Member Creepybits Posted June 21, 2022 Member Share Posted June 21, 2022 (edited) 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. 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: 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. 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. In the next step, you must click on the bet you wish to verify. This one, for example. If you don’t trust the results, you do a manual calculation. 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. 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. Edited June 29, 2022 by NoWins Grammar 2 Link to comment Share on other sites More sharing options...
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Umxalkeakwb Posted January 19, 2023 Share Posted January 19, 2023 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 Link to comment Share on other sites More sharing options...
Member Creepybits Posted January 19, 2023 Author Member Share Posted January 19, 2023 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. 1 Link to comment Share on other sites More sharing options...
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