Probability Games

A colleague of the mathematics brand posed this question to me today: Say you're playing five card draw poker and you have two tens. You're playing with four other players and you get the feeling you don't have the strongest hand. What are the odds that, if you discard three, you'll draw another ten?

Answers? Anyone? Bueller?

We both agreed that in simple terms you'd say (before you drew the first card), you have a 2 in 47 chance (there's two tens left and there's 47 cards left which you haven't seen). If after the first card drawn you didn't have a ten, you would have a 2 in 46 chance and then a 2 in 45 chance for the third.

But he argued that because other players already have cards that the probability changes--that you have LESS cards out there to draw from. I guess if you were God and could see everybody's cards, you could then calculate the odds. But he was saying, realistically, the probability is different even though you don't KNOW what the other cards are.

I'm not sure what I think about that. I mean, if you have that hand, it doesn't matter what cards are in other peoples hands or in the deck--there are 47 cards you haven't seen. But somehow, the idea of odds changing simply by the redistribution of the cards is intriguing--even if it is a crock of crapola.

If you sensed that the other players had a better hand than a pair of tens, you'd have to figure there are jacks, aces, queens, etc. out there and you could take that into consideration. But that's not what my poker buddy was talking about. I guess it's a philosophical question...if a tree farts in the woods and nobody's there to hear it, does it happen? If there are other cards in player's hands which you can't see does probability change? Philosophy and mathematics...it's like chicken and waffles...tasty but kind of messed up.

Ode to a Nice Guy

To the one who has always been there
Like the sparrow’s pretty twittering
Amidst the street blather of car horns.
To that teethy grin that greets me
Like a tearless day:

Every time I see
Pain or fear or sorrow
I find you too.
Always a guide to me.
To the one who has sat by my side as I cried
Heartbroken sobs,
Who held my hair back when I got sick
And who feeds my dog
And picked me up after getting dumped by Nick
Who fixed my car
Who brought me flowers for no reason at all
Who loved me but never demanded a thing in return
To the one who drives my sister to school
And who cleans our pool
Just to show my parents how cool he is
To the one who makes me feel like a queen
Just for being seen
Just for being me
To the one whose waited patiently
For me to see
what you see in me:

Thank you. Thank you for being the king,
The nicest of the nice guys.

Now I am asking
Just one more thing of you.

Can you feed my dog tonight?
My folks are out of town and I’m going out with this totally hot guy I met outside a bar.

This past weekend saw a basketball brawl in the stands in Detroit, an on-field fight between two college football squads--all this a week after a handful of pro football players in Cleveland concluded their pre-games warm-ups by punching each other in the face. Violence and sports certainly is a problem, and, while many are chastizing and moralizing, I am fraternizing with a solution to the problem.

It is clear that professional sports and college institutions are harboring terrorists. It's also clear that these miscreants are trying to make weapons of mass destruction--or at least of minor destruction (the gateway weapon). Did you see the crying children? Did you see the explosion of fists, cups and blood (possibly ketchup)? This kind of horror cannot be tolerated. We simply cannot allow this kind of brutality to be forced upon America by these violent individuals who cause fear, 430 instant replays and a boost in ratings.

Our only recourse is a premptive strike.

We must destroy the NBA. If they continue to harbor terrorists (and they most certainly will), we must invade, dismantle all weapons (including hook shots) and depose the tyranical NBA commisioner. We will roll on. We will fight the good fight. We will bring democracy to the NBA and make sure only the white guys get paid a lot of money. And if the NFL, NHL and other professional sports do not get the message then we will deal with them preemptively too. We will leave professional bowlers alone because they are too slow to do much harm. But we will watch them closely.

But we cannot stop there. What about the fans? Are they not too harboring terrorists? I'm sure I saw somebody of Middle Eastern persuasion in the stands leading the fisticuffs against our NBA players. Okay, maybe the oafish white guy in the blue jacket throwing random sucker punches wasn't Mid-Eastern, but he was certainly Mid-Western--and that is just as dangerous. We must dismantle the fans. All of them. If they resist, we will not back down. We know where we stand. We will not rest until every American is safe and that will not happen while Americans are unsafe. Once we have freed the stands of all fans, the stands will be free to follow their destinies. The stands will govern themselves and hold elections . . . free elections with no fans to spill beer on them, harass them with feet or indimate them with loud clapping motions after a dunk.

