Requesting help in TKO card counting system

[steger24]

A couple friends and I have been counting cards for a couple years now, and for the most part it has gone pretty well. We have run into a rather long streak of bad luck lately however, which prompted this post. We are each down about $5k ($15k collectively) in the last 500 hours (1500 collective hours). We play at separate tables but pool our money together in an attempt to neutralize the volatility. We use the TKO system which we learned from the book The Color of Blackjack, which assigns 10-A as -1, and 2-7 as 1, and 8-9 as 0. We follow the warm line outline which assigns 9 as the key count at 1 deck, 12 at 2 decks, 15 at 3, 18 at 4, 21 at 5, and a max bet at 24 no matter how far into the shoe we are (at a 6 deck shoe). At a 4 deck shoe the warm line is 7 at 1 deck, 10 at 2, 13 at 3, and a max bet at 16.
We adhere to the typical KO deviation indices, but we have also added a few of our own, as the KO book only discusses a couple, and we wanted to expand. We created the following deviation indices chart by checking the true count deviations outlined for Hi-Lo and for Advanced Omega 2 and computing the appropriate running count to match them in TKO. I understand that they may not be perfect, but we figured they would be close, and that they would provide us with a good outline at the very least. If we are wrong, please let us know. Here they are.
2D’s 4D’s 6D’s TC
+5 +11 +16 0: s16 vs 10
+6 +12 +18 1: d9 vs 2
+6 +13 +20 2: s12 vs 3, dA8 vs 5, dA6 vs 2, dA3 vs 4, Sur15 vs 9
+7 +14 +22 3: s16 vs A, split 9,9 vs 7, split 9,9 vs A, dA8 vs 4, split 7,7 vs 8, split 4,4 vs 4, Sur14 vs 10
+7 +15 +24 4: s16 vs 9, s15 vs 10, d10 vs 10, split 10,10 vs 6, s12 vs 2, d10 vs A, d9 vs 7, d8 vs 5, dA2 vs 4, split 3,3 vs 8, dA9 vs 6, Sur16 vs 8
+8 +16 +24 5: s15 vs A, split 10,10 vs 5, dA8 vs 3, dA5 vs 3, split 2,2 vs 8, dA9 vs 5, Bet Over on Over/Under 13 Side Bet, don’t split 8’s vs 10,
+8 +17 +26 6: split 10,10 vs 4, d8 vs 4, dA9 vs 4
+9 +18 +28 7: s16 vs 8, d9 vs 8
+9 +19 +28 8: s15 vs 9, dA4 vs 3, dA3 vs 3, dA2 vs 3, dA8 vs 2, dA9 vs 3, split 4,4 vs 3, split 10,10 vs 3
+10 +20 +30 9: s16 vs 7,
+10 +21 +32 10: s15 vs 8, d8 vs 3, d7 vs 5
+11 +22 +34 11: s15 vs 7, d7 vs 6

We are playing with very good conditions (1 deck penetration, 2-3 people at a table, DAS, etc.) and have spent probably 200 of the last 500 hours back counting and then calling each other in. Our bet spreads range from 1-6 at a 2 deck to as high as 1-15 at a 6 deck (I've been told this is unwise, I need no more words of caution in this regard). Given our outstanding playing conditions, and our large bet spreads, to go along with our hours of back counting, we are completely flummoxed as to why we are having such poor luck. We have been successful in the past, so we assumed we had been playing the system properly, but our recent misfortune has brought a cloud of doubt. We are looking for some answers, and any and all advice would be much appreciated. I would be happy to answer any questions you have which may allow you more insight into our system. Even if we have been messing up in one regard or another however, I would think that simply varying our bet should be enough to give us an advantage over the house. We are really in the dumps lately, and are unsure if we can continue under these circumstances. Thank you for your time and help.

[seriousplayer]

We are playing with very good conditions (1 deck penetration, 2-3 people at a table, DAS, etc.) and have spent probably 200 of the last 500 hours back counting and then calling each other in. Our bet spreads range from 1-6 at a 2 deck to as high as 1-15 at a 6 deck (I've been told this is unwise, I need no more words of caution in this regard). Given our outstanding playing conditions, and our large bet spreads, to go along with our hours of back counting, we are completely flummoxed as to why we are having such poor luck. We have been successful in the past, so we assumed we had been playing the system properly, but our recent misfortune has brought a cloud of doubt.

