AsymBacGuy above in post #773.
"...Say that at a random coin flip succession you have to choose from one of those HTHHTT or HHHHHH pattern coming out first.
All intermediate patterns do not count, so you will win or lose just when one of the two patterns will show up first.
Different studies, albeit being made on different patterns lenght, have demonstrated that the former HTHHTT pattern will show up by a lesser 'waiting time' than the HHHHHH pattern, despite of having the same probability to appear.
So we do not know about all other patterns coming out, but we do know that we're favorite to first cross the HTHHTT pattern than the HHHHHH pattern, so in some way the 'waiting time' matters. ..."
I agree Asym and wait-time distance between shorter patterns are even more important IMO(as related to Bac). With that said I also think we need to be cautious when comparing a coin toss vs a near-5050 proposition such as so called even-chance games like Bac. Due mainly to how the casino treats a Push and Tie results, which obviously a coin toss has neither.
In my opinion one of the best pieces of research on coin tosses and similar probability events was written by a Dr. R.S. Nickerson back in early 2000s I believe. In part below (I will post whole article once we have capability to upload pics and such).
Reasoning about probabilities can be tricky. Some probability problems
are notoriously opaque, even occasionally for people well-versed in prob␂ability theory. Examples include
• the three-doors or car-or-goat problem ("the Monty Hall problem") [Vos
Savant 1990a; 1990b],
• the sibling-gender problem [Bar-Hillel and Falk 1982],
• the condemned-prisoner problem [Gardner 1961, 226–232],
• Bertrand's paradox [Nickerson 2005], and
• the exchange paradox (two-envelope problem) [Nickerson and Falk 2006].
The UMAP Journal 28 (4) (2007) 503–532. ␂c Copyright 2007 by COMAP, Inc. All rights reserved.
Permission to make digital or hard copies of part or all of this work for personal or classroom use
is granted without fee provided that copies are not made or distributed for profit or commercial
advantage and that copies bear this notice.
"...Say that at a random coin flip succession you have to choose from one of those HTHHTT or HHHHHH pattern coming out first.
All intermediate patterns do not count, so you will win or lose just when one of the two patterns will show up first.
Different studies, albeit being made on different patterns lenght, have demonstrated that the former HTHHTT pattern will show up by a lesser 'waiting time' than the HHHHHH pattern, despite of having the same probability to appear.
So we do not know about all other patterns coming out, but we do know that we're favorite to first cross the HTHHTT pattern than the HHHHHH pattern, so in some way the 'waiting time' matters. ..."
I agree Asym and wait-time distance between shorter patterns are even more important IMO(as related to Bac). With that said I also think we need to be cautious when comparing a coin toss vs a near-5050 proposition such as so called even-chance games like Bac. Due mainly to how the casino treats a Push and Tie results, which obviously a coin toss has neither.
In my opinion one of the best pieces of research on coin tosses and similar probability events was written by a Dr. R.S. Nickerson back in early 2000s I believe. In part below (I will post whole article once we have capability to upload pics and such).
Reasoning about probabilities can be tricky. Some probability problems
are notoriously opaque, even occasionally for people well-versed in prob␂ability theory. Examples include
• the three-doors or car-or-goat problem ("the Monty Hall problem") [Vos
Savant 1990a; 1990b],
• the sibling-gender problem [Bar-Hillel and Falk 1982],
• the condemned-prisoner problem [Gardner 1961, 226–232],
• Bertrand's paradox [Nickerson 2005], and
• the exchange paradox (two-envelope problem) [Nickerson and Falk 2006].
The UMAP Journal 28 (4) (2007) 503–532. ␂c Copyright 2007 by COMAP, Inc. All rights reserved.
Permission to make digital or hard copies of part or all of this work for personal or classroom use
is granted without fee provided that copies are not made or distributed for profit or commercial
advantage and that copies bear this notice.