On Apr 18, 2012, at 8:59 AM, matt20482002 wrote:
> OK, you converted 23 of 200 flushes. That's 11.5%. Whenever you have
> 4 cards to a flush, there are 9 cards left in the deck that can make
> the hand and 48 cards total. So, that is 18.75% you should expect to
> make or 37.5 hands of 200. Was what you experienced bad luck?
> Consult the binomial distribution. http://en.wikipedia.org/wiki/Binomial_distribution
>
> Your n=200 and p=.1875, np=37.5 and the variance is np(1-p)=30.5.
> The square root of that is the standard deviation = 5.5. So, what
> happened to you was (37.5-23)/5.5 = 2.6 standard deviations below
> the mean.
>
Thanks for the refresher on binomial distributions. I haven't seen
the np(1-p) variance thing in so many years.
P.S. 47 cards left for the draw (not 48).
What would be interesting is for x hands, what is the expected best/
worst streak of certain types of hands (and what's the std dev on
those streaks).
My mind is just too lazy to sit down & figure out the equations, but
the result would be something like...
If you have 1,000 flush draws, your best & worst 50-hand flush streaks
will probably be 3/50 (+/- 2) and 20/50 (+/- 5).
Any mathematicians out there handy with this stuff?
Streaks often have some really non-intuitive behaviors.
-----
Here's another quirky streak thing.
If we play a 50-50 game, in the *long run* we will be highly likely
close to even.
Guess how often we will flip from "losing" to "winning" (or vice-versa)?
I think in 100,000 trials (or 1,000,000 trials), the expected number
of crossings is 5-6. (I haven't seen the result in decades, so I
could be a little off here).
or have a bad losing streak.
This matches our real-world experience, that we tend to either "get
lucky" and have a long winning streak.
------
To translate to the flush draw issue. Once you are on a bad streak of
flush draws, the streak will probably go for quite a while before
rebalancing.
e.g. If you converted 23 of 200 flushes, what is the expected number
of flush draws you will need before you are statistically even?
I don't know, but my raw guess would be that you might need
1,000-2,000 flushes before you draw even.
Mitchell
P.S. I have seen some analysis along these lines for "Risk of Ruin"
and "How much do you expect to lose before going permanently positive
when playing blackjack?"
e.g. When playing $5 blackjack (with $5-25 spread), you might expect
to lose $600 before going permanently positive ($600 is totally made
up).
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