller than one would be lead to believe. That would mean the .5 extra payoff for player's blackjack will weigh more than dealer's busting. Again, this is only part of the picture and one cannot make an absoluate conclusion here.

But take this to the edge where there are only 10/A cards left, and now it becomes pure luck as to who gets what, with, as you said, that extra .5 payoff being the only edge we see, which appears to be worse than the previous case where the dealer could get a stiff and break.

gorilla player,

In the above selection from your post, you seem to be missing some vital points that lead to the player having a HUGE advantage over the dealer in this situation.

Consider playing BJ with an infinite deck consisting of nothing but X's and A's with four X's for every Ace, to keep the usual 4:1 ratio of X:A. Here, the odds of receiving an A-X BJ are (1/5)*(4/5)=4/25, and the odds of an X-A BJ are (4/5)*(1/5)=4/25, so the odds of being dealt a BJ are 2*4/25 = 8/25 = 32%. By similar reasoning, you'll start with A-A (1/5)^2=1/25 = 4% of the time, and X-X (4/5)^2=16/25 = 64% of the time.

The dealer has two possible upcards: A or X. Which would you rather see? The answer is not intuitively obvious. Let's consider each in turn.

Now 1/5 of the time the dealer will have an A up... do you want even money or insurance? Can you say "Hell, yes!"? After all, the dealer has an 80% chance of a BJ. However, you should be hoping assiduously that you lose the insurance bet, because in that situation you'll clean up! If he doesn't have a BJ, then you know that he has an Ace in the hole, for a soft 12. What's the dealer's only hope of NOT busting? That's right: he has to draw five more Aces before drawing two X's (or SIX more Aces, if the table is H17... this is one situation where H17 is better than S17 for the player). Thus, if the dealer shows an Ace and you lose the insurance bet, you'll split 'til the cows come home. Here, if RSA is allowed, that's just icing on the cake! Therefore, you (almost) can't lose against the dealer's mighty Ace!

The other 4/5 of the time the dealer will show an X. Now 20% of the time he'll have an Ace in the hole: you'll push 32% of these hands with your own BJ and lose the other 68%.

If he doesn't have a BJ, you know he has a pat 20, so how should you play your hand? Again, 32% of the time you'll have a BJ, so take your 3:2. (If you DD, you'll win 80% of the time and lose 20%, so 3:2 is better. However, if BJ pays 6:5, EV(DD)=EV(Stand); if BJ pays 1:1, then DD).

Against his pat 20, 4% of the time you'll have A-A, so then you'll split and pray that RSA is allowed, since you know 12 is a loser.

Finally, 68% of the time you'll be facing his pat 20 with a pat 20 of your own, so what do you do then? That's right: you split 'em! (Just out of curiousity, what is the index for splitting 10's vs. a 10 in a normal BJ game?) Here though, you have nothing to lose: each X will either get an A (20% of the time) or another X, which you will continue to split as long as possible. Every one of your resulting hands will either win or push: thus, you can't lose when splitting X's vs. his pat 20!

In the end, the only dealer hand that will cost you much money is the X up BJ vs. your non-BJ. The odds of this are (4/25)*(1-8/25)=10.88%, or roughly 1 hand in 9. The only other hands that you will lose are when you split A's and receive another A that you cannot split again (either because RSA is not allowed or you've already split to the maximum allowed number of hands), and the dealer has either a pat 20 or he gets the miracle five or six A's draw to his soft 12. However, you get A-A only 4% of the time, so these hands will not contribute very much to the overall picture.

All the other hands (85+%) will be non-losers for you, and most of them will in fact be big winners due to the multiple splits.

In the end, even if BJ's pay even money, I'd play this game all day long!

Dog Hand

I had not considered the insurance issue at all, obviously. I was just noticing that in an actual game, a way high TC didn't turn into a way-high win. IE when you insure, you push if the dealer has 21.

I just posed the question based on a couple of such observed TC values over the past year, one of them being the practice session earlier this week.

My original question was, and still is, as the TC rises, we generally attribute a .5% advantage to each increment of the TC. Does this continue all the way up to a TC of 20 and beyond? IE a deck with nothing but 7-8-9-10-A cards? Logic said "yes" but the observation
suggested "maybe not"...

gorilla player,

The BJ Stats website I cited earlier used a sim with half a billion hands, and found only one with a TC of +21. To check whether or not the EV grows linearly (or even monotonically) with TC for TC above +20, we would need a truly gigantic sim. Say we wanted 100 hands sampled at TC = +21... we would need a fifty billion hand simulation. Even then we might not get significantly many hands at +22, +23, etc.

Anyone got a spare Cray lying fallow?

Dog Hand

I do have access to hardware that fast or faster. And I'm going to work on some distributed code to use this new cluster we are putting together here (we are looking at 64 nodes, each node will be a dual-cpu (but each cpu will be dual core for a total of 4 cpus per node) opteron-based box.

Will have plenty of horsepower to even reach to one trillion hands, once a distributed sim is completed. :)

However, this should be doable at a smaller scale, just by removing cards from the initial deck so that the running count starts off high at the beginning...

Will have plenty of horsepower to even reach to one trillion hands, once a distributed sim is completed. :)

20 trillion rounds were simmed with CVCX for Blackjack Attack 3e Chapter 10.

However, this should be doable at a smaller scale, just by removing cards from the initial deck so that the running count starts off high at the beginning...

That would not give the correct answer.