Inside the Poker Mind - A question for John Feeney

[WaltD]

Hi John, et al,

Enjoying reading the book Inside The Poker Mind. Good thoughtful discussions. But I have a bone to pick regarding an example you use to make a point in the section 'A Coin Toss Rush?' I may agree with the point you are trying to make, but your example is actually contrary to the point itself. You ask to reader to imagine a universe of millions of coin tosses, from which a subset of 100 groupings where the sequence of consecutive Head tosses equals or exceeds 10, the extension beyond ten unknown. You then query the reader to challenge the supposition that there are equal chances that the next event in each sequence has equal probability of being either a Head or a Tail. In my humble opinion, in actuality, the probability is higher for a Heads event rather than equal probability. The reasoning is fairly simple. You have a biased subset, where the requirement is that each element of the set be a sequence of AT LEAST ten Head consecutive tosses with no upper end cap. So, for the postulate that you propose to be correct, exactly 50 of the events are exactly 10 Head tosses in length and the remaining 50 are of length 11 to X. This proposition itself fails in the face of simple probability theory. There is likely a definite positive bias towards a length of ten , ie. a probability there are more event groupings of length ten, than say 12, or 15. This would subscribe to a standard bell curve distribution of the event groupings. However, there is a distinct probability thet the next event WILL be a Head as opposed to a Tail, based on the proposition you present, in counterpoint to the point you are trying to make in the section.

Which makes me wonder, is there such a thing as a Coin Toss Rush?

Looking forward to your reply.

WaltD

[maurile]

[ QUOTE ]
You ask to reader to imagine a universe of millions of coin tosses, from which a subset of 100 groupings where the sequence of consecutive Head tosses equals or exceeds 10, the extension beyond ten unknown. You then query the reader to challenge the supposition that there are equal chances that the next event in each sequence has equal probability of being either a Head or a Tail.

[/ QUOTE ]
If I'm following you correctly, all the coins have already been flipped. We are randomly picking out 100 groupings of flips that turned up at least 10 heads in a row. (That is, we have no selection bias beyond that criterion: we are not favoring or disfavoring streaks that went beyond 10 flips.)

The expected number of streaks that will end right there, for a total of 10 heads in a row, is 50.

The expected number of streaks that end after 11 heads in a row is 25.

The expected number of streaks that end after 12 heads in a row is 12.5.

And so on.

This assumes a fair coin.

So the 11th flip will be just as likely to be heads as tails. On average, half of the 100 will be heads and half will be tails.

[John Feeney]

Hi Walt -- You pose an interesting question. maurile has already answered it quite well and directly in terms of the probabilities. Another way to think about it might be this:

Consider that sequence of millions of recorded coin tosses (e.g., TTHHTTTHTTTTHTHHTHTT...). I propose that I will cover them up, now moving the cover from left to right to let you see any number of tosses except those which remain covered. So you can look at what’s “happened,” but not at what is “going to happen.” You can stop me at any toss as I move forward. Having now even more information than I gave you in the book version (where you got to pick out sequences in which the first ten tosses were heads, not knowing that happened on the 11th toss), do you think you can stop me as I move the cover forward, and identify any toss which is more likely to be followed by a head than is some other still unseen toss?

[Rick Nebiolo]

John,

On a related note (I think /images/graemlins/grin.gif) years ago before anyone played defense in the NBA professional statisticians followed a team (I believe it was the 83 Sixers) that shot almost exactly 50% for the year. Most fans believe in "streak shooting" but according to the statistical analysis hitting your previous X shots didn't make it any more or less likely you would hit your next one.

In other words, basketball fans and players believe in streak shooting because streaks are noticed.

~ Rick

[Paul2432]

Hey Rick,

Check out this thread (http://forumserver.twoplustwo.com/showflat.php?Cat=&Number=1429164&page=&view=&sb=5& o=&fpart=1&vc=1) where I brought up the same concept. A lot of otherwise intelligent people refused to accept that there is no such thing as a hot hand.

