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)

FinSaint · 11-18-2011, 10:12 PM

Originally Posted by pinch

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.

But I think that they use a special "NFL coin," so it won't probably behave in the same way as a "normal coin" would. If I remember correctly it has the NFL emblem on the other side and something football related on the other one as well... or it could be that they have many different alternative variations.

pinch · 11-18-2011, 10:20 PM

Originally Posted by FinSaint

But I think that they use a special "NFL coin," so it won't probably behave in the same way as a "normal coin" would. If I remember correctly it has the NFL emblem on the other side and something football related on the other one as well... or it could be that they have many different alternative variations.

Good Point. Maybe we'd have better luck at rock/paper/scissors?

11-18-2011, 09:56 PM	#1
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)

11-18-2011, 10:12 PM	#2
FinSaint Site Donor 2015 Join Date: Aug 2011 Location: Finland... formerly Southern Virginia Posts: 4,963	Originally Posted by pinch 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. But I think that they use a special "NFL coin," so it won't probably behave in the same way as a "normal coin" would. If I remember correctly it has the NFL emblem on the other side and something football related on the other one as well... or it could be that they have many different alternative variations.

11-18-2011, 10:20 PM	#3
pinch 100th Post Join Date: Jun 2011 Location: Diamondhead, MS Posts: 272 Blog Entries: 1	Originally Posted by FinSaint But I think that they use a special "NFL coin," so it won't probably behave in the same way as a "normal coin" would. If I remember correctly it has the NFL emblem on the other side and something football related on the other one as well... or it could be that they have many different alternative variations. Good Point. Maybe we'd have better luck at rock/paper/scissors?