From reading your post it is not the system that you are using that is causing you problems. It is the table conditions. You mention that "We are playing with very good conditions (1 deck penetration, 2-3 at a table DAS, etc)". No it is not good conditions that you are playing. 1 deck penetration and 2-3 at a table is not a playable game for double deck is not a playable game. For a 1 deck penetration in a 2 deck game it is only playable when you are playing head up. You being successful in Blackjack has nothing to do with the count system you are using.

I would only backcount and do call-in om 6 deck shoe game. I would play all in 2 deck games because the edge for the player in double deck is more volatile compare to shoe games. What is the complete rule set that you are playing for double deck and 6 decks games.

[Three]

What IRC are you using? I believe COB uses -4*#decks being used.

We created the following deviation indices chart by checking the true count deviations outlined for Hi-Lo and for Advanced Omega 2 and computing the appropriate running count to match them in TKO. I understand that they may not be perfect, but we figured they would be close, and that they would provide us with a good outline at the very least. If we are wrong, please let us know. Here they are.
2D’s 4D’s 6D’s TC
+5 +11 +16 0: s16 vs 10
+6 +12 +18 1: d9 vs 2
+6 +13 +20 2: s12 vs 3, dA8 vs 5, dA6 vs 2, dA3 vs 4, Sur15 vs 9
+7 +14 +22 3: s16 vs A, split 9,9 vs 7, split 9,9 vs A, dA8 vs 4, split 7,7 vs 8, split 4,4 vs 4, Sur14 vs 10
+7 +15 +24 4: s16 vs 9, s15 vs 10, d10 vs 10, split 10,10 vs 6, s12 vs 2, d10 vs A, d9 vs 7, d8 vs 5, dA2 vs 4, split 3,3 vs 8, dA9 vs 6, Sur16 vs 8
+8 +16 +24 5: s15 vs A, split 10,10 vs 5, dA8 vs 3, dA5 vs 3, split 2,2 vs 8, dA9 vs 5, Bet Over on Over/Under 13 Side Bet, don’t split 8’s vs 10,
+8 +17 +26 6: split 10,10 vs 4, d8 vs 4, dA9 vs 4
+9 +18 +28 7: s16 vs 8, d9 vs 8
+9 +19 +28 8: s15 vs 9, dA4 vs 3, dA3 vs 3, dA2 vs 3, dA8 vs 2, dA9 vs 3, split 4,4 vs 3, split 10,10 vs 3
+10 +20 +30 9: s16 vs 7,
+10 +21 +32 10: s15 vs 8, d8 vs 3, d7 vs 5
+11 +22 +34 11: s15 vs 7, d7 vs 6

Just looking at s16vT which has an index of 0. In a 6 deck game the index is met at:
1 deck into shoe: IRC + 4
2 decks into the shoe: IRC + 8
3 decks in : IRC + 12
4 decks in IRC + 16
5 decks in: IRC + 20

Assuming you used IRC of 0 and your chart of indices is for 3 different games rather than 1 game at different depths, you are employing your index plays late in the shoe before the criterion is met and after the HILO index is met early in the shoe.

A balanced RC can be derived by TKO count (T) if IRC is 0 and the number of decks already seen (N):
RC = T - 4*N
If we set a constant D as the Total number of decks
TC = (T -4*N)/(D - N)
If we solve for T:
T = TC*(D - N) + 4*N

If you use this formula you will get a set TKO RC's for IRC=0 for various depths of penetration in the shoe. Make TC the HILO index and use the appropriate values for D and N. Now including the 7 in the main count might slightly change some HILO indices but if you are worried about your index plays using this true counted TKO will give even more accurate index plays than the warm line which when at the deepest pen after 4 decks have been dealt and you are most likely to have your top bets out is making you use index RC that are too low. That is very costly just as not using the index until way after it is reached early in the shoe.

Just look at the true counted set of indices for depth I did for the special case where the HILO index is 0 (the term TC*(D - N) drops out because it is 0). That shows how a balanced counter would use an index as you play through a shoe translated to TKO with IRC=0.

[Three]

A balanced RC can be derived by TKO count (T) if IRC is 0 and the number of decks already seen (N):
RC = T - 4*N
If we set a constant D as the Total number of decks
TC = (T -4*N)/(D - N)
If we solve for T:
T = TC*(D - N) + 4*N

You can either use the formula for TC to true count TKO or use a set of depth based indices derived from the last equation for each matchup. If you do the latter set TC in the equation to the HILO index and solve for various depths. One way uses little math in the casino but requires more memorization. The other requires far less memorization but more math at the table. Play to your teams strengths. Anybody can memorize a ton of information. Not everyone can do the math in a reasonable amount of time.

