Pen Question

[BramSToker]

Hey guys, I don't want to come across as an idiot or anything but I had a random thought the other day about penetration that I'm sure is incorrect somehow but I'd like if someone could explain why.
Anyway, the thought process is as follows: if you apply penetration, for simplicity let's say we cut the deck in half, the count of each side could be anything, that is the max would be all the 10s or low cards and some neutrals in one half. More often though youd think statistically with a good shuffle, with a machine for example, that the count of each would be around 0. Slice it an infinite number of times, and the distribution would seem to favor that each side gets a count of 0. Could you then use that logic to suggest that in the long run, the pen wouldn't make a difference because the expected count of what is removed would approach 0? I assume you can't because every expert says pen is really important, but anyone care to explain?
Thanks guys

[Nikky_Flash]

i get what your saying , but ... decreased pen decreases expected dollar per hour results for a counter , remember we put big bets out when its rich in tens and aces making up for your "absoulte zero " idea , but decreasing pen seems to hurt the casino more because they waste all that time shuffleing and figuring out who put the cut card in last time , but the new guy won't do it either , but we got good table wins when that guy cut etc..., when they could be stickin it to all the muggles , or rps

[Norm]

More often though youd think statistically with a good shuffle, with a machine for example, that the count of each would be around 0.

It would be quite rare for it to be exactly zero. The common mistake is thinking that random means evenly distributed. Evenly distributed would be non-random. The smaller the set of cards, the less likely that the count is zero.

[BramSToker]

It would be quite rare for it to be exactly zero. The common mistake is thinking that random means evenly distributed. Evenly distributed would be non-random. The smaller the set of cards, the less likely that the count is zero.

Yes I understand that, that was why I said around zero and later more clearly "approaches" zero. As in, -2 and -1 are going to be far more common than counts of -5 in the pen, so having less of an impact on the count. Are you suggesting 0 wouldnt be the most common result in a distribution followed by 1 and -1, ect? Not being fastidious actually asking

[Norm]

Zero would be most most common (assuming truncation) -- but, it would be nowhere near 50%. So, it would not be likely. Exactly zero (no integerization) would be rare indeed.

[BramSToker]

Zero would be most most common (assuming truncation) -- but, it would be nowhere near 50%. So, it would not be likely. Exactly zero (no integerization) would be rare indeed.

Well thanks for the input, but saying its 'rare' when it is the most likely outcome just seems like an unimportant distinction. I was just trying to muse that over your entire career if you played for example 6 deck 1 deck pen, the likelihoods of facing high neg or pos counts hiding in the pen would balance out equally, and also that it would "usually" (I haven't actually done the distribution but even if it is a small set of cards, which you correctly stated would make it more random, I'm talking about an infinite # of trials) end up being beteween -2 and 2, which a good way to allow for could be just to require a higher count than usual to make deviations. Honestly just wanted to know if it holds water or not, maybe indices already take it into account bc you pretty much have to play with pen

[Bodarc]

BramStoker I just ran a frequency distribution on 6D H17 DAS DOA NRSA etc I got a zero count approximately 15.5% of the time. Approx 47% of the time it was below zero and approx 38% of the time it was above zero. They won't all be the same but they will be in the general neighborhood so you can see it is way below 50%.

If you had a plus card followed by a minus card followed by a plus card followed............then it would work out as 0 but you have approx 16 or so numbers you are spreading the counts over and the cards do not follow such a close range. You have runs of high cards and runs of low cards etc. That is what makes it random.

Do not confuse your count with a frequency distribution. If you are using a balanced count then your count will approach zero as you near the end of the deck but the frequency of counts going through the deck can be all over the place.

Hope this helps

[Nyne]

The count within a particular slug of cards will average zero, but we don't flat bet, so the average is relatively uninteresting. We want big swings in the count. The SD of the true count is proportional to 1 over the square root of the number of cards in the slug. That means the smaller the number of cards in the slug (the cutoffs in this case), the bigger the swings you can expect in the true count, which means we can identify more advantageous situations to bet more money. If we can identify mild positive or mild negative situations (as with poor pen games), that's not so great. If we can identify strong advantages and bet a lot, and strong disadvantages and sit out (as we can with deep pen and big TC swings), we have a much stronger game.

[Three]

If the deck is dealt to one card left what is the TC for a level 1 system at the shuffle. We will assume HILo:
A low card left, 2-6, 5 cards of 13 possible (38.45% of the time), RC =-1, TC = -52
A high card left, 10-A, 5 cards of 13 possible (38.45% of the time), RC = +1, TC = +52
Neutral card left, 3 cards of 13 possible (23.1% of the time), RC = 0, TC = 0

So fewer cards left are supposed to make the TC more likely to be close to 0? I don't think so.

[bigplayer]

Deeper pen means more knowledge and more value of each removed card. You make more money by betting big or small in extreme counts and to get those counts you need fewer cards so that a few cards removed can drive the count way up.

[moo321]

You have an advantage away from the center of the distribution. So, increasing the variability of counts increases the area of the distribution that is within the relevant are (an advantage). You want a long tail.