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Forum: Probability 10-03-2002, 03:03 PM
Replies: 36
Views: 626
Posted By heihojin
Re: Envelopes! (Problem #1) Long

The main problem is that I find it nonsensical to discuss unbounded probability distributions. It may just be because I haven't yet encountered such in my math education, but I've always considered...
Forum: Probability 10-03-2002, 06:00 AM
Replies: 36
Views: 626
Posted By heihojin
Re: Envelopes! (Problem #1)

irchans,

Could you explain your reasoning for both of these solutions?

In the first case, I can understand how one might think that given an amount Y in the first envelope, that the probability...
Forum: Probability 10-03-2002, 03:07 AM
Replies: 1
Views: 118
Posted By heihojin
Re: Updating Probability Estimates

In your table titled "Player 1 Action Probabilities," the values in the BC row do not sum to 1.


heihojin
Forum: Probability 10-02-2002, 11:51 PM
Replies: 36
Views: 626
Posted By heihojin
Re: Commentary on Solution to game #2

To expound on irchans's reply, to calculate optimal strategy you are assuming that your opponent knows the rules of the game, and that your opponent is attempting to maximize his or her expected...
Forum: Probability 09-26-2002, 12:56 PM
Replies: 5
Views: 149
Posted By heihojin
Re: Variance

Any statement that your variance per unit of time will change as a result of playing more than one hand assumes that all other things are equal, i.e. you are playing an identical strategy against...
Forum: Probability 09-26-2002, 01:26 AM
Replies: 1
Views: 120
Posted By heihojin
Re: Odds calculations

Holding the bet has an expectation of (6/11) * $10 - (5/11) * $10 = $0.91. Selling the bet has an expectation of $1. You should definitely sell.

Your friend's expectation in purchasing the bet...
Forum: Probability 09-26-2002, 01:10 AM
Replies: 5
Views: 149
Posted By heihojin
Re: Variance

Dave wrote: "In blackjack, a person or team can reduce their variance by playing more than one hand at a table."

Just as an addendum to what irchans and BruceZ have said, the reduction in variance...
Forum: Probability 09-25-2002, 12:17 AM
Replies: 28
Views: 377
Posted By heihojin
Ignore the previous post.

I'm just full of errors today. I misunderstood irchans; in fact, in my original post, I had assumed independence of events A and B by assuming P(B|!A) = 1.

Again, sorry for the error.


heihojin
Forum: Probability 09-25-2002, 12:02 AM
Replies: 28
Views: 377
Posted By heihojin
Re: Does It Matter?

This is a recant of my previous post. This was not immediately obvious to me when I posted it this morning; rather, a counterexample to my previous argument occurred to me earlier today after I woke...
Forum: Probability 09-24-2002, 11:09 PM
Replies: 28
Views: 377
Posted By heihojin
Re: Does It Matter?

As a correction to my last post, I wrote "Because P(C|B) is greater for switching than not, you should switch. Notice that this is regardless of the probability of event B occurring, so long as it is...
Forum: Probability 09-24-2002, 10:08 PM
Replies: 28
Views: 377
Posted By heihojin
Re: Summary

irchans states: "Heihojin's formula seems to fail in this case due to lack of independence." irchans then assumes that events A and B are independent.

This is not correct, because event B is only...
Forum: Probability 09-24-2002, 12:06 PM
Replies: 28
Views: 377
Posted By heihojin
Re: Does It Matter?

Whether or not the propositioner could have turned over a black card is irrelevant, so long as the probability of that event occurring is less than 1.

Let the following events be defined:

A:...
Forum: Probability 09-23-2002, 04:50 PM
Replies: 6
Views: 138
Posted By heihojin
Re: Independence

Keep in mind that the exact calculations for those events I defined are only correct if neither player has a flush draw in the given example, including the possibility of a four-flush on board. The...
Forum: Probability 09-23-2002, 04:39 PM
Replies: 6
Views: 138
Posted By heihojin
Independence

The word "independent" means, when describing events in the context of probability, that the information that one event occurs does not affect the probability that another event occurs. In...
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