Coin Toss???

pinch · 11-18-2011, 09:56 PM

Originally Posted by Memnoch_TP

That's the dicey thing about coin toss statistics. The mathematical calculations give that string of results a 1:2048 probability, but the results of the previous 11 tosses have no effect on the next toss. So the chances of us losing the next coin toss are not 1:4096, they are 1:2.

Yes, each individual coin toss has to be considered independently, and each should equate to 1:2. However, the chance that we lose 11 straight (or win 11 straight for that matter) is (1 / 2^11). Since 2 to the 11th power is 2048, there was only a 1:2048 chance that a team could lose 11 times in a row.

The fact is that ANY known 1:2 chance over a consecutive 11 series is 1:2048. So the chance that we see in a coin toss result:

T:T:T:T:T:T:T:T:T:T:T is 1:2048
H:H:H:H:H:H:H:H:H:H:H is 1:2048
H:T:H:T:T:H:T:H:T:T:T is 1:2048

or 11 saints consecutive coin toss wins or losses:

W:W:W:W:W:W:W:W:W:W:W is 1:2048
L:L:L:L:L:L:L:L:L:L:L is 1:2048 (this is the series that we've experienced)
W:L:W:W:L:W:L:W:L:W:L is 1:2048

If we lose next week, then one could say that there was a 1:4096 chance that we lose 12 straight, but the probability of that one coin toss is still 1:2.

Maybe we should start asking the league to spin the coin instead of tossing it? According to Penn & Teller, a spun coin will land on tails closer to 60% of the time because of the extra metal on the head-side of the coin. Then they just have to let us choose the outcome every time and we should re-gain our edge over time!

Edit: Actually we WILL regain our edge over time, as every other team will eventually lose 11 straight as we did (over millions of years, of course)

11-18-2011, 09:56 PM	#14
pinch 100th Post Join Date: Jun 2011 Location: Diamondhead, MS Posts: 272 Blog Entries: 1	Originally Posted by Memnoch_TP That's the dicey thing about coin toss statistics. The mathematical calculations give that string of results a 1:2048 probability, but the results of the previous 11 tosses have no effect on the next toss. So the chances of us losing the next coin toss are not 1:4096, they are 1:2. Yes, each individual coin toss has to be considered independently, and each should equate to 1:2. However, the chance that we lose 11 straight (or win 11 straight for that matter) is (1 / 2^11). Since 2 to the 11th power is 2048, there was only a 1:2048 chance that a team could lose 11 times in a row. The fact is that ANY known 1:2 chance over a consecutive 11 series is 1:2048. So the chance that we see in a coin toss result: T:T:T:T:T:T:T:T:T:T:T is 1:2048 H:H:H:H:H:H:H:H:H:H:H is 1:2048 H:T:H:T:T:H:T:H:T:T:T is 1:2048 or 11 saints consecutive coin toss wins or losses: W:W:W:W:W:W:W:W:W:W:W is 1:2048 L:L:L:L:L:L:L:L:L:L:L is 1:2048 (this is the series that we've experienced) W:L:W:W:L:W:L:W:L:W:L is 1:2048 If we lose next week, then one could say that there was a 1:4096 chance that we lose 12 straight, but the probability of that one coin toss is still 1:2. Maybe we should start asking the league to spin the coin instead of tossing it? According to Penn & Teller, a spun coin will land on tails closer to 60% of the time because of the extra metal on the head-side of the coin. Then they just have to let us choose the outcome every time and we should re-gain our edge over time! Edit: Actually we WILL regain our edge over time, as every other team will eventually lose 11 straight as we did (over millions of years, of course)