Probablility

[stophon]

If you are playing an 8 deck shoe and you see 23 ten cards in a row off the top, are you any more likely to see a low card as the next card than you would be at a more normal ~-3 tc?

The math says no your not, but it seems to me you still see alot of tens at a t.c. of -3. It also seems like the odds of getting that 24th ten card should be smaller than just 13/49 or ~1/4 (i think thats about the probalility of getting a ten at a tc of -3)

 

[johndoe]

If you are playing an 8 deck shoe and you see 23 ten cards in a row off the top, are you any more likely to see a low card as the next card than you would be at a more normal ~-3 tc?

The math says no your not, but it seems to me you still see alot of tens at a t.c. of -3. It also seems like the odds of getting that 24th ten card should be smaller than just 13/49 or ~1/4 (i think thats about the probalility of getting a ten at a tc of -3)

The math doesn't lie. You still have lots of 10's left, even at TC-3. But fewer than TC=0. You have to trust the math. Be careful of imprecise and biased observations or hunches.

 

[sagefr0g]

a few links on this sort of stuff

here is a neat program k_c made on this sort of stuff:
http://www.blackjackinfo.com/bb/attachment.php?attachmentid=2033&d=1234207402

and some links talking about it on these pages:
http://www.blackjackinfo.com/bb/showthread.php?t=12979&page=2

 

[stophon]

Do you mean the excel stuff?
I code VB. Would be fun to learn how to code like he did. Very cool. Thx.

 

[FLASH1296]

If you are playing an 8 deck shoe and you see 23 ten cards in a row off the top, are you any more likely to see a low card as the next card than you would be at a more normal ~-3 tc?

The math says no your not, but it seems to me you still see alot of tens at a t.c. of -3.
It also seems like the odds of getting that 24th ten card should be smaller than just 13/49 or ~1/4
(i think thats about the probalility of getting a ten at a tc of -3)

At a T C of 0 probability = 16:36 The % of 10's is 31%. Odds of almost 2 to 1.
At a T C of -3 probability = 13:39 The % of 10's is 25%. Odds of exactly 3 to 1.

 

[stophon]

At a T C of -3 probability = 13:39 The % of 10's is 25%. Odds of exactly 3 to 1.

[/SIZE]

[/COLOR][/SIZE]

Wait a second, that doesn't make sense. A TC of -3 is saying that 3 ten cards have been played per deck left. So that would make the odds 13/52 right? 4 to 1?

I don't see where you get the number 39, thats 3/4 of a deck...

 

[FLASH1296]

Wait a second, that doesn't make sense. A TC of -3 is saying that 3 ten cards have been played per deck left. So that would make the odds 13/52 right? 4 to 1?

I don't see where you get the number 39, thats 3/4 of a deck...

Odds are actually a ratio such as 2-1, 8-5, 99-1, etc.

If there are 3 face cards removed from the deck then you are left with a deck of 52 cards -- only there are 3 LESS face cards than the normal 16. That leaves 13. That means that you now have 13 face Cards and 39 NON-Face Cards. 13 + 39 =52 So the ODDS are the ratio of 39:13 That reduces to 3 to 1.

 

[Kasi]

If there are 3 face cards removed from the deck then you are left with a deck of 52 cards -- only there are 3 LESS face cards than the normal 16. That leaves 13. That means that you now have 13 face Cards and 39 NON-Face Cards

Or maybe it might mean, after 3 faces are removed you only have 49 rather than 52 cards left so you have 13 face-cards and 36 non-face cards left.

 

[FLASH1296]

You are dealing with a 52 card deck or its equivalent at all times.

The True Count used to be termed, (more correctly). the "Count Per Deck"

When you compute the True Count you are computing the count as it relates to a 52 card deck at all times.

That is what is TRUE about the T. C.

 

[Kasi]

When you compute the True Count you are computing the count as it relates to a 52 card deck at all times.

Thanks for the tip, Sherlock.

Not sure I understand all this but does that mean when 3 faces are dealt off the top of one deck, the TC is now -3.18 if using exact cards?

When you said a TC of -3, were you flooring, rounding or truncating?

Does that still mean with a TC of -3.18, or -4, or -3, the chances of a face are still now 13/36 and not exactly one-third? Or are they still 13/39 because 13+39=52 and that's what all this True Counting is about?

Let me get this straight - if 3 faces come off the top, the chances are 13/39 of another face, so if 10 faces come off the top the chances must be 6/39? Or maybe 6/46 so 6+46=52?

I need another FLASH of inspiration.

 

[FLASH1296]

Everything is "normalized" to a single 52 card deck.

If you had 26 cards remaining and your Running Count was +2 Your True Count would be +4 because your half-deck running count has to be normalized to a whole deck. If there were 2 decks remaining, the normalization requires division by 2 (the number of decks unseen) so the T.C. would be +1. In the first case where there is just 26 cards remaining (a half deck) you are dividing by 1/2. Any time you divide by a fraction, you are actually multiplying. In the 26 card example given 1/2 becomes 2/1 and then you multiply 'across'.

