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Coin Flip - 50/50 or 1 in a million


Creepybits

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COIN FLIP

 

Flipping a coin to choose between two alternatives, settling a dispute or gambling can be traced back to ancient Rome. In ancient Rome, the game was called navia aut caput, which translates to ship or head, referring to the Roman coin which had a ship on one side and the head of the emperor on the other.

Flipping a coin in real life isn’t a 50/50 chance, contrary to popular belief. The coin will land on the same side as it started 51 out of 100 times. You also have a slight chance that the coin ends up standing on its edge. At optimal conditions, such as a flat surface and a coin in which the edge hasn’t been rounded, the chance of landing a coin on its edge is 1/6000.

In the digital variant of the coin flip, these variables have been taken away, making the game a 50/50 chance.

image.png.b281165b2320f7a416b37327b228830e.png

 

So, what are the odds of getting heads x consecutive times in a row?

The chance of getting heads (or tail) x consecutive times in a row is calculated very similarly to getting the ball to go left x consecutive times in the game of Plinko

 

 

Flip nr                      Chance

     1                                 50%

    2                                 25%

    3                                 12.5%

    4                                 6.25%

    5                                 3.125%

 

Globally there’s a 3.125% chance of getting heads (or tails) 5 consecutive times in a row. However, most often, you will not have your first five coin flips to end up with the same side five straight times in a row. How many flips should you expect to do before getting 5 in a row? The equation to find out how many flips are expected to get 5 in a row looks as follows:

 

image.png.ef5cd72145a7714b09e91af49245c1dc.png

 

Where e = the expected number of flips. Solving the equation will show that e = 62.

 

The number of expected flips you must do to get 5 of either heads or tails in a row is 62. You can, of course, get five consecutive heads within five flips, or 10 or 100. The calculations above are just a statistical measure of the probability of getting heads five straight times in a row. Otherwise, there wouldn’t be much gambling to it!

 

The current record

When writing this, the current record for coin flip at BC.game is 16 heads in a row.

 

image.png.a8dcc5c10c6a3efd60960b453a4a3258.png

 

What are the odds of hitting heads 16 consecutive times in a row? Let’s find out!

 

 

Flip Nr                  Chance

   1                                 50%

   2                                 25%

   3                                 12.5%

   4                                 6.25%

   5                                 3.125%

   6                                 1.5625%

   7                                 0.78125%

   8                                 0.390625%

   9                                 0.1953125%

  10                                0.09765625%

  11                                 0.048828125%

  12                                0.0244140625%

  13                                0.01220703125%

  14                                0.006103515625%

  15                                0.0030517578125%

  16                                0.00152587890625%

 

Rounded to 6 decimals, the answer is 0.001526% chance! That’s almost as rare as the famous 1 in a million (0.0001%). To get 17 consecutive heads (or tails) and break the current record, there’s a 0.000763% chance.

 

 

Provable Fair

To verify a bet, you must first change to a new seed by clicking on the Acorn symbol at the bottom of the game.

 

image.png.3001d904dd715aeab127b40db82c78a3.png

 

In the next step, you must click on the bet you wish to verify.

This one, for example.

 

image.png.a19bee03fd2e23ff75e62e3170373c12.png

 

image.png.12946ccb10720701fddfe97e11477a7e.png

 

If you don’t trust the results, you do a manual calculation.                  image.png.47659ad96a7552fd9f67720089a25662.png

 

 

hmac_sha256 is the client seed, server seed, nonce and round in hexadecimal. The first eight hexadecimal are calculated in groups of 2 after being converted to decimal numbers.

 

Round 1

HEX              Decimal

0d                  13

6b                  107

75                  117               

8a                  138

 

 

Then the calculation continues like this.

