The cookbook

[Sonny]

Lets say you tracked a slug of 26 cards that had a count of -10 (excess of high cards)

Now lets say that this slug got mixed in with half deck that had a count of +8 (excess low cards)

In that case you have a 1-deck segment with a running count of –2. Just play that segment as though the RC (and TC) started at +2. No formula required. The NSR is for estimating the count when a tracked slug gets mixed with an unknown slug. If you use the NSR formula for a segment where both slugs are known then you will end up overestimating your advantage and overbetting your bankroll.

under these conditions the multiplier -1.5

and number of pseudo decks is 1.75

Right, for a 4D game where a tracked half-deck slug gets mixed with a random half-deck slug. For any other situation those numbers would be different. For example, in an 8D game the multiplier would be –1.75 for 1.88 pseudo decks.

-Sonny-

 

[iCountNTrack]

I think you misunderstood me Sonny, clearly if you knew the count for both segments you would not use the NRS formula. I am giving an example where we the NRS would fail (obviously we had no knowledge that the slug that got mixed in had a count of +8) because you will be over-betting thinking your EV is 4-5% while in reality it is nowhere near that.

 

[iCountNTrack]

Right, for a 4D game where a tracked half-deck slug gets mixed with a random half-deck slug. For any other situation those numbers would be different. For example, in an 8D game the multiplier would be –1.75 for 1.88 pseudo decks.

-Sonny-

LOL Sonny I have known the NRS formula since 1992 but thanks anyway

 

[Sonny]

I think you misunderstood me Sonny, clearly if you knew the count for both segments you would not use the NRS formula. I am giving an example where we the NRS would fail (obviously we had no knowledge that the slug that got mixed in had a count of +8) because you will be over-betting thinking your EV is 4-5% while in reality it is nowhere near that.

I must have misread your post. Sorry about that. It looks like you meant to say that a –10 slug got mixed with a slug that we assumed was random but actually had a value of +8. In that case the NSR would give us very inaccurate results. However, that is just one case. The NSR formula is meant to be used as a means to estimate the value of the unknown slug. There will be times when it is much higher or much lower than the actual results, but in terms of an estimation it seems pretty reliable. I’m sure you already know this, but maybe my ramblings can be useful to other readers.

In general the NSR TC will be more extreme and less volatile than the “old fashioned” method because it assumes that the cards being dealt have a resonable probability of being from either slug. The TCs will tend to be higher and they will drop more gradually. If a bunch or high cards come out, the NSR doesn’t drop as fast because it assumes that some of those cards were from the unknown slug. In many cases it will overestimate your advantage, but I don’t know to what degree. My use of the formula has been very limited.

Welcome aboard, by the way! It's nice to see the Advanced Strategies forum get a little action.

-Sonny-

 

[iCountNTrack]

Thanks Sonny, it is good to join a Blackjack forum...

I know NRS works just not as well as people claim, 4-5% EV is a myth my extensive simulations show it is only about 0.3 % increase from simple card couting (Hi-Lo, 1-15 bet spread).
The 4-5% EV is only obtained from brute force shuffle tracking where you know the count for each slug and there total after the mix.

 

[callipygian]

I know NRS works just not as well as people claim, 4-5% EV is a myth my extensive simulations show it is only about 0.3 % increase from simple card couting (Hi-Lo, 1-15 bet spread).

Is EV here being used in the strict definition of EV (units won per units bet)?

4-5% EV sounds about right, and 0.3% as a normalized win rate seems like a 4-5% EV multiplied by the fraction of hands in which a NRS can be exploited.

 

[rukus]

I must have misread your post. Sorry about that. It looks like you meant to say that a –10 slug got mixed with a slug that we assumed was random but actually had a value of +8. In that case the NSR would give us very inaccurate results. However, that is just one case. The NSR formula is meant to be used as a means to estimate the value of the unknown slug. There will be times when it is much higher or much lower than the actual results, but in terms of an estimation it seems pretty reliable. I’m sure you already know this, but maybe my ramblings can be useful to other readers.

If a bunch or high cards come out, the NSR doesn’t drop as fast because it assumes that some of those cards were from the unknown slug. In many cases it will overestimate your advantage, but I don’t know to what degree. My use of the formula has been very limited.

