Throwing 1,000 Consecutive Heads

rossum

Well-known member
Can we throw 1,000 consecutive heads on a fair coin? Yes, providing we go the right way about it. The raw chance is low, 1 in 2^1000, but it can be done.

Start with 5,000 blank cards, plus a lot more spare cards. And pens, we'll need pens to write on the cards. Plus, of course, a coin to toss.

For each of your 5,000 cards toss the coin. If it comes up tails, throw that card away. If it comes up heads, take two blank card, mark each with an 'H' for heads, and put them in a new pile. You should end up with about 5,000 cards in the new pile, each marked with an 'H'.

Now start on the new pile, which is now the old pile, if that makes sense. For each card in the (new) old pile throw the coin. If it comes up tails, throw that card away. It it comes up heads, pick two blank cards and mark them 'HH', because you now have two consecutive heads. Throw away the old card with a single 'H' on it. Again you will have about 5,000 cards with "HH".

Repeat the process. Tails means throw the card away. Heads means two more cards, each with an additional 'H', because you rolled heads.

Repeat, repeat, repeat until you end up with a tired wrist and about 5,000 cards each with 1,000 consecutive H's on them.

Looking back through the route by which every card in your final pile got there, each card is the result of 1,000 consecutive heads on the coin. Any time tails came up, that card was binned, so there are no tails on the final set of cards, only heads. One thousand consecutive heads.

How does this thought experiment relate to evolution?

Throwing tails is equivalent to not having any descendants. Throwing heads is equivalent to having descendants. In the real world, the chances are not 50/50, but there is some probability. Every one of your ancestors managed to breed successfully. If even one ancestor didn't succeed, then you wouldn't be here. You are the end of a very very long line of successful breeders, with not one single failure. Not one.

The H's on the cards are an analogue of the DNA passed from parents to offspring. That DNA is the DNA of successful breeders, and only of successful breeders—all heads with no tails. Unsuccessful breeders did not pass their DNA on to any modern descendants; if the coin came up tails that card was thrown away.

The 5,000 current cards are the breeding population. Each round of die rolls is a generation. Throwing away old cards is the previous generation dying away.

The thought experiment with cards, coin and pen is a very simple model of evolution. It shows how evolution can beat seemingly impossible odds by spreading out the odds over time. A journey of a thousand miles starts with a single step. A lot of steps will come after, but only successful breeders can take each following step on the journey.
 

The Pixie

Well-known member
The fact is that the creationists and IDists around here have no answer to the OP - as so often happens. All they have is ferengi's sad attempts to derail the thread. Pathetic really, but then creationism is a faith position that requires the theist to ignore evidence they do not like.
 

Eightcrackers

Well-known member
The thought experiment with cards, coin and pen is a very simple model of evolution. It shows how evolution can beat seemingly impossible odds by spreading out the odds over time. A journey of a thousand miles starts with a single step. A lot of steps will come after, but only successful breeders can take each following step on the journey.
What evolution-deniers ignore with regard to the coin analogy is

1. the sheer number of coins being tossed, and
2. the fact that successes are preserved, and failures are eliminated.
 

rossum

Well-known member
To add a little more to my OP, 2^1000 is 1.07e+301, which is a huge number of possibilities. However, the coin flipping model I give does not have to examine all of those possibilities. Any sequence that starts: T... is never followed. That is half of all possible sequences. No time is wasted following them, because they start with tails. Similarly, sequences that start HT... are never followed further. That is again half of the remaining possible sequences. At each round of the model, half of the possible further sequencees are eliminated.

Despite the very large number of possible sequences that could be followed, the great majority of possible sequences are cut off short, and ignored thereafter. Because of that systematic weeding out of failing sequences at the earliest possible opportunity, the model quickly converges on the single allowed sequence: HHHH...HHH.
 

CrowCross

Super Member
The fact is that the creationists and IDists around here have no answer to the OP - as so often happens. All they have is ferengi's sad attempts to derail the thread. Pathetic really, but then creationism is a faith position that requires the theist to ignore evidence they do not like.
Kinda like you ignoring my polite request that you tell us how an assembly line of organelle can evolve.
 

rossum

Well-known member
Why 2 cards? Why not 4 cards?
In order to save the forests by not cutting down so many trees to make the cards. Try working out how many cards you would need after 1,000 rounds if you made 4 new cards after every throw of heads.

Two cards gives you a roughly stable population of cards. Four cards would give you an increasing populaiton of cards.
 

The Pixie

Well-known member
Kinda like you ignoring my polite request that you tell us how an assembly line of organelle can evolve.
There is something incredible about people who can tell bare-faced lies and think they can get away with it.

Far from ignoring it, I started a thread about it.

You know that, because you posted on it NINE times. Do you think this makes you look good, CrowCross?
 

CrowCross

Super Member
In order to save the forests by not cutting down so many trees to make the cards. Try working out how many cards you would need after 1,000 rounds if you made 4 new cards after every throw of heads.

Two cards gives you a roughly stable population of cards. Four cards would give you an increasing populaiton of cards.
That makes no sense....as always, you grab numerous out of the air with no logical reason.
 

CrowCross

Super Member
There is something incredible about people who can tell bare-faced lies and think they can get away with it.

Far from ignoring it, I started a thread about it.

You know that, because you posted on it NINE times. Do you think this makes you look good, CrowCross?
You were refuted HERE.
 

Temujin

Well-known member
That makes no sense....as always, you grab numerous out of the air with no logical reason.
It makes obvious sense. The number of cards represents the size of the population. By choosing two, the population stays roughly the same size, making your maths easy for you.
 
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