New deck at cut

[DSchles]

This is a stupid argument, so I'll end it here and won't write again. To make it as simple as possible, you don't have a clue as to what you're talking about, and your numbers above are absurd and ridiculous. I gave you one site. Here's a second one with identical results to the first: http://www.beatingbonuses.com/calc_streak.htm

If you flip a fair coin 1,000 times, the probability that you'll get a streak of even 9 is 62.4% (that's either heads or tails, so half for one or the other). In other words, it would be unusual NOT to have such a streak.

Write whatever you want. I won't reply. I've been doing this stuff probably since before you were born, and I have no desire to joust with you, especially since you're spouting nonsense.

Don

[toolyp]

This is a stupid argument, so I'll end it here and won't write again. To make it as simple as possible, you don't have a clue as to what you're talking about, and your numbers above are absurd and ridiculous. I gave you one site. Here's a second one with identical results to the first: http://www.beatingbonuses.com/calc_streak.htm

If you flip a fair coin 1,000 times, the probability that you'll get a streak of even 9 is 62.4% (that's either heads or tails, so half for one or the other). In other words, it would be unusual NOT to have such a streak.

Write whatever you want. I won't reply. I've been doing this stuff probably since before you were born, and I have no desire to joust with you, especially since you're spouting nonsense.

Don

Problem is, you and your “calculators” do not grasp the concept of streak. You calculate a streak ignoring the existence of other streaks of different lengths. You simply calculate “9 heads in a row”. 0.5^9=0.001953125; 1 in 512. You are just at the beginning of a run, its not a streak.

Warren Weaver’s “Lady Luck” book to the rescue! Read carefully how he establishes a streak (pg 346). For example, 5 heads in a row; THHHHHT. Observe the limits: T. You must have the opposite event surrounding the event we calculate. You have also all kinds of streaks in 1000 trials. THT, HTH, HTTTTTH, etc.

Accurate calculations of number of streaks consider the correct 9-head streak as THHHHHHHHHT. Notice, 11 elements. Naturally the streak begins with T followed by 9 consecutive H and ending with T. In this case, the probability for such configuration is 21.5%. Being under 50% it was rounded down. That’s why it appeared as 0 under streak length 9. So in around 1 in 5 runs of 1000 tosses there will be a 9-H streak. Of course, there could be a 9-T streak instead.

“…I'll end it here and won't write again…Write whatever you want. I won't reply.” Obviously. We all know pride is very hard to swallow. No offence, just my honest opinion (meant to have been my signature).

[toolyp]

Problem is, you and your “calculators” do not grasp the concept of streak. You calculate a streak ignoring the existence of other streaks of different lengths. You simply calculate “9 heads in a row”. 0.5^9=0.001953125; 1 in 512. You are just at the beginning of a run, its not a streak.

Warren Weaver’s “Lady Luck” book to the rescue! Read carefully how he establishes a streak (pg 346). For example, 5 heads in a row; THHHHHT. Observe the limits: T. You must have the opposite event surrounding the event we calculate. You have also all kinds of streaks in 1000 trials. THT, HTH, HTTTTTH, etc.

Accurate calculations of number of streaks consider the correct 9-head streak as THHHHHHHHHT. Notice, 11 elements. Naturally the streak begins with T followed by 9 consecutive H and ending with T. In this case, the probability for such configuration is 21.5%. Being under 50% it was rounded down. That’s why it appeared as 0 under streak length 9. So in around 1 in 5 runs of 1000 tosses there will be a 9-H streak. Of course, there could be a 9-T streak instead.

“…I'll end it here and won't write again…Write whatever you want. I won't reply.” Obviously. We all know pride is very hard to swallow. No offence, just my honest opinion (meant to have been my signature).

Lets consider blackjack as per Don’s calculator: p=0.48

                     Probability p = .48
                     Number of Trials N = 1000
 
 =============================================================================
  Streak Lengths       1     2    3    4    5    6    7    8    9   10  TOTAL
 =============================================================================
  Winning Streaks W   130   62   30   14    7    3    2    1    0    0   475
 -----------------------------------------------------------------------------
  Losing Streaks  L   120   62   32   17    9    5    2    1    1    0   514
 =============================================================================

Now there is one 9-hand losing streak.

No doubt, the player has more single wins (LWL) than single losses (WLW). A curiosity - the number of 2-win and 2-L streaks are equal (62 in 1000). An exploit?