SD. All Aces out first hand. Count then climbs...Do we bet up at all?????

Let me paraphrase...I had a situation where all four aces came out on the first hand after the shuffle. Then the count began to climb on subsequent hands. I elected to flat bet since I assumed that I couldn't get any edge against the dealer since a 3:2 payout for a BJ was no longer viable (until after the shuffle). This may be one of those notorious gray areas. I hope not since this problem creeps up from time to time. I know that there are two additional benefits to high counts, besides getting more blackjacks: dealer busts more often and our double-downs fare better (esp. 11 or 10 vs. 6, e.g.). I just wasn't sure if these advantages - minus any aces - would be enough to offset the houses edge.
So�you BJ pros, grade my performance...How'd I do? (Go easy, now. I just got rid of my training wheels) Thanks in advance. 49.

The most important thing is betting your money properly. Do yourself a favor and read Playing Blackjack as a Business.

As Igor said, you should be learning some sort of plus/minus or hi-lo count system after you have mastered basic strategy. For a single deck game, any valid system would tell you that if the count went positive before the dealer shuffled, you would increase your bet. Most systems count big cards (Aces AND Tens) vs. little cards(2,3,4,5,6 and possibly 7's). As soon as you have seen an excess of little cards vs. high cards, the system would tell you to bet more next round.

As an example, suppose you saw all 4 aces come out, NO tens come out, and 5 or more little cards come out, all on the first round. The count would then tell you to increase your bet.

There are some excellent books for beginners on this site. Also Playing Blackjack as a Business is OK for single deck only, but it is a very old book and outdated in some ways.

AB

The answer is that, yes, he was thinking correctly. Doubling on elevens would probably improve. Doubling on tens (and nines, if an available option) would probably be slightly worse with an absence of aces. I probably wouldn't split nines, either, if all the aces were gone.

I'd probably continue to increase my bets with a climbing count, but more conservatively. I'd be more focused on preparing to watch the dealer shuffle that slug containing four aces. ;)

Your thinking is just fine, 49.

First, the High-Low system is accurate. Your High-Low count told you to raise your bet; that was the correct thing to do.

Second, we have a more serious issue here: playing hunches. Many counters fall victim to this. They don�t know what their index is, so they make a guess.

You know from Sims that if you play your system, you will win. Why make a guess about deviating from that system? Most such guesses will cost you money, as this one did.

He was playing a game in which BJs pay even-money. By that, I mean he and the dealer will break even on the money they receive on blackjacks (which is "zilch").

Since we discourage players from playing 6:5 blackjack, I can't see how we should encourage him to increase his bet here, when he has no chance of getting a blackjack at all.

I assume, therefore, that I'm missing something. Could you please explain the difference between this game and an 1:1 blackjack game? The only differences I see are the situations I've already described. I just can't see following a typical bet-ramp based on the count in this game.

Thank you so much for truly understanding my problem. Your post made me feel much better (Oops, we're not supposed to have feelings...we're machines, right? :)) Math prof, you're brilliant so I can only assume that my wording is sloppy and my point is not clearly made...again. Arnold Ziffel Buys a Laptop hit the nail on the head: I felt like I was playing a 1:1 game instead Of a 3:2 game (till the end of that deck, at least). I do hope you guys will give the original question some consideration; I think it does have merit. Thanks again. (I love this board!) 49.

Each HiLo true point is worth approximately 0.5%.

Now let me address your question of a hypothetical 6:5 game. Suppose you watched the first round of a 6:5 game, and the a bund of low cards came out. You count, and the RC of +6; the TC is a little higher.
The house edge on LV Strip 6:5 game is 1.45. The +6 TC increases the player edge by about 6*0.5=3%. This means that the overall edge on the next round is -1.45+3.0 which is about 1.5%.

If you are allowed to Wong in, then you could make a good positive EV bet on the next hand.

The same thinking would apply to a hypothetical game in which BJ paid even money. The house edge of the top would be higher, so the calculations would be a little different. But if enough low cards came out, you would be able to Wong in with an advantage.

Note that there is a difference between Wonging in on the next round, and sitting down to play a session of 6:5 from the top.

Now to get back to the original question. This situation is not that rare. In many single decks you will have all 4 Aces fall before the last round. Under the logic presented here, we should stop using High-Low whenever the last Ace come out.

Again, this is what I call a �hunch play�. The books tell you how ot play one way, but you don�t quite believe it, so you make up your own �improvements�. Now there is a lot of room to make improvements to High-Low, but my experience is that most hunch plays cost the players money.