-Sonny-

i think sonny is correct here. the NRS formula allows you to estimate and update an average measure of what a slug mixed with some random slug equates to in terms of TC. the key word is average. in iCountNTrack's specific example (or "many" others), the formula might overestimate the actual TC. but there are an equal number of opposite examples where the formula might underestimate the advantage (say if you mixed the known slug with an unknown slug of high cards). the key is that the best we can do without brute force tracking every segment as iCountNTrack suggests is to use the AVERAGE that we can get from the NRS formula. on averagee, the count will fall linearly, but we all know it doesnt work that way in any specific scenario. also, i would argue that the NRS formula helps guard against overestimating an advantage by forcing you to use a count of the "psuedo decks" remaining for your divisor instead of the actual smaller size of the playzone (slug+unknown cards).

iCountNTrack im sure you know this but for others i will repeat: in fact, the greatest thing about using the NRS formula is that you can update the TC as you play through a playzone. so if you had indeed inadvertantly mixed a slug of tens/aces with a +8 slug, you can update your TC as the cards come out. if you see all the +8 cards come out early, your adjusted TC will only go up and you can bet higher because you KNOW that by the end of the play zone if you tracked properly, the high cards must come eventually. as a matter of fact, this is why the NRS would be preferable to the constant TC method snyder recommends - you can update your TC as the low cards come and raise your bets towards the end of the playzone when you KNOW the high cards are coming if they havent already.

now as for what NRS is worth vs constant TC estimates or even what ST is worth in general over a regular counter's EV, i am wrestling with this problem myself. i would love to be able to figure out a true EV estimate from ST a shoe (or specific beatable parts of a discard tray). wonder if its time to invest in CVShuffle.

but i do think the 4-5% EV estimate is around what we should expect purely from a common sense point of view. even if a ST can track only one or two segments of a shoe and either cut in a high slug or out a low slug, on average he will see many more higher TC situations than a normal counter, ie the frequency of TCs seen by a STer should shift upwards towards higher TCs. this alone would increase EV.

and i echo sonny's sentiments. good to see the AT section alive!

 

[iCountNTrack]

i think sonny is correct here. the NRS formula allows you to estimate and update an average

iCountNTrack im sure you know this but for others i will repeat: in fact, the greatest thing about using the NRS formula is that you can update the TC as you play through a playzone. so if you had indeed inadvertantly mixed a slug of tens/aces with a +8 slug, you can update your TC as the cards come out. if you see all the +8 cards come out early, your adjusted TC will only go up and you can bet higher because you KNOW that by the end of the play zone if you tracked properly, the high cards must come eventually. as a matter of fact, this is why the NRS would be preferable to the constant TC method snyder recommends - you can update your TC as the low cards come and raise your bets towards the end of the playzone when you KNOW the high cards are coming if they havent already.


but i do think the 4-5% EV estimate is around what we should expect purely from a common sense point of view. even if a ST can track only one or two segments of a shoe and either cut in a high slug or out a low slug, on average he will see many more higher TC situations than a normal counter, ie the frequency of TCs seen by a STer should shift upwards towards higher TCs. this alone would increase EV.

If you actually have knowledge of the count of each of the slug that got mixed in to make your playing zone, you don't need to use the NRS formula, and you shouldn't anyway because the total count is more accurate than the one expected from NRS, and you don't need the use the NRS to update the count because you can do it without the NRS. so for instance if you mixed a -8 slug with a -4 slug you know your playing zone has a -12 count, so for you can adjust the count as the cards are dealt accordingly so you start in your head with a count of +12 for every low card count increases by one unit and for every high card it decreases by one unit and so on.

The following is picture shoes the result of my simulations (400,000,000 hands), the top part is 4 decks 75% penetration, S17, DAS, hi-lo full indices, 1-15 bet spread without Shuffle Tracking, the lower row shows includes shuffle tracking using the NRS formula (for negative and positive slugs, the slug tracked was the first half deck)

IBA Initial Bet Advantage or EV, you can see that it only increases by 0.2% when ST NRS is used, however the SCORE (from BlackJack Attack) is higher when ST NRS is used, NO (the number of hands needed to overcome negative fluctuations with one standard deviation) is lower.

However, we have to be very careful as the shuffle i used "4 Deck Riffle and Restack" is a really simple and primitive and it only happens in your dreams.

 

[rukus]

If you actually have knowledge of the count of each of the slug that got mixed in to make your playing zone, you don't need to use the NRS formula, and you shouldn't anyway because the total count is more accurate than the one expected from NRS, and you don't need the use the NRS to update the count because you can do it without the NRS. so for instance if you mixed a -8 slug with a -4 slug you know your playing zone has a -12 count, so for you can adjust the count as the cards are dealt accordingly so you start in your head with a count of +12 for every low card count increases by one unit and for every high card it decreases by one unit and so on.

The following is picture shoes the result of my simulations (400,000,000 hands), the top part is 4 decks 75% penetration, S17, DAS, hi-lo full indices, 1-15 bet spread without Shuffle Tracking, the lower row shows includes shuffle tracking using the NRS formula (for negative and positive slugs, the slug tracked was the first half deck)

IBA Initial Bet Advantage or EV, you can see that it only increases by 0.2% when ST NRS is used, however the SCORE (from BlackJack Attack) is higher when ST NRS is used, NO (the number of hands needed to overcome negative fluctuations with one standard deviation) is lower.