[Marvin]

A couple friends and I have been counting cards for a couple years now, and for the most part it has gone pretty well. We have run into a rather long streak of bad luck lately however, which prompted this post. We are each down about $5k ($15k collectively) in the last 500 hours (1500 collective hours). We play at separate tables but pool our money together in an attempt to neutralize the volatility. We use the TKO system which we learned from the book The Color of Blackjack, which assigns 10-A as -1, and 2-7 as 1, and 8-9 as 0. We follow the warm line outline which assigns 9 as the key count at 1 deck, 12 at 2 decks, 15 at 3, 18 at 4, 21 at 5, and a max bet at 24 no matter how far into the shoe we are (at a 6 deck shoe). At a 4 deck shoe the warm line is 7 at 1 deck, 10 at 2, 13 at 3, and a max bet at 16.
We adhere to the typical KO deviation indices, but we have also added a few of our own, as the KO book only discusses a couple, and we wanted to expand. We created the following deviation indices chart by checking the true count deviations outlined for Hi-Lo and for Advanced Omega 2 and computing the appropriate running count to match them in TKO. I understand that they may not be perfect, but we figured they would be close, and that they would provide us with a good outline at the very least. If we are wrong, please let us know. Here they are.
2D’s 4D’s 6D’s TC
+5 +11 +16 0: s16 vs 10
+6 +12 +18 1: d9 vs 2
+6 +13 +20 2: s12 vs 3, dA8 vs 5, dA6 vs 2, dA3 vs 4, Sur15 vs 9
+7 +14 +22 3: s16 vs A, split 9,9 vs 7, split 9,9 vs A, dA8 vs 4, split 7,7 vs 8, split 4,4 vs 4, Sur14 vs 10
+7 +15 +24 4: s16 vs 9, s15 vs 10, d10 vs 10, split 10,10 vs 6, s12 vs 2, d10 vs A, d9 vs 7, d8 vs 5, dA2 vs 4, split 3,3 vs 8, dA9 vs 6, Sur16 vs 8
+8 +16 +24 5: s15 vs A, split 10,10 vs 5, dA8 vs 3, dA5 vs 3, split 2,2 vs 8, dA9 vs 5, Bet Over on Over/Under 13 Side Bet, don’t split 8’s vs 10,
+8 +17 +26 6: split 10,10 vs 4, d8 vs 4, dA9 vs 4
+9 +18 +28 7: s16 vs 8, d9 vs 8
+9 +19 +28 8: s15 vs 9, dA4 vs 3, dA3 vs 3, dA2 vs 3, dA8 vs 2, dA9 vs 3, split 4,4 vs 3, split 10,10 vs 3
+10 +20 +30 9: s16 vs 7,
+10 +21 +32 10: s15 vs 8, d8 vs 3, d7 vs 5
+11 +22 +34 11: s15 vs 7, d7 vs 6

We are playing with very good conditions (1 deck penetration, 2-3 people at a table, DAS, etc.) and have spent probably 200 of the last 500 hours back counting and then calling each other in. Our bet spreads range from 1-6 at a 2 deck to as high as 1-15 at a 6 deck (I've been told this is unwise, I need no more words of caution in this regard). Given our outstanding playing conditions, and our large bet spreads, to go along with our hours of back counting, we are completely flummoxed as to why we are having such poor luck. We have been successful in the past, so we assumed we had been playing the system properly, but our recent misfortune has brought a cloud of doubt. We are looking for some answers, and any and all advice would be much appreciated. I would be happy to answer any questions you have which may allow you more insight into our system. Even if we have been messing up in one regard or another however, I would think that simply varying our bet should be enough to give us an advantage over the house. We are really in the dumps lately, and are unsure if we can continue under these circumstances. Thank you for your time and help.