There have been numerous sims of High-Low (and other count systems) by various reputable authors. From these, you can get a good idea of your overall EV and Variance. In all theses sims, these cases (all Aces gone) do occur. It isn�t like the computer was rigged so as not to allow this to happen. So this scenario is already included in the results. This means one of several things. Either it is so rare that it won�t effect your game and so you should not worry about it. Or, the High-Low system still works in this scenario.

49 and Counting, Mathprof said you were playing hilo is that correct? Anyway hilo counts all the low cards 2-6 as having the same impact even though say the 5 is twice as powerful as the 2(So if you saw the 4 fives come out on the first hand and the count was neutral i'd be jacking up my bet,you have just made a good observation) single deck can mean an observation makes you play far different to multi-deck.(weird strategy variations)Did you do the right thing?Maybe if you were playing,
2-6 +1
7,8,aces zero
9,tens -1
then I reckon there is a good chance you did.(if you keep a side count of aces the above is a good one for single deck)

He said:

"I elected to flat bet since I assumed that I couldn't get any edge against the dealer since a 3:2 payout for a BJ was no longer viable (until after the shuffle)."

"He was playing a game in which BJs pay even-money."

Since there were no longer any BJs to be had, the player receives the same amount for a BJ as the dealer. Hence, the "zilch" in my original post. :)

He wanted to use something other than count value to determine bet size. He was not thinking correctly.

I read many posts by new players that reflect an unfamiliary with information and concepts with which they really should be familiar. This ignorance and uncertainty is expensive and unnecessary and brings up a question that is, or should be, asked by anyone trying to school themselves from nada to functional proficiency in the least time: what should I read first to learn what I need to know? This is my suggestion and in this order:

Cardcounting for the Casino Executive - Zender cuts to the meat in a business-like manner because there's more to the job than making sure the fills are done correctly. The whole purpose of his book is to cut to the meat in a business-like manner, and it does this for a system player wannabe just as it does for a neophite game supervisor.

Beat the Dealer - I recommend reading both the '62 and '66 editions. The '62 edition was the one on the Time's best seller list for half a year and contains the Ultimate Count values, but it was the '66 edition that has caused the casinos all the problems because it contained Thorp's rendering of the Dubner Point Coint. The Dubner Count is the progenitor of all other published blackjack point counts. You can fortify your appreciation by spending some time in a well-stocked university library looking up the many magazine articles where Thorp's writings appeared before publication of his book(s). The articles are more complete.

The Casino Gambler's Guide - The late Alan Wilson (PhD!) was, literally, a rocket scientist and a pioneer of blackjack analysis. He began his work before Roger Baldwin et al began theirs. His first determinations of basic strategy were made done manually, drawing from a subset of playing cards unseen by the casino patron. He used an approach which mixed direct calculation with such sampling. Later he was able to squeeze his calculations onto the scarce unreserved computer time of his employers.

The Theory of Gambling and Statistical Logic - Richard Epstein was another pioneer game analyst. Later editions contain deparure tables for Griffin I.

Playing Blackjack as a Business - Revere's book is dated, but not outdated as many novices claim. The betting advice is dangerously optimistic, and some who knew him attribute unwholesome motives to promulgating it this way. I don't know, but I had heard rumors of unsavory reputation and avoided visiting 1517 Rexford Place during his lifetime. But Revere was responsible for creating more twenty-one system players than anyone else during the '70s. Revere found Thorp's method of deriving point count decision indices (dividing the running count by the number of unseen cards) to be unworthy of the effort and devised the True Count as is used by every point count today. His methods of self-training and use of the Inquiry Method for memorization (he didn't call it that) of departure tables still work better than any computerized methodology I've seen. His chapter on the RPC contains in-depth anaysis of the four deck shoe game. And all his electronic calculations were done by Julian Braun. Just remember that his betting adice is unreliable.

As for reading Baldwin, Maisel, Cantney and MeDermott (I think I got that right), you can read the original publication in the September 1956 issue of JASA, the one that inspired Thorp to program and Wilson to bemoan the end of the beatable game (this is a half-century ago, folks!) in the bjmath linked to by this site. The 1957 Playing Blackjack to Win, which was written for the public and contained suggestions as to the possible implication of unbalanced depleted decks is unavailable. I have been looking for it for closing in on four decades. I do know that the original copyright was extended by a Roger R. Baldwin (the Roger Baldwin? An heir? I dont know.) under the revised copyright statute and the book will not be in the public domain till way into this century, long after my acutuarial mortality. Too bad.

