Gambling Winning and Losing Streaks, and the

Standard Deviation Here is an Excel spreadsheet set up to simulate

an even-money coin flip game — heads wins one dollar and tails loses one dollar. The graph shows the change in bankroll for

100 flips. If you were to flip a real coin and have a

friend record and graph the results, it would take you about 15 minutes for 100 flips. But here I can press the F9 key and get a

new set of results in one second. Based on statistics, I can predict what’s

likely to happen in future sessions. First of all, because this is a fair game,

I expect the numbers of winning and losing sessions to be about equal. Now look at these horizontal lines. I’ve spaced them at 10 units, which is the

standard deviation for the win or loss after 100 coin flips. It’s like an “average distance” away from

the single most likely result, an exact match of 50 wins and 50 losses. The final result will end up within one standard

deviation, between HERE and HERE, about 2/3 of the time; and within two standard deviations,

between HERE and HERE, 95% of the time, and within 3 standard deviations, somewhere on

this graph, almost always, 99.7% of the time. I’ll press the F9 key 20 times to generate

20 sessions of 100 flips each, or 2000 flips all together. I expect about 13 sessions to end up within

one standard deviation, and about 19 out of 20 sessions within 2 standard deviations,

with only about 1 session outside of that range, and none ending completely off the

graph, more than 3 standard deviations. I also predict we’ll see a winning streak

of 10 or more consecutive wins without a single loss, AND a losing streak of 10 or more consecutive

losses without a single win. If fact, I would not be surprised to see multiple

instances of these streaks. OK, here we go, 20 sessions. 1, 2, ooh, that’s a big deviation. I expect to see this once out of 20 times. And here, is that a 10, 10 consecutive winning

streak? From point 73 to 82. Almost! Let’s see, was than number 3? Here’s number 4, 5, 6, 7, 8, 9, 10. Here’s our big losing streak, more than 10,

let’s see. From point 55 to point 65, exactly 10. I forgot where we were. Was that 13? Here’s your big losing streak, right here. 14, 15, 16, 17, 18, 19, and 20. Later on I’ll tally the results in the description

section. If you would like to play around with this

simulation yourself, I have another video that shows you how to set it up in Excel,

step by step. You can have it up and running in 5 or 10

minutes. So what about sessions shorter or longer than

100 flips? This chart is a summary. For a session of this number of flips, you

have a standard deviation in your win or loss of this much. The average final result is break even, as

shown here. A moderately UNLUCKY final result, one standard

deviation down, is this much; and a moderately LUCKY final result, one standard deviation

up, is this much. In 2/3 of the sessions, you can expect to

end up somewhere between these results, and 1/3 of the time, something more extreme. Because this is a fair coin flip game, the

chance of a positive result is 50%. As the sessions get longer and longer, the

standard deviation gets bigger and bigger, but the deviation as a fraction of the number

of expected wins gets smaller and smaller, as indictated in this column. For example, for 50 flips, you can expect

to win about 25 times, with a standard variation of about 7%. But for 2,500 flips, you can expect to win

about half of that, 1,250 times, with a variation of just 1%. The longer you play, the closer you will end

up with the expected results, fraction-wise. This becomes really important for UNFAIR games,

when you have a statistical disadvantage. That’s the subject of Part 2.

Mit chang?

This has to be john

who gives a fuck about coin flips ? do they have that bet anywhere without taking a percentage??