However, we have to be very careful as the shuffle i used "4 Deck Riffle and Restack" is a really simple and primitive and it only happens in your dreams.

hmm, interesting, but i sill find it hard to believe it only goes up by 0.2%. maybe not the 4-5% others quote, but i would think it HAS to be more than .2%. NOW that SCORE increase makes sense to me - a 50% increase in SCORE/decrease in N0 sounds good to me.

yes of course if you track all discard segments you do not need NRS because you have all the info you need already between the two segments.

can anyone else who's simmed this (QFIT maybe?) weigh in on the gain?

 

[takinfromindians97]

cookbook

I have the cookbook and i think its worth haveing as a book in your collection and if your looking to save a few bucks on it you can buy it used from some places. I bought mine used and it came looking like it had never been opend and i payed less then half price.

 

[alienated]

That's the role of N

iCountNTrack, your numerical example illustrates why N is needed in the formula, and why N needs to be greater than q (actual playzone size): it's because, hypothetically, or notionally, the expected big cards did not come out because they were stuck behind the "virtual shuffle point."

Provided it was reasonable to assume the slug was randomly mixed with the unknowns, the NRS formula gives the correct TC, so you will not be overbetting. You will be betting correctly, given the information you have (embodied in the true count). It is the same as in a count game where you reach the shuffle point and the running count is sky high. You expected to see more of those big cards but they were out of play. It's annoying, but you didn't overbet. Implicit in your true count was the possibility that this unfortunate event would occur. That's why true count is running count divided by decks remaining, not decks remaining till the shuffle point. Just as d > p (d = total decks used, p = shuffle point) in a count game unless pen is 100%, N > q in an NRS track game unless all cards in the playzone are "slug" cards.

(If you have a good reason to think the slug is not randomly shuffled through the playzone, and can account for this, you can do better that using the NRS formula and the NRS formula may not be applicable.)

I agree with your point that NRS tracking often does not add hugely to profitability, especially compared to aggressive wonging. (The closer k is to q, the stronger the track.) I think there are cover benefits, though, which can enable putting in more hours of play than with straight counting.

 

[alienated]

Profitability

Having said that, your sim of the scenario you considered does show a strong improvement in win rate, SCORE, N0, etc as you note. The increase in action shows that you are identifying more big bet situations, so the 0.2% increase in advantage refers to a bigger "outlay" of chips.

iCountNTrack, one other thing that I think is not always fully appreciated about the NRS formula and its parameters is that it provides quite a general way to analyze games. You correctly mention that you considered a simple shuffle that would be hard to find for actual play. But your sim results actually apply equally to any game (with the same rule set) in which, by whatever means, you can track a half deck into a single deck in a game using ? decks (sorry, I forgot whether you considered 6, 8 or some other number of decks).

More generally, we could describe a game with the following parameters:

d, p, q, k

where d = number of decks, p = shuffle point, q = size of playzone, k = slug size.

Suppose, to take an example, that we can track 1 deck (possibly from disparate parts of the shoe) randomly shuffled into a 2 deck playzone in a 6 deck shoe with 4 decks dealt. So we have:

(d, p, q, k) = (6, 4, 2, 1)

The values of d, q, and k imply values for the NRS formula's N and r.

If you can analyze the profitability of this game (either analytically or through simulation), your results will apply to any game or any situation that produces these parameters. It doesn't matter what shuffle was used, or which cards you tracked. All that matters is that d = 6, q = 2, k = 1.

This also gives a handy way to select games. If you run sims for idealized shuffles (not necessarily realistic ones) that produce appropriate values for d, q, and k, you can rank different scenarios for profitability, risk/return, etc. For 4/6 deck games, you might consider the following cases:

(d, p, q, k) = (6, 4, 3, 0.75)
(d, p, q, k) = (6, 4, 3, 1.50)
(d, p, q, k) = (6, 4, 3, 2.25)
(d, p, q, k) = (6, 4, 3, 3.00)

Analyzing these cards can give upper limits on the profitability of various "best half" scenarios. Analysis can be undertaken for different rule sets, penetration levels, etc. Approaches other than "best half" can be analyzed similarly.

So your sim gives an upper limit to the profitability of one category of track game: namely, 1 deck shuffled into 2, irrespective of how (as long as randomly).

 

[iCountNTrack]

Great posts Alienated! as instructive as always
I would like to add one thing, NRS does work irrespective of the type of shuffle as long as q<N as you have mentioned. However, the performance of the method decreases as the shuffle gets more complex for instance:

SCORE/NO is 51/19000 for a stutter shuffle vs 65/15000 for the simple riffle restack.

I hadn't mentioned this in my previous post, but the shuffle precision was exact and error free, including errors will quickly deteriorate the NRS perfomance, but that is a whole other story.