Epistemology and the subjective nature of probability

"In The Beginning, Everything Was Even Money".

So begins the hypothetical "Gamblers' Bible". However, as with many bon mots it hides a greater truth. Because, of course, in the beginning, everything was even money. Either something was, or it was not. Since there was no "law of probability" or, indeed, law of anything, the chance of something happening or not happening was, as far as any observer could know (although, of course, the existence of the observer would change the situation, a la Schroedinger's Cat) 50%.

I mention this because many unsophisticated poker players have a kind of problem with this when it comes to cards. You see, cards are not like dice. The state of affairs (the order of the deck) is decided before the hand begins. This isn't the case with craps, where the state of affairs is decided by a future event.

Most poker players, even the dumbest ones, have no difficulty with coping with the idea that the "chance" that, say, the club that they want will come on the river is still about 18%, even though the order of the deck has been determined. After all, no-one knows what that card is, so it makes no difference, does it?

But here's where Schroedinger's Cat comes into play. Suppose the dealer peeks at the card. Suppose he knows what it is?

Our dumb player can probably just about carry on here, but already his head is going into a spin. How can something be an 18% chance when the dealer knows whether it is a club or it isn't? Surely the chance is now 100% or 0%?

And what if another player gets to look at the card. Indeed, what if everyone in the hand knows what the river card is, apart from the poor guy who has to decide whether or not to call?

At this point, many a poker player goes into some kind of existential cataclysm. As far as he is concerned, he should call on the basis of pot odds. But, for God's sake, everyone else knows. Either it is a club, or it isn't a club. 100% or 0%. Hell, let's split the difference. It's 50:50. Let's call.

OK, I have taken a hypothetical case, but you'd be surprised how many intelligent people take this kind of approach to important decisions in life. If something has already happened, but we don't know what the result was, many people take the "it either is, or it isn't" line, rather than taking the correct line that, it doesn't matter whether something has happened already or not. All that matters, if we do not know the result, is the probability .

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I have to post this. The Stars 10 billionth hand took place last night. All participants in the hand were guaranteed $10,000, while the winner of the hand got $100,000. The hand occurred at a 1c-2c table.

Here's what ensued. I pass no comment, but I do highlight the parts which are rather interesting.

PokerStars Game #10000000000: Hold'em No Limit ($0.01/$0.02) - 2007/05/19 - 16:51:40 (ET)
Table 'Venusia' 6-max Seat #4 is the button
Seat 1: Rechargeable ($4.83 in chips)
Seat 2: inwooke ($1.73 in chips)
Seat 3: The_Moog ($6.43 in chips)
Seat 4: XTedForrestX ($2.95 in chips)
Seat 5: Ferius ($3.10 in chips)
Seat 6: justine0003 ($0.82 in chips)
Ferius: posts small blind $0.01
justine0003: posts big blind $0.02
*** HOLE CARDS ***
HostJeff [observer] said, "Guess what?"
justine0003 said, "?"
The_Moog said, "wowowow"
HostJeff [observer] said, "Don't leave your seat -- you're all winners."
The_Moog said, "YES"
MktgScottY [observer] said, "Let the best hand win"
The_Moog said, "gl table"
MktgScottY [observer] said, "Here we go"
Rechargeable: raises $4.81 to $4.83 and is all-in
inwooke: folds
The_Moog: raises $1.60 to $6.43 and is all-in
XTedForrestX: folds
Ferius: calls $3.09 and is all-in
justine0003: calls $0.80 and is all-in.


Marvellous.

PJ