Re: Why online poker is better for the money player.


Hank Youngerman wrote:
> First, Paul, in the example you gave, the taking side's roll doesn't
> matter. Your point is that the rolling side has 27 winners 5 of the
> 27 winners and only 1 of the 9 losers is doubles, so if doubles come
> up more often, it slighly favors the 27 winners.
>
> In fact, I calculate that if doubles come up 16.71% of the time, the
> odds of getting off in 1 are 75.006%. I do not know a single player
> in the world who would let themselves be swayed by this .006%. Other
> factors - whether they feel lucky or not, are ahead or behind, whether
> they are steaming, or playing a weaker player and want him to feel
> successful so he will keep playing - are going to have more influence
> than .006%.
>
> I also don't know what the odds on heads are, and I don't think many
> people could notice a 50.3%/49.7% difference on their own.
>
> For example, suppose you allowed someone who has a gambling nature to
> watch you toss coins, but sufficiently fast so that he cannot possibly
> be counting the results. (Assume you can keep him from counting.)
> After tossing 1,000,000 of them, you offer to let him bet you on
> whether more heads or tails came up, but he has to give you 53-47
> odds. If your 50.3% theory is true, then it's overwhelmingly likely
> that heads won, but I think most gamblers would think it's a 50/50
> proposition and not really want to give odds.
>
>
>
> On 26 Oct 2005 09:50:47 -0700, pauldepstein@xxxxxxx wrote:
>
> >
> >Hank Youngerman wrote:
> >> Patti B's original post suggested that there might be a glitch in the
> >> programming. She predicted 16.83% doubles - about 101% of the
> >> expected number.
> >>
> >> I would agree that a good PNRG should not give this result. However,
> >> the reality is that such a difference, if it actually existed, would
> >> be far too small for a human observer to notice. Nor would it be
> >> enough to change one's play strategy. Really, think about it. Would
> >> you start leaving single number shots rather than double because the
> >> odds are now 1.01 to 2 rather than 1.00 to 2? Would you start taking
> >> cubes you'd have passed before because the increased number of doubles
> >> means the trailer has a better chance to catch up.
> >>
> >>
> >>
> >>
> >> On 22 Oct 2005 11:16:14 -0700, pauldepstein@xxxxxxx wrote:
> >>
> >> >
> >> >Tom Keith wrote:
> >> >> Paul Eptsein wrote:
> >> >> > Over a vast number of games played on fibs (sorry, I can't give exact
> >> >> > figures), it was once documented that doubles had come up 16.71% of the
> >> >> > time, and that this missed, by some margin, the 95% confidence
> >> >> > interval.
> >> >> >
> >> >> > What is the explanation for this? As an "all dice are random"
> >> >> > believer, I would expect that this is a case of people collecting more
> >> >> > and more statistics, and inevitably coming across some surprising
> >> >> > percentage figures.
> >> >> >
> >> >> > Is that the case? It's been quite a while since I saw this "too many
> >> >> > doubles" statistic. What is the doubles percentage on fibs now?
> >> >>
> >> >> As you point out, even random dice will fall outside a 95% confidence
> >> >> interval 1/20 of the time. So when you find an unusual result, it is
> >> >> necessary to follow up with another test to see if the first one was
> >> >> just a fluke or is really an indication that something is wrong.
> >> >>
> >> >> In 1996/1997, Stephen Turner tested FIBS dice again to see if Patti's
> >> >> results would be repeated. You can read his post here:
> >> >>
> >> >> http://www.bkgm.com/rgb/rgb.cgi?view+262
> >> >>
> >> >> Tom
> >> >
> >> >Hi Tom,
> >> >
> >> >Thanks for this reference which shows that there is no evidence for
> >> >non-randomness on fibs.
> >> >
> >> >I intended to make the following point: It is not the case that all
> >> >suspicions of non-randomness are based on statistical ignorance,
> >> >anecdotal evidence, basic misconceptions of probability, biased human
> >> >memory, etc etc.
> >> >
> >> >I'm sure the vast majority of non-randomness suspicions can be
> >> >explained thus. However, the pattib.org non-randomness investigation
> >> >was an unusual example of grounds for suspicion, even among those
> >> >well-informed in the relevant areas of backgammon, psychology,
> >> >probability, statistics etc.
> >> >
> >> >You have shown that the suspicion has been laid to rest by a more
> >> >recent experiment.
> >> >
> >> >Paul
> >
> >I tend to think that people are generally quite sensitive to small
> >deviations from randomness. When a coin is tossed, I think (admittedly
> >anecdotal) that most people prefer to guess heads. And, in reality, if
> >you toss a coin a few feet and let it fall on the surface, coins are
> >more usually heads because of the way most coins are weighted. I don't
> >know the exact details of the experiment but tossing a U.S penny into
> >the air and letting it fall leads to a probability of heads of 50.3%
> >My opinion is that there is a causal link between this greater heads
> >frequency and the general preference for heads.
> >
> >Your point that it would be wrong to let such deviations affect your
> >play is correct. But you might do this if you were absolutely unable
> >to choose between two plays or cube decisions. For example, if you saw
> >a race as right on the take/pass border, you should take if doubles
> >have a 16.83% probability. [Next paragraph gives an exception.]
> >
> >For a concrete example, suppose you have a certain bearoff next roll.
> >However, your opponent has one on his six point, and no other checkers.
> > Your opponent offers you the cube. Instead of being an exactly
> >marginal take/pass, it is now a pass if the probability of doubles has
> >been increased. Yes, I know this appears to contradict my previous
> >paragraph. The reason for the apparent contradiction is that, in this
> >instance, the underdog can't be helped by rolling doubles.
> >
> >Paul Epstein

