RE: "Top of the Format" Entering Part 2. People please come and help find the Metagame.
It's actually 6.25% chance of zero heads. Behold:
I find that it easier to calculate multiple coin flips as individual flips. So, there is a 50% chance flip 1 will be a heads, 50% chance of flip 2 being heads, and so forth. W can convert these percents to fractions, because it is easier. We now multiply. So, we have:
50/100 * 50/100 * 50/100 * 50/100 =
We can make this easier and reduce the fractions.
1/2 * 1/2 * 1/2 * 1/2 =
That leaves with us with 1/16 chance of all tails, and a 1/16 chance of getting all heads. The important thing to remember is that for each calculation you make for calculating the chance of x ammount of heads and y ammount of tails, there is an equal chance of y ammount of heads and x ammount of tails. That means there is a 6.25% (1/16) chance of getting all tails, and 6.25% chance of getting all heads.
The mistake that people make is that they add up the percents instead of multiplying. So if you have 50% chance of one heads, and 25% chance two heads, instead of adding 50% and 25%, you should lower 25% to 1/4 (25/100). 1/4 of the time you will flip H H, 1/4 of the time you will hit TT. 1/4 of the time you will flip TH, and 1/4 of the time you will flip HT. Assuming your using a card that does not care about the order of the heads (unlike Meganium MT), you have 25% chance of two Heads or two Tails, and then a 50 percent chance of a combination of Heads and Tails. Combination is the key word here.
To take it one more step, you have a 1/8 chance of flipping HHH, and a 1/8 chance of flipping TTT, both being the same result (all flips being the same thing) giving us 2/8 of the time you will flip all three coins the same result. You have a 1/8 chance of flipping THH, a 1/8 of flipping HTH, a 1/8 chance of flipping HHT, a 1/8 chance of flipping HTT, a 1/8 chance of flipping THT, and a 1/8 chance of flipping TTH. All these are the same result (all flips having one heads or one tails. On the flip side, it is the same result in the fact that they all have two of the same result.) meaning that 6/8 of the time you will flip a combination of one head or tails and the other two coins the opposite of the first. I took a little shortcut, because 3/8 of the time you will have a combination of 1 Heads and 2 Tails, and 3/8 of the time you will flip a combination of 1 Tails and 2 Heads. Both are the same, and add up to 6/8. So, 2/8 [chance of flipping 3 of the same result] + (3/8 [chances of flipping a combination of 1 Heads and 2 Tails] + 3/8 [chances of flipping a combination of 1 Tails and 2 heads]) = 8/8 (100%).
I could go into the 1/16, but I won't. We all get the picture.
It's actually 6.25% chance of zero heads. Behold:
I find that it easier to calculate multiple coin flips as individual flips. So, there is a 50% chance flip 1 will be a heads, 50% chance of flip 2 being heads, and so forth. W can convert these percents to fractions, because it is easier. We now multiply. So, we have:
50/100 * 50/100 * 50/100 * 50/100 =
We can make this easier and reduce the fractions.
1/2 * 1/2 * 1/2 * 1/2 =
That leaves with us with 1/16 chance of all tails, and a 1/16 chance of getting all heads. The important thing to remember is that for each calculation you make for calculating the chance of x ammount of heads and y ammount of tails, there is an equal chance of y ammount of heads and x ammount of tails. That means there is a 6.25% (1/16) chance of getting all tails, and 6.25% chance of getting all heads.
The mistake that people make is that they add up the percents instead of multiplying. So if you have 50% chance of one heads, and 25% chance two heads, instead of adding 50% and 25%, you should lower 25% to 1/4 (25/100). 1/4 of the time you will flip H H, 1/4 of the time you will hit TT. 1/4 of the time you will flip TH, and 1/4 of the time you will flip HT. Assuming your using a card that does not care about the order of the heads (unlike Meganium MT), you have 25% chance of two Heads or two Tails, and then a 50 percent chance of a combination of Heads and Tails. Combination is the key word here.
To take it one more step, you have a 1/8 chance of flipping HHH, and a 1/8 chance of flipping TTT, both being the same result (all flips being the same thing) giving us 2/8 of the time you will flip all three coins the same result. You have a 1/8 chance of flipping THH, a 1/8 of flipping HTH, a 1/8 chance of flipping HHT, a 1/8 chance of flipping HTT, a 1/8 chance of flipping THT, and a 1/8 chance of flipping TTH. All these are the same result (all flips having one heads or one tails. On the flip side, it is the same result in the fact that they all have two of the same result.) meaning that 6/8 of the time you will flip a combination of one head or tails and the other two coins the opposite of the first. I took a little shortcut, because 3/8 of the time you will have a combination of 1 Heads and 2 Tails, and 3/8 of the time you will flip a combination of 1 Tails and 2 Heads. Both are the same, and add up to 6/8. So, 2/8 [chance of flipping 3 of the same result] + (3/8 [chances of flipping a combination of 1 Heads and 2 Tails] + 3/8 [chances of flipping a combination of 1 Tails and 2 heads]) = 8/8 (100%).
I could go into the 1/16, but I won't. We all get the picture.