Walter: I agree with your example. A very good example of "Blind Luck".
I might add: There is some reasonable logic that tends to support losing
streaks down in the negative counts. There are times when the 47.5 win
rate can drift down in the 30-40 range. The -1 or 4 loss walk idea serves
its purpose well.

Grifter: Go to bjstats.com, select tables on the left, then select:
6 Decks
High/Low
No sort
No cover
S17,DAS
TABLE- cumulative win,loss&tied % by TC^

Look at the win loss numbers starting at zero and going both ways. It's
about midway in the table and I think it excludes pushes(47.5)

It takes high neg counts that don't come very often, but losing 10 in a
row don't come very often as well.

Ray

Grifter: I understand the importance of the circumstances that exist at
the neg counts and I think I related this to Sage as a combination of
things which, of course affect the EV. They were: win rate, doubles,BJ and
hit/stand/split decisions as being less effective.

As regards streaks: The win rates for positive counts is, for the most part,
stable. It changes very little up thru high positive counts. Down thru the
negative counts the changes are greater. It does not matter how low the
percentages are in the run that we looked at because the changes are
very close to a linear translation and can be normalized or extraplolated
for the same volumes as the positive counts. The lower EV in the negative
counts is an effect, not the cause. The cause(s) are: Lower win rate, less
BJ and double posibilities, and less effective decisions for hit/stand/split.

In my opinion these are the circumstances that increase the probability
of losing streaks in high negative counts. No such circumstances exist
for winning streak probabilities that I can identify. But, in the high positive
counts the EV is much greater even though the win rate remains stable.

Ray

Mike: I should have made it more clear that I was talking about the
percentages listed in the sim and not related to the play of a hand,etc.
Sorry for the confusion it may have caused...........

Ray – Nice post, but you basically said the same thing you said before with more words. I honestly don’t know where you are getting ‘off base’ so I will start from the beginning again.

The ‘quick and dirty’ numbers I gave you yesterday were close enough, but you sidestepped them so here is the whole gamut. The results below are based on the numbers you told me to look at, and reflect the cumulative WP for all negative counts from -1 to -10 inclusive; which covers 99.94% of all occurrences.

1. Ray said, "There are times when the 47.5 win rate can drift down in the 30-40 range.”

The above statement is false…….See following:

Counts………………………Cum. WP
-1................................47.39
-1,-2............................47.33
-1,-2,-3........................47.28
-1,-2,-3,-4....................47.26
-1,-2,-3,,…-5................47.24
-1,-2,-3,,…-6................47.22
-1,-2,-3,,…-7................47.22
-1,-2,-3,,…-8................47.22
-1,-2,-3,,…-9................47.21
-1,-2,-3,,…-10..............47.21

As you can see, the ‘drift’ is negligible……only 0.18% going all the way down to -10, and never gets even remotely close to the 30 - 40.

2. Ray said, “The win rates for positive counts is, for the most part, stable. It changes very little up thru high positive counts.”

The above statement is false……The following is a reverse of the above, showing the cumulative WP for plus counts of +1 to +10, inclusive.

Counts………………………Cum. WP
+1...............................47.93
+1,+2..........................48.15
+1,+2,+3.....................48.46
+1,+2,+3,+4................48.77
+1,+2,+3,…+5..............48.96
+1,+2,+3,…+6..............49.08
+1,+2,+3,…+7..............49.14
+1,+2,+3,…+8..............49.17
+1,+2,+3,…+9..............49.19
+1,+2,+3,…+10............49.20

Your statement above is not only incorrect, it is actually backwards. As you can see, with positive counts over the same 1-10 spread we now have a drift upward of 1.27%.

Hope this helps, and let me know if you have any questions.

Regards……Grifter

Ray - That's it!...There's your glitch.....You just said, "It appears to me that the numbers are Cum WP up or down thru the counts and need no further elaboration. As best as I can determine, this is what they mean when they say each position contains the results of the previous."

No, unless I'm missing something entirely, the numbers on the chart are not cumulative. They are stand alone numbers for each event (i.e. -1, -2, etc.)......However, my charts above are cumulative, thus the difference; and cumulative is what you want to use.

Re Anomalies: There are anomalies that occur in both the individual positve and negative counts, and yes they do show up because of low occurence frequency. That is why I stopped my charts at +/- 10......That covers 99.94% of the total occurences.

Re 10 in a Row: but to that I would say; losing 10 in a row is an anomalie that would, in my opinion, require something far less favorable than a 47.5 win rate......That would depend entirely on the size of your sample. If you had 10 L streak in a set of 100 hands, in all likelyhood the WP for those 100 hands would be less than 47.5%. Conversely, if you had a 10 L streak in say 1,000 hands; it is possible that the overall WP would be over 47.5%.

Regards.....Grifter

Ray - You're welcome, but no thanks necessary. Just return the favor and catch mine when I make 'em. :wink: ......Grif'

Grifter/Ray If I understand your discussions?? The charts indicate the low counts do not affect the results as much negative as the high counts affect the results positive. (Is that because when the count is in the process of going low, high cards are coming out and that is good for the player?)
The charts confirm, when the high cards come out, (low count) the W/L rates don't change much from the expected, but when the low cards come out (high count) the W/L rate gets better for the player. Does that mean low cards are much better for the dealer than high cards are for the player? It is not an even swap, high cards are less important that low cards?
So I understand why to bet more with high counts. But it seems that neutral counts and low counts are about the same W/L, is that right?
If I understand it correctly, why quit the shoe with a low count if you don't also quite the shoe with a neutral count? :?:

Walt said:

Streaks happen because streaks happen... it's a natural outcome for a game with a 48/52% win/loss pattern

I agree, but with all due respect, flip a coin 20 times, you'll find streaks too, and that's as 50/50 as you can get! Are streaks less prevelant in a 50/50 than a 48/52???

composition of remaining cards vs independent outcomes. yeah, that makes perfect sense. I just wrote without thinking it through. 8)
but it still is strange how streaks happen even in a 50/50 independent outcome scenario. the same probability to get 10 heads in a row as it is to get alternating 10 outcomes. the streak info in previous posts is very helpful, and encouraging, with the losing streaks I've seen so far, it should be payday for me from now on, and my kids too....and their kids....... 8)