I suspect that where we disagree is really just a matter of what constitutes a "hunch" and what constitutes an intelligent decision. Please check my math and see if this makes sense:

In a single-deck game, each player can expect to receive a BJ approximately every 21 hands. This means that the player can expect to receive a "profit" of a half-unit every 21 hands. Assuming that 100 hands per hour is easily attainable in single-deck and that the player and dealer will receive BJs in equal amounts, over the course of an hour a player's profit from BJs alone will be ~2.38 units ((100 / 21) * .5 units).

In the particular situation described by 49_and_Counting, he won't be getting any BJs at all for the remainder of that deck. Whatever advantage the TC tells him he has, he must bet before the next hand knowing that he's giving up approximately .024 units before the cards even hit the table.

Of course, as you pointed out, the sims DO include plenty of occasions when all four aces disappear in the first round. The advantage at each TC along the number-line is derived from decks having all sorts of "first hands". In some decks, there are first rounds in which NO aces come out on the first hand, one ace comes out, two aces come out, etc. It is more than just a "hunch" for "49" to realize that, of the five basic situations (0-4 aces remaining), the four most prosperous ones for the player have been eliminated. In fact, if we assume that 13 cards were played in the first round, more than three-fourths of all simulated decks can now be tossed out the window, because they're no longer relevant. That three-fourths surely represents (as a group) a sizable chunk of the more lucrative decks. With them eliminated, we have no way to nail down just what our advantage is at each TC. We only know that whatever advantage-figure we usually associate with a particular TC is too high. Since we don't have any more data than that, I'd definitely go with a conservative bet-ramp. You may see that as a "hunch"; I just see it as a logical adjustment.

From Beat The Dealer by Edward O. Thorp (p. 118 in my copy):

"Your results improve further if you adjust your bet size for an excess or shortage of Aces. When all the Aces are gone, subtract 4 percent from your estimated advantage. When the deck has twice as many Aces as normal, add 4 per cent to your estimated advantage."

Of course, Thorp's figure may not be accurate, although I'm sure it's in the ball park. Also, he brings up this point while discussing his Ten-Count system. Nonetheless, it wouldn't be a stretch at all if 49_and_Counting assumes that his disadvantage has dropped by some amount. He will have deduced on his own what Thorp reported after running who-knows-how-many simulations. If "49" reached your TC of +6 for a "3%" advantage, Thorp's adjustment (or something close to it) puts him back into a negative EV situation, or at best a "neutral" one.

To put it another way, you have the choice of sitting down at a table where all four aces have just been dealt, or at a table where no aces have been played. At both tables, the count is identical. If you'd prefer to play one over the other, you're essentially saying that you're willing to bet more money at one table than the other. If you had the opportunity to play both tables at the same time, are you saying that the size of your bets at each table would be identical, as long as the counts at each table were identical? Would you be incorporating a "hunch" to bet more at the table where no aces have been played?

Your list of recommended reading material looks great. Thanks for posting it! :)

"He wanted to use something other than count value to determine bet size. He was not thinking correctly."

If "49" noticed that an ace is going to be the next card dealt and he's going to receive it (as his first card), are you saying he should use only the count to determine his bet-size?

Playing with "information" pays better than playing the count, and is also much older. Germane to my previous comments, Revere mentioned, in a diatribe upon the incompetence of pit supervisors, five instances where a player who is "playing perfectly" mades plays that should be red flags to a competent pitboss. Revere didn't expound, but all five are information-based, either from an identified hole card or the undealt top card. Before Thorp published, flashed cards, marked cards or dealer collusion were the main concern. Card counters were inconsequential eccentrics.

I did a quick CA to compute the effects of Ace-removal single deck game. In the interests of speed, I used approximation techniques, but they good enough to show the effects.

The rules are H17, as are most SD games in this country. The EV�s are computed using �perfect play�, and your play with indices will be slightly worse. Again, I don�t think this will be a significant factor.