(13 / (256^1)) = 0.050781250

(107 / (256^2)) = 0.001632690

(117 / (256^3)) = 0.000006974

(138 / (256^4)) = 0.104841893

 

 

Add it all together: 0.050781250 + 0.001632690 + 0.000006974 + 0.104841893 = 0.157262807

The final number is 0.157262807, which is less than 1. Any number less than one is considered heads, and any number greater than one is considered tails.

Then you continue to do the same calculation for each consecutive round.

 

Here’s an example of the calculation of getting tails.

 

image.png.9b4a510b14b0513ea1dfb5a6506ab32a.png

 

HEX              Decimals

a9                  169

10                  16

a3                  163

25                  35

 

(169 / (256^1)) = 0.660156250

(16 / (256^2)) = 0.000244141

(163 / (256^3) = 0.000009716

(35 / (256^4)) = 0.000000008

0.660156250 + 0.000244141 + 0.000009716 + 0.000000008 = 1.320820229

1.320820229 is more than 1, so coin will end up with tails.

 

 

 

 

 

 

 

 

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  • 1 month later...
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  • 5 months later...
Quote

Rounded to 6 decimals, the answer is 0.001526% chance! That’s almost as rare as the famous 1 in a million (0.0001%). To get 17 consecutive heads (or tails) and break the current record, there’s a 0.000763% chance.

This is off, by a fair way, happy to be corrected on this, the post just seemed off.

I worked it to be 1 in 65,536 which is a lot of difference. And 1 In a million not appearing till 20 flips

 

Flip Nr        Chance                        1 In ;
1                    50.000000%            1 In 2 
2                    25.000000%             1 In 4 
3                    12.500000%             1 In 8 
4                    6.250000%                 1 In 16 
5                    3.125000%                 1 In 32 
6                    1.562500%                 1 In 64 
7                    0.781250%                 1 In 128 
8                    0.390625%                 1 In 256 
9                    0.195313%                 1 In 512 
10                0.097656%                 1 In 1,024 
11                0.048828%                 1 In 2,048 
12                0.024414%                 1 In 4,096 
13                0.012207%                 1 In 8,192 
14                0.006104%                 1 In 16,384 
15                0.003052%                 1 In 32,768 
16                0.001526%                 1 In 65,536 
17                0.000763%                 1 In 131,072 
18                0.000381%                1 In 262,144 
19                0.000191%                 1 In 524,288 
20                0.000095%                 1 In 1,048,576 
21                0.000048%                 1 In 2,097,152 
 

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2 hours ago, Umxalkeakwb said:

This is off, by a fair way, happy to be corrected on this, the post just seemed off.

I worked it to be 1 in 65,536 which is a lot of difference. And 1 In a million not appearing till 20 flips

 

Flip Nr        Chance                        1 In ;
1                    50.000000%            1 In 2 
2                    25.000000%             1 In 4 
3                    12.500000%             1 In 8 
4                    6.250000%                 1 In 16 
5                    3.125000%                 1 In 32 
6                    1.562500%                 1 In 64 
7                    0.781250%                 1 In 128 
8                    0.390625%                 1 In 256 
9                    0.195313%                 1 In 512 
10                0.097656%                 1 In 1,024 
11                0.048828%                 1 In 2,048 
12                0.024414%                 1 In 4,096 
13                0.012207%                 1 In 8,192 
14                0.006104%                 1 In 16,384 
15                0.003052%                 1 In 32,768 
16                0.001526%                 1 In 65,536 
17                0.000763%                 1 In 131,072 
18                0.000381%                1 In 262,144 
19                0.000191%                 1 In 524,288 
20                0.000095%                 1 In 1,048,576 
21                0.000048%                 1 In 2,097,152 
 

 

Thanks for reading. I'm not sure what's wrong according to you. You've got the same numbers on the 16th and 17th as I have. And if you meant the "one in a million" you must have missed what's written before that: "That’s almost as rare" (with emphasis on "almost"). And it's also used as the famous saying, rather than an exact measurement. If I thought it was exactly 1 in a million, I would have written exactly that.

 

 

 

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