Paul

[Rick Nebiolo]

[ QUOTE ]
Check out this thread (http://forumserver.twoplustwo.com/showflat.php?Cat=&Number=1429164&page=&view=&sb=5& o=&fpart=1&vc=1) where I brought up the same concept. A lot of otherwise intelligent people refused to accept that there is no such thing as a hot hand. - Paul

[/ QUOTE ]

Thanks, I skimmed the links and they looked like fun reads if I ever get the time. The hot hand in basketball has been discussed a few times (slightly less than the Monty Hall three doors puzzle) over the years here on 2+2, but with the state of the search tools, darn if I'll find you the links /images/graemlins/grin.gif

~ Rick

[DocMartin]

There is a "hot hand". And no I dont play basketball (I think its a ridiculous sport), I have a couple degrees in motor behavior. It has little to do with "muscle memory", all experts have the capability to perform at a high level, it is confidence and attentional focus that make the difference. Increased attention and confidence in doing a task will increase performance (there are many studies that support this) . After several successful attempts at a skill, confidence tends to increase and performance will as well (up to the performers potential).

[maurile]

[ QUOTE ]
There is a "hot hand".

[/ QUOTE ]
I agree. Sometimes the rim just seems a lot bigger than other times.

Just looking at streaks from a simple statistical viewpoint isn't worth much. When a player has a hot hand, he'll start taking more shots (including harder shots) than he otherwise would. When he's cold, he'll pass up otherwise decent shots and wait for layups.

How do the statistical studies about "hot hands" account for this?

[Paul2432]

[ QUOTE ]
[ QUOTE ]
There is a "hot hand".

[/ QUOTE ]
I agree. Sometimes the rim just seems a lot bigger than other times.

Just looking at streaks from a simple statistical viewpoint isn't worth much. When a player has a hot hand, he'll start taking more shots (including harder shots) than he otherwise would. When he's cold, he'll pass up otherwise decent shots and wait for layups.

How do the statistical studies about "hot hands" account for this?

[/ QUOTE ]

The hot hand has been studied extensively. Read the links I posted in the thread I linked to above. If I remember right, one study used either free throws, or the NBA 3-point shooting constest, to control against the effect you mention. Results were the same. There is no hot hand.

Paul

[Rick Nebiolo]

[ QUOTE ]
[ QUOTE ]
There is a "hot hand".

[/ QUOTE ]
I agree. Sometimes the rim just seems a lot bigger than other times.

Just looking at streaks from a simple statistical viewpoint isn't worth much. When a player has a hot hand, he'll start taking more shots (including harder shots) than he otherwise would. When he's cold, he'll pass up otherwise decent shots and wait for layups.

How do the statistical studies about "hot hands" account for this?

[/ QUOTE ]

Don't know the details of the stat studies but obviously the player who is perceived by his teammates as having a hot hand gets to take the next shot more often (unless the teammate who already has the ball is named Kobe). Any increase in focus (mentioned in the post above) is probably balanced by the fact the defense is paying more attention, leading to more difficult shots.

~ Rick

PS I remember another study that shows a curve ball doesn't really "break" near the plate, it just has a bigger arc and is perceived as breaking as it approaches the batter.

[Paul2432]

[ QUOTE ]
Increased attention and confidence in doing a task will increase performance (there are many studies that support this) .

[/ QUOTE ]

Please post some links to the studies or provide some citations.

Do you think players in the NBA lack confidence and don't pay attention?

Paul

[pastabatman]

Just wanted to add that athletic performance is a very poor analogy when trying to teach someone probablility concepts. You want to simplify the scenario, not drag in tons of factors that allow the unconvinced to argue that random event generators have memory of past events.

[maurile]

[ QUOTE ]
Read the links I posted in the thread I linked to above. If I remember right, one study used either free throws, or the NBA 3-point shooting constest, to control against the effect you mention. Results were the same. There is no hot hand.

[/ QUOTE ]
I'll read the links before arguing this further, but I can't imagine how using free throws (in game situations) or the 3-point shooting contest would help. A hot hand lasts longer than the 3-point shooting contest would take (so how could you compare a player's shooting percentage when he has a hot hand to his shooting percentage when he doesn't have one, if you're using a single 3-point contest?), but doesn't last long enough to measure free throws over the course of several games.

If I were trying to test the hot hand theory, I'd use free throws in practice. Have each player shoot a few hundred free throws a day, and see if any players have some days that are better than others to an extent outside the expected range if there were no hot hand phenomenon.

[John Feeney]

Yeah, it sounds like the research doesn't support the "hot hand" idea, even though you might think that would be an area where being "on" a streak could occur. But it does bring in lots of variables that would seem to make it hard to study.

Apart from the hot hand thing, though, I'm wondering if we were able to clarify the issue for Walt, the original poster. Odd that he hasn't been back to the thread. 8-/