The first column is he number of Aces removed. The second is the overall EV. The third is the change in EV over the full pack. Then the TC and the ratio of EV/TC:

 

Removed	EV	Total Change		TC	Change/TC 

Aces 

0		-0.17%		0.0	 

1		-0.71%		-0.54%		-1.0	0.53% 

2		-1.30%		-1.12%		-2.1	0.54% 

3		-1.92%		-1.75%		-3.2	0.55% 

4		-2.59%		-2.42%		-4.3	0.56% 

Perhaps I should clarify one thing: I don't consider myself a newbie any more since I have been successfully counting for months now, my bankroll going from several hundred dollars to over $3,000. Sure, Dame Fortune has smiled on my initial journey: it could have just as well gone the other way. I think I have one solid asset that will make me into a long-term winner: I keep putting the money out during high counts regardless of how many times I get slammed! It seems to be paying dividends, as my bankroll has climbed steadily.

Pardon my comment about the "training wheels". I was trying to be cute and inadvertantly gave the impression that I was brand new at counting which, as I just stated, I am not. I'll take the blame for that one.

And a little more from a human-interest perspective. The math is very hard for me, anymore. This is a pity because I excelled at it during high school and college. My fellow classmates still remember how "smart" I was back then. It's just that those higher math skills fell into disuse over a lifetime (boy, I won't be on Math Prof's list of most-admired counters! ; )). I've read nearly a dozen books on blackjack, the ones most commonly referred to on this site. During the math chapters, my eyes glazed over. The Theory of Blackjack by Peter Griffin - although a masterpiece - was unfathomable to me. There were parts of Blackjack Attack by Don Schlesinger (another masterpiece) that I couldn't understand. Perhaps down the line I will throw myself into the math element more and thereby improve my game further. So, for now I've got some work cut out for me. Please bear with me while I try to sort this counting thing out. Thanks 49.

Sometimes it is not just about the count. If it were, no one would bother with ace reckoned counts. Losing all the aces early is something to consider. Particularly in 1D where a quick trip to the restroom will get put you into the next deck, with fresh aces. Consider losing all four aces and four dueces in the first hand versus losing no aces but instead four tens and four dueces. Let us assume we are using hi-lo. Which is better in terms of EV? A book not on your list, Peter Griffin's TOB, will help with this one.

Also curious is Griffin's revelation about comparing the EV of a deck composed of half tens and half aces to one composed only of 7's and 8's, in equal amounts. A zero count event. (Chapter ten)

regards,
adhoc

If it's wise to increase your wager when you KNOW that an ace is coming, why is it unwise to decrease your wager when you know an ace definitely isn't coming? That was the case with 49_and_Counting. (BTW, I turn 50 tomorrow. That just hit me!);)

...then the absence of four aces off the top of the deck puts us at a disadvantage of -2.59%. A subsequent rise in the TC from -4.3 to +6 would put us in a favorable position of +2.47% (-2.59 + (10.3 * .5)). However, I'm not yet confident that we should still be using the rule-of-thumb of +.5% for each increase in TC. That figure clearly assumes an even distribution of all possible outcomes; the sims used to estimate that figure assured us of that. But in the case under discussion, many of the more benefical subsets from those sims have been eliminated. It seems reasonable to me to assume that my advantage is not as good as a typical advantage at any particular TC. For example, your figures show that a loss of just one TC represents at least 6% more more than the -.5% rule-of-thumb (.53% vs .5%, due to the fact that an Ace is removed. It's my contention that any increase of just one TC will represent less than the .5% increase we've come to expect, because all of the Aces have been taken out of play.

Is it possible to sim the advantage at, say, +4TC, +5TC and +6TC for both situations? In one case, assume all Aces are gone from the deck. In the other, assume "normal" play (aces come out of the deck at random, as in normal play). I think a comparison of the two sets of advantage-figures at each TC would convince me of my error.

I have no problem understanding why 49_and_Counting reached the conclusion he did. As I pointed out in an earlier post, others have come to the same conclusion: The player's advantage is decreased with an absence of Aces. I have to admit, however, that a TC of +6 implies that a significant number of small cards have come out in a hurry. With 39 cards remaining in the single-deck game, nine of the thirteen cards played would have to be small cards (the other four cards being the missing Aces) for the floored TC to climb to +6 (RC of +5, times 1.33). More than half of all small cards (13 of 24, the Aces playing like small cards) would already be missing from the deck. The chances of a dealer drawing a stiff is reduced, but his chances of busting when he gets one are greatly increased. The harm done to a player when all Aces are removed may be more than offset by the advantage of being able to stand and watch the dealer bust, as well as the player having the ability to double down with increased confidence. If that turns out to be the case, I'd be off the mark by adopting a more cautious approach.

But I might still be missing something here. We may just have to agree to disagree. :)