A few general points about unbalanced systems, assume IRC 0 for any running count examples I provide; hope this is not too confusing:
1) Indexes will be accurate at the pivot (+4 TC for KO) and get less accurate the further away you get from this point unless you do a real TC conversion or have the index numbers memorized per deck remaining:
2) With more than 1 deck left undealt, the TC will be compressed towards +4. So, if 2 decks are undealt in a 6 deck game and the running count is 30, the TC is +7 ( TC at 24 will always be +4, the additional +6 RC is divided by the remaining decks and added to the +4). Same place in the shoe, running count of 18 means the TC is +1)
3) The further away from +4 TC the index number, the less accurate your method is and the less useful the index.

At Tthree pointed out, the 16v10 is TC of 0, which is pretty far from the +4. With 5 decks left to go, this index is +4; with 1 deck left to go this index is +20...

The Ebook version of Norm's Modern Blackjack has a table of the most important indexes by number of decks remaining. I think that it would be useful and eye opening for you to see.

Regarding your specific indexes, I would advise the following rounding:
16v10 already described. Although, if you're doing callins and backcounting, always stand.
9v2, A8v5, A8v6, 12v3, use the CoB warm line. If h17 game then A8v6 is a BS play.
At the pivot (+24 in 6D, +16 in 4D, +8 in 2D) double 8v6,8v5,9v7, 10vA; A8v4; Stand 12v2; Split 99v7, Split 99vA
At 1 below pivot (+23 in 6d, etc) take insurance, surrender 15v9,
at 1 above the pivot stand on 15v10.
Your stand vs Ace indexes are way too low. I wouldn't use those in TKO and just surrender or hit.
Double 10V10, split 10v6,5, double A9v anything... should use risk averse indexes since bankroll seems to be a concern. In your position I wouldn't double 10v10 until TC +6 or +7, same with 10 splits and A9 doubles.
Anything you have as TC 6 or higher, forget about using unless you do a real TC conversion. It'll hurt more than it helps. For example, if you get a great shoe, and get a RC of +30 with 3 decks to go in a 6D game, at that point the TC is only +6, and each of those +7 or higher indexes will subtract value.

When in doubt, go with basic strategy, and only trust index numbers near the warm line and near the pivot.

Your money will be made or lost by betting at the right time and avoiding betting at he wrong time.
1-15 spread when playing all on a 6D H17 game is not great. If you're wonging aggressively then you don't need much of a spread at all; just avoid the negative situations.

Given the time you've devoted to this, I would strongly advise you to buy CVCX and CVData and run your own sims. You'll realize that increasing the bet spread from 15:1 to 16:1 on a play all situation will make more difference than all the non-pivot, non-insurance index numbers combined. Avoiding a few extra rounds at negative counts each hour is worth more still.

Best of luck to you.

Marv

[seriousplayer]

In your position I wouldn't double 10v10 until TC +6 or +7, same with 10 splits and A9 doubles.
Anything you have as TC 6 or higher, forget about using unless you do a real TC conversion. It'll hurt more than it helps. For example, if you get a great shoe, and get a RC of +30 with 3 decks to go in a 6D game, at that point the TC is only +6, and each of those +7 or higher indexes will subtract value.

When in doubt, go with basic strategy, and only trust index numbers near the warm line and near the pivot.

Marv

True Counting KO indices could be accomplished by memorizing indices for each deck cutoff point in the shoe and using these indices as a moving running count. As for doubling 10 vs 10 the illustrious 18 index for that is TC => +4 as EV max. The TC + 4 also match the KO pivot of +4 so it is accurate to make that play in KO. For Risk Averse it is TC = +7 or higher to double 10 vs 10.

I think it is safe to use indices generated from CVData for splitting 10 vs 5,6 either as running count or moving running count. In Modern Blackjack Norm have the indices as +28 and +27 setting IRC=0 and they are risk averse plays.

"The Ebook version of Norm's Modern Blackjack has a table of the most important indexes by number of decks remaining." In Modern Blackjack Second Edition Volume 1 on page 237 (Real KO Indices) the table for indices by numbers of decks remaining does not say if those indices are for S17 or H17. If is it for S17 you might need to generate separate moving running count indices for H17 using CVDATA. Generating those types of indices using CVDATA is time consuming.