So what is TRUE is that you are always normalizing to a one deck equivalent.

Here is a more extreme example. With 13 cards [1/4 deck] remaining unseen your R.C. is -5 so ... take the 1/4 of a deck and flip it over to make it into 4/1 and multiply 'across'.

So, your -5 R.C. [times 4] equals a -20 T.C.

 

[stophon]

Does that still mean with a TC of -3.18, or -4, or -3, the chances of a face are still now 13/36 and not exactly one-third? Or are they still 13/39 because 13+39=52 and that's what all this True Counting is about?

Let me get this straight - if 3 faces come off the top, the chances are 13/39 of another face, so if 10 faces come off the top the chances must be 6/39? Or maybe 6/46 so 6+46=52?

I think flash was being tricky with his wording. Odds are (P of First Event)P of Other event(s)) while probability (chance) is (P of First event)/(Total events).

So your chances of drawing a face is 1/4 and your odds are 1:3.

But i think your odds are incorrect flash, as are mine. The Hi-Lo count merely counts the ratio of high to low cards. There could be a 25 low cards, 22 high cards and 5 neutral cards remainig and the count would still be a T.C. of -3 but the odds of drawing a high card would be 22:30, much higher than the previous 13:39.

However I guess your odds are right on average? It should be noted though that they are not always true. The 7s, 8s and 9s mess things up.

 

[Kasi]

I think flash was being tricky with his wording. Odds are (P of First Event)P of Other event(s)) while probability (chance) is (P of First event)/(Total events).

So your chances of drawing a face is 1/4 and your odds are 1:3.

But i think your odds are incorrect flash, as are mine. The Hi-Lo count merely counts the ratio of high to low cards. There could be a 25 low cards, 22 high cards and 5 neutral cards remainig and the count would still be a T.C. of -3 but the odds of drawing a high card would be 22:30, much higher than the previous 13:39.

However I guess your odds are right on average? It should be noted though that they are not always true. The 7s, 8s and 9s mess things up.

"Tricky" doesn't begin to descibe it lol.

If he wants to talk about the probability of 10's being drawn at some TC that's one thing.

If he wants to talk about the probability of 10's being drawn without regard to TC's that's another thing.

Like you say, TC's are about the ratio of high-cards to low cards. The ratio of 10's to Aces is 4/5. They are both equally worth -1RC.

Like you say, the first 40 cards dealt could be all + and all -, and the 16 cards left be all 7.8.9's.

So to say the ratio of 10's is what he says it is is, whether using BS or TC's, whether as an average or not if using TC's, how can I delicately put it, wrong.

What you say makes alot more sense to me than what the FLASH says lol.

On the other hand, I rarely understand the planet the FLASH is living on lol.

Which probably only means he and I are living on different planets.

No big deal lol.

 

[Pelerus]

To respond to the original question:

What is the probability of a coin landing on "tails" 24 times in a row?
0.00000596%

What is the probability of a coin landing on tails once, given that it has landed on tails the past 23 times consecutively?
50% :whip:

I could be wrong, but my "gambler's fallacy radar" went off when I read the OP.

Of course, maybe one of our l337 shuffle track()rs will tell us different...:joker:

 

[1357111317]

To respond to the original question:

What is the probability of a coin landing on "tails" 24 times in a row?
0.00000596%

What is the probability of a coin landing on tails once, given that it has landed on tails the past 23 times consecutively?
50% :whip:

I could be wrong, but my "gambler's fallacy radar" went off when I read the OP.

Of course, maybe one of our l337 shuffle track()rs will tell us different...:joker:

You are correct pelerus if we are dealing with a perfectly random coin. However in blackjack I would say that in most cases the order that the cards come out of the shoe is far from random. Now this of course entirely depends on the shuffle but in most cases shuffles are far from random.

If the shuffle was completely random then the odds of drawing the 24th 10 would simply be 63/289 or 21%. However due to nonrandom shuffles I would say the actual number would be much lower. Now I am not much of an expert on blackjack shuffles with the exception of the one shuffle I deal with frequently but unless I saw a span of two hands that were almost entirely tens in the previous shoe, I would imagine that the odds of the next card being a ten would be much much lower than the odds of drawing a 10 from a completely randomely shuffled shoe (21%).

 

[FLASH1296]

Kasi said:

"Like you say, TC's are about the ratio of high-cards to low cards. The ratio of 10's to Aces is 4/5. They are both equally worth -1RC."

The ratio of 10's to Aces is 4/1. There is only one Ace for each quartet of 10's.

Stophon said:

I don't see where you get the number 39, thats 3/4 of a deck..."

You are correct that 39 is 3/4 of a deck, but that is moot here.

removing 3 of the 16 Face Cards leaves 13. 52 - 13 = 39

 

[stophon]

Stophon said:

I don't see where you get the number 39, thats 3/4 of a deck..."

You are correct that 39 is 3/4 of a deck, but that is moot here.

removing 3 of the 16 Face Cards leaves 13. 52 - 13 = 39

I know flash, you already responded to that post and corrected me awhile ago. I didn't realize you were talking about odds...