Hank,

I am surprised you don't know anyone who would be swayed by the extra
0.006%. Isn't there some satisfaction to be had by playing the game as
correctly as possible, in the mathematical sense?

I did lay out an (admittedly tenuous) argument. Which of the steps (if
any) do you disagree with?
1) Most people like to guess "heads" when guessing on coin tosses. (I
have no evidence -- but it's based on my experience of how people
behave. When people guess "tails" it actually stands out, to me, as
being a bit unusual.)

2)Most coins do land heads more than 50% of the time because of the
weighting. (Such experiments are written up in Spitznagel's Selected
Topics in Mathematics.)

3) Since I can't see any other reason for fact 1), I postulate fact 2)
as explaining fact 1.

4) Since fact 2 probably does explain fact 1, it is false to say that
people can't intuitively detect small changes from random behaviour.

Note also what happened when Patti investigated claims of Fibs' excess
of doubles. Her investigation was a response to claims that doubles
came up too frequently. In fact, they did come up more frequently than
expected, and the deviation was significant. My guess is that the "too
many doubles" claims were partly a response to an intuitive knowledge
of this deviation. Needless to say, the deviation was shown to have
been due to chance.

Paul Epstein

.

Relevant Pages

  • Re: Why online poker is better for the money player.
    ... 27 winners and only 1 of the 9 losers is doubles, ... I also don't know what the odds on heads are, ... watch you toss coins, but sufficiently fast so that he cannot possibly ... >>>anecdotal evidence, basic misconceptions of probability, biased human ...
    (rec.games.backgammon)
  • Re: Me and David C. Ullrich
    ... > Two coins have been flipped, ... Did the flipper flip the coins and discover a head? ... it landed heads. ... At least one is a head, heads were chose, at least one is a tail, tails ...
    (sci.math)
  • Re: Me and David C. Ullrich
    ... >>> Two coins have been flipped, ... >> Did the flipper flip the coins and discover a head? ... >> At least one is a head, heads were chose, at least one is a tail, tails ... >> were chosen, given at least one tail, tails were chosen. ...
    (sci.math)
  • Re: OT: The two coin problem, and Wuzzys error.
    ... about their coins, what are the odds that "both of his coins are the ... and it's heads staring back at him. ... If the probability the man says tails when he has one of each is 1, ...
    (rec.gambling.poker)
  • Re: triple double
    ... Likewise, three doubles in a row is pretty common, despite being "unusual". ... Ask someone to write down off the top of their head 1000 "random" coin ... coin tosses (being all heads or all tails) as normal so if you ask them ... didn't even register the non doubles in the middle!). ...
    (rec.games.backgammon)