[steger24]

I can't believe I forgot to mention this on my original post, but after reading your replies I noticed my mistake. We do in fact adjust our RC deviation indices as the shoe advances. For instance, after 1 deck at a 6 deck shoe, according to TKO, if the RC is at 9, you up your bet and begin S16 vs 10. At this point we would need the RC to advance plus15 in order to push out a max bet (at an RC of 24). You will notice that we have new deviations every 2 RC numbers (16, 18, 20, 22, 24, etc). In this situation, we would begin s16vs10 at 9, and we would have 4 "steps" in between 16 and 24 (18, 20, 22, 24). So in this situation, we would divide the remaining 15 RC necessary to reach the deviations at 24 by the 4 "steps". Meaning that at 1 deck in, our deviations at 16 are used at a RC of 9, our deviations at 18 are used at an RC of 13, deviations at 20 at are used at an RC of 17, and deviations at 22 are used at an RC of 21, and finally 24 at 24. We do the same thing with adjusting our bet spread. Once we go over 24 however, our deviations remain absolute at the RC indicated, as we are under the impression that an RC of 28 1 deck in yields the same advantage as an RC of 28 at 5 decks in. Are we correct in this logic? Are we doing this properly or are we oversimplifying and therefore costing ourselves? Once again, I apologize I did not mention this earlier, and all of the help is appreciated. Thank you

[muckz]

I can't believe I forgot to mention this on my original post, but after reading your replies I noticed my mistake. We do in fact adjust our RC deviation indices as the shoe advances. For instance, after 1 deck at a 6 deck shoe, according to TKO, if the RC is at 9, you up your bet and begin S16 vs 10. At this point we would need the RC to advance plus15 in order to push out a max bet (at an RC of 24). You will notice that we have new deviations every 2 RC numbers (16, 18, 20, 22, 24, etc). In this situation, we would begin s16vs10 at 9, and we would have 4 "steps" in between 16 and 24 (18, 20, 22, 24). So in this situation, we would divide the remaining 15 RC necessary to reach the deviations at 24 by the 4 "steps". Meaning that at 1 deck in, our deviations at 16 are used at a RC of 9, our deviations at 18 are used at an RC of 13, deviations at 20 at are used at an RC of 17, and deviations at 22 are used at an RC of 21, and finally 24 at 24. We do the same thing with adjusting our bet spread. Once we go over 24 however, our deviations remain absolute at the RC indicated, as we are under the impression that an RC of 28 1 deck in yields the same advantage as an RC of 28 at 5 decks in. Are we correct in this logic? Are we doing this properly or are we oversimplifying and therefore costing ourselves? Once again, I apologize I did not mention this earlier, and all of the help is appreciated. Thank you

Some of this post was beyond my concentration right now. I do have a comment about your betting.

increasing bets at rc9 with 1d gone is not a good play. For most games the house still has advantage, and for good s17 rules there is little gain at the 1 TC mark (rc9). Norm's sottware may tell you to increase marginally at tc 1 for TKO, the increase in n0 and risk is not worth it for the small increase in EV.
As general rule you should only begin increasing at TC 2, which is rc = 14 with 1 deck played in a 6 deck game.

The only RC that you have a constant advantage is our pivot point of rc 24, aka TC 4. Even then it is inconsistent for advantage due to floating advantage in shoe games.

I suggest you make a spreadsheet in excel with the formula (RC - 4*(decks played))/Decks remaining
Make it span RC's -10 to +30 for decks remaining 1-6. This will help you communicate more in TC's instead of RC's which is far easier to understand for most people familiar with TKO or counting in general.

[muckz]

Some of this post was beyond my concentration right now. I do have a comment about your betting.

increasing bets at rc9 with 1d gone is not a good play. For most games the house still has advantage, and for good s17 rules there is little gain at the 1 TC mark (rc9). Norm's sottware may tell you to increase marginally at tc 1 for TKO, the increase in n0 and risk is not worth it for the small increase in EV.
As general rule you should only begin increasing at TC 2, which is rc = 14 with 1 deck played in a 6 deck game.

The only RC that you have a constant advantage is our pivot point of rc 24, aka TC 4. Even then it is inconsistent for advantage due to floating advantage in shoe games.

I suggest you make a spreadsheet in excel with the formula (RC - 4*(decks played))/Decks remaining
Make it span RC's -10 to +30 for decks remaining 1-6. This will help you communicate more in TC's instead of RC's which is far easier to understand for most people familiar with TKO or counting in general.

Another thing, If you are only playing maybe 2 games with the same rules and decks all the time it may be worth it to just use KO full betting and index plays. Contrary to popular belief it is very strong and is most likely stronger than what you are doing now. The catch is that you have to learn indices for every different game and the optimal bet spreads can get a little ridiculous. If I only played one game it would be my first choice for simplicity.