This is only a start, but I think we have to start somewhere. That somewhere is here and that sometime is now. We will not rest until Rush Limbaugh says we are safe or something that is not entirely silly. Until the war on terrorism is won, we are all losers. And America is not about losing but winning (even if we have to cheat), and winning is what we do.

Or somebody gets his ass kicked.

Making a case for Racism

Working in a predominately white, upper class high school which churns out college-bound students by the sackful, I am presented with difficult problems every day. Should I tell my 16 year old teaching assistant to ask for a Humvee or a BMW for her birthday? Should I bring apple or pumpkin pie to the Thanksgiving party?

I have one black student, a freshman. I'll call him Will. I know that he's black because when I look around my English classroom he's the one who isn't white. He is also incredibly smart. We trade books to read, he writes about liking Charles Dickens and other American and English classics, he writes amazing poetry--and he is completely failing my class. Rarely does he turn in homework or raise his hand to speak in class. He blows off studying and, as a result, his test scores are low.

Usually in this situation, I just let the kid fail; it's his choice. But this time I called a meeting with his family, and Will signed a contract (which I wrote) stating that he'd turn in his homework or he'd stay in at lunch with me making up the work (and if he didn't there would be further consequences). Well, Will didn't live up to his end of the bargain, and I wrote him a referral--he had to visit the administration office (and get detention). My hopes: the more we tightened up, the more he'd be inclined to just do the work.

I got a vist from the administrator assigned to Will (after I wrote the first referral). Evidently, Will had been involved in a fight the week before--strictly a fight between some frehsman boys (with no racial overtones at all in the adm's eyes). Will's family saw it differently, and they complained about racism to the superintendent. Thus, this administrator was concerned, rightly so, about my plan of attack and the potential consequences. His point: in my years of teaching at this school, I had rarely imposed a student contract or set such a rigid plan in motion with a student. Implications: was this racially motivated? Or, more to the point, could it be construed by others as being racially motivated?

I felt bad about the situation I'd placed this administrator in; I set him up by not getting him involved with the process. But I also saw clearly the fear that surround the issue of racism at work. I think that fear overshadows, at least in this case, the good we're trying--and suppossed to be trying--to do.

The plan with Will was the right thing to do. Unfortunately, it's not going to work. The kid still isn't doing what's expected of him. I'll have to scrap this plan, and I may just have to let him fail. The interesing question that was raised out of all of this for me: Was my involvement racially motivated? That is, did I get involved because Will is black? Honestly, I'm not sure. My initial reaction is that this kid is special--he is super-smart and I just plain like him. But maybe it is, partly at least, because he's my sole black student. What if that's true? Some might argue that that is racism at work right there. Will is a sullen, quiet kid in class, and I think some of my colleagues here and elsewhere may judge him based on that and, possibly, because of the color of his skin. Shouldn't he get more now because he is black? The world will certainly offer him less because of his skin color. Isn't it our duty to find those smart, talented black men (and women) and do whatever it takes to grant them success? More importantly, is it our duty to put MORE effort into these young black students than our white students?

That's the tough question I'm mulling over now. I think the tough answer is yes. That answer doesn't seem to sit well because it's not "fair." No, it's not. And that's the point. "Yes" exposes what we know intellectually but don't truly confront or act upon: that our insitutions including, our school systems, are racist. They help white students succeed. Talking about it is one thing, but having the white and black students in front of our faces and actively making choices to confront these instituions is hard.

So do I let Will fail? At this point, having put so much time and energy into him with little to no results, I would let a white kid fail. I have a feeling Will is at least partly rebelling against his surroundings; he feels different, and he is very, very aware of the racial make-up of this community. Knowing that, at what point do i just back-off? Like I said, if he were white, I'd have backed-off already. In this case, however, maybe I should be racist.