## You draw two cards, simultaneously, from a 52-card deck. What is the probability that at least one is an ace?

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For one card, this is easy: the odds are one in thirteen, for there are four aces in 52 cards, and 4/52 = 1/13.

With a second card drawn at the same time, we must consider the 12/13ths of the time that the first card drawn is not an ace. When this happens, 51 cards remain, with four of them aces, so there is an additional  4/51sts of this 12/13ths that must be added to the 1/13th for the first card drawn.

Therefore, the odds of drawing at least one ace, in two cards drawn from a standard deck, are 1/13 + (4/51)(12/13) = (1/13)(51/51) + (4/51)(12/13) = (51 + 48)/[(51)(13)] = 99/663 = 33/221, or 33 out of 221 attempts, which is as far as the fraction will reduce. In decimal form, as a percentage, this happens ~14.93% of the time.

If I made an error above, please let me know in a comment. I do not claim to be infallible.

[Image credit: I found the image above here.]

# Not Poker — Chess. I Am Not Captain Kirk.

Something I have in common with the fictional Captain Kirk, from the original Star Trek series, is that I enjoy playing both poker and chess. In the scene depicted above, from the episode “The Corbomite Maneuver,” the Enterprise is facing an adversary who dramatically outpowers them — and Kirk escapes the situation with an outrageous bluff, right after making this reference to the game of poker.

Unlike Captain Kirk, however, I am not skilled at bluffing, with two consequences:  (1) I’m a terrible poker player, and (2) I do not attempt bluffing as a strategy, unless I am actually playing poker.

I’ve been an activist for a large variety of causes, for decades, and, because of this activism, have acquired a rather large number of adversaries. Many of them have figured out that I don’t bluff, but some — rather surprisingly, considering they have known me for years — have not. The amusing thing, to me, is that I’ve always been quite open about this, but some still fail to realize it, despite my candor on the subject. When engaged in any struggle, I only make statements I believe to be true, for one simple reason: I’m so terrible at bluffing, or other forms of lying, that any untrue statement I were to make would be instantly recognized as dishonest. Since I figured this out, about myself, decades ago, I deliberately choose to only employ strategies which are completely honest. It would be stupid, after all, for me to employ strategies with which I know I have weak skills.

So, unless I’m actually playing real poker, and am engaged in any sort of struggle, I’m basically playing metaphorical chess. This involves figuring out what my opponents are thinking, devising strategies to counter theirs, and remaining at least three moves ahead of my adversaries, at all times. I’m far more like Mr. Spock than I am like Captain Kirk, and always have been. This isn’t going to change.

I find it hilarious that I can post these absolutely-true statements right here,  on the Internet, where anyone can see them — and have full confidence that those who persist in their mistaken belief that I’m bluffing, about anything, will continue to make this enormous error in judgment — until it’s too late. For them, that is.