[Marvin]

I can't believe I forgot to mention this on my original post, but after reading your replies I noticed my mistake. We do in fact adjust our RC deviation indices as the shoe advances. For instance, after 1 deck at a 6 deck shoe, according to TKO, if the RC is at 9, you up your bet and begin S16 vs 10. At this point we would need the RC to advance plus15 in order to push out a max bet (at an RC of 24).

Not correct.
Assuming 6 decks and an initial running count of 0.
A RC of 24 gives you essentially the same advantage and accurate index numbers anywhere in the shoe, a TC of +4.

To calculate the true count take the RC, subtract 4 for each deck played (the unbalance built into KO), and divide by the number of decks unseen.

1 deck in, when the RC 15, the TC is 2.2 (15-4)/5 ; this is too early for max bet unless the max bet is being dictated by low table max and not your bankroll. If you are pushing out your max at this point then you are over betting your BR.
On an H17 game your edge at this point is less than 1%.

Edit... just noticed that I may have misread what you wrote. If you meant that from the +9 RC point at 1 deck in, you need to wait for the RC to increase by an additional 15 (+24 total RC) then you are correct, and you can ignore the above. If, however, you meant that at 1 deck in you would push out your max be at a +15 RC then that's incorrect.

You will notice that we have new deviations every 2 RC numbers (16, 18, 20, 22, 24, etc). In this situation, we would begin s16vs10 at 9, and we would have 4 "steps" in between 16 and 24 (18, 20, 22, 24). So in this situation, we would divide the remaining 15 RC necessary to reach the deviations at 24 by the 4 "steps". Meaning that at 1 deck in, our deviations at 16 are used at a RC of 9, our deviations at 18 are used at an RC of 13, deviations at 20 at are used at an RC of 17, and deviations at 22 are used at an RC of 21, and finally 24 at 24. We do the same thing with adjusting our bet spread. Once we go over 24 however, our deviations remain absolute at the RC indicated, as we are under the impression that an RC of 28 1 deck in yields the same advantage as an RC of 28 at 5 decks in. Are we correct in this logic?

Not correct. TC = RC only with 1 deck left to go (after adjusting for the unbalance).

For example:
2 decks in (4 decks to go) a RC of 28 = (28-8)/4 = TC 5;
5 decks in (1 deck to go) a RC of 28 = (28-20)/1 = TC 8;
5 decks in (1 deck to go) a RC of 25 = (25-20)/1 = TC 5;

Are we doing this properly or are we oversimplifying and therefore costing ourselves? Once again, I apologize I did not mention this earlier, and all of the help is appreciated. Thank you

Again, at 24 you're at +4 TC anywhere in the shoe. With 1 deck left to go, RC = TC after offset, so with 1 deck to go, a RC or 23 = TC+3, a RC of 31 = TC +11, and a RC 16 = TC -4.

With more than 1 deck to go, the TCs are compressed towards the +4.
I'll try to post an Excel worksheet that will give you a better visual of KO TCs at various depths and RCs.

Most important though, if you don't want to push out your max bet until a +4 TC, then don't push it out until +24 RC on a 6 deck shoe, regardless of how many decks are un-dealt.

A RC <24 will always have a TC <4 on a 6 deck shoe, regardless of depth; a RC >24 will always have a TC >4 in a 6 deck shoe, regardless of depth.

Can't figure out how to attach an Excel file. Here's a pic of the relevant info. Also included the warm line in light green and the hot area in dark green.
TKO - Copy.jpg

[Three]

if the RC is at 9, you up your bet and begin S16 vs 10. At this point we would need the RC to advance plus15 in order to push out a max bet (at an RC of 24).

1 deck in, when the RC 15, the TC is 2.2 (15-4)/5 ; this is too early for max bet unless the max bet is being dictated by low table max and not your bankroll. If you are pushing out your max at this point then you are over betting your BR.
On an H17 game your edge at this point is less than 1%.

You are correct Marvin but reread the quote from Steger. You didn't understand what he wrote. The pronoun "this" before "point" is referring to a RC of 9.

Sorry looks like you caught it but decided not to amend rather than change your post.

[Three]

Can't figure out how to attach an Excel file. Here's a pic of the relevant info. Also included the warm line in light green and the hot area in dark green.

Nice visual there Marvin. As someone who doesn't use unbalanced counts it gets the point across very quick and quite well.