Luck and first principles

Now that there seems to be at least one other person occasionally reading this blog, I've decided I should probably supplement the content so it's not all just boring brags or whining about beats. So I'm adding boring general thoughts and pontifications on poker.
First: luck in tournaments. I know a few serious poker players who felt Doyle Brunson let the side down when he said luck was a bigger factor than skill before the Irish Open. But I think there's little doubt that in any one tournament, luck plays a bigger role than skill (in the long run, the reverse is true of course).
I think a lot of players focus on one very narrow aspect of luck: the suck out (and selectively when they are done unto them). Good players tend to get their money in good so they will be sucked out on more, and suck out less, than bad players. That's not to say they can't get lucky. As I've said before, to win three consecutive races where you're 70/30 favourite is almost as lucky as to win one where you're the 30/70 dog.
Your marginal decisions can greatly result the outcome of a tournament, as can the marginal decisions of others. Harrington has an example of what he calls "hidden luck" in his first tournament book. Looking at a hand where he had a marginal decision as to whether to call or raise with AK, he showed that not only would the outcome have been very different for him if he'd raised, but also for every other player at the table with an interest in the hand.
There are other manifestations of hidden luck. Ever looked down at a raggy ace and decide you'd try a blind steal if it was folded round to you, only for someone to raise ahead of you, and then the BB pushes because he just woke up with Aces? Lucky. Or decided that the guy who raised from the cutoff for the third time in a row needs to be taught a lesson so by God you're shoving your 10-5 off from the BB, only for Tighty McTight to beat you to it from the SB with some muck like Queens, and runs into the blind stealer's Aces? Lucky you again.
It's lucky to get it all in preflop with Jacks against 10's. Guy could just as easily have had queens. Lucky to pick up Aces when someone else has Kings. Lucky to get AK when he's got AQ. Etc. etc.
There's also the timing of your luck. When I was all in shortstacked with 8's at the weekend against 5's and a 5 hit the turn but an 8 hit the river, my first reaction was I was glad my 8's had held up. My second was I'd rather my Kings had stood up against the 5's in my exit from the WSOP ME. If you get lucky in your local pub freezeout, does it make up for the time you got unlucky in the Irish Open?
The second thing I want to witter on about is the importance of being able to think from first principles. While in Vegas I read a Mike Caro column in which he was asked was it essential to know the maths underlying poker and he said no, so long as you knew the corect strategies which had been worked out by those who do. Of course he's right: if someone tells you that you need 2 to 1 pot odds to call an allin with a flush draw, you don't need to know how the 2 to 1 was calculated. You don't need to understand why it's push or fold when you're shortstacked so long as you do it. You don't even need to know why it's sometimes better to push with Q10 (on the button, folded round to you) than with AQ (in second position, when a tight player has raised UTG).
That said, it helps to understand the maths. Sometimes what appears like a standard situation has some subtle differences that totally change the optimal strategy. These most often arise on the bubble of a tournament, or in satellites. An example arose at the end of the last tournament I played in Vegas, the Caesar's Palace nightly $170 game.
We'd played down to a final table of 10, with 9 prizes. I have a slightly below average but comfortable stack. It's folded around to a guy with a smaller stack, who shoves from the cutoff. I've played with him a bit to know he shoves light here and assess his range as almost any Ace, any two paint cards, any pair. Coversely, with a genuine biggy like a premium pair or a big ace, he'd either do a small raise or a trappy call. I look down at A10s in the BB which is well ahead of that range so I have an easy call. Granted I'm not very much ahead of most of his likely holdings, but if you want to win tournaments rather than sneak up the money ladder, you have to be willing to make those calls. He had KQ and I lost.
Now I'm virtually microstacked, with an M less than one if I fold my SB. Standard short stack strategy would be to get it in next hand. I look down at 63off and know that I'll be at least a 30/70 dog if I put the chips in. There's a bunch of callers and the clear expectation is that I'll shove and it'll be checked down to burst the bubble. There's general consternation when I actually fold, leaving myself with a stack of precisely 10 antes.
The first point is that even if I somehow win the hand and quadruple up, I'm still short. I still need to get it in some time in the next orbit, almost certainly as a 30/70 dog. And even if I win that, I'll still be the shortest stack at the table! Given that my chances of winning with the 63o are probably 10% at best, I'm a 33 to 1 at least for that to happen.
The other point of my fold is the effect it had on the table dynamic. I made it quite clear my intention was to fold any two cards, even pocket aces, until I was all in on my ante. I even said so aloud several times, in effect telling the other three short stacks at the table that if their intention was to fold everything until I was out, they'd be microstacked themselves and no longer in the running for the major prizes by the time that happened.
A few hands later, one of them shoved and lost. I was in the money. A few hands later, another shoved and sucked out. A few hands later, I was all in on the ante. I was nominal BB in the hand but had nothing else to post. Several players said things like "Dude you should have been all in 20 hands ago". Amusingly, one guy shoved allin with only KQ (same guy I'd lost to originally with the A10) giving me protection and 8 to 1 on my ante. I hit one of my two undercards to scoop the antes. Now I was in the bizarre position that if I somehow won the next hand, I'd almost be back in the tournament with 2.5BB. I shoved blind with, it turns out, Ace 10, the big blind had J10, and sucked out.
Everyone else at the table was convinced I'd played my short stack incorrectly, because they read somewhere that when you drop below 10 BBs you have to shove virtually any two cards. But when you're microstacked to the point that you'll still be the shortie even with two lucky double ups, and there are other guys who can't afford to wait and let the blinds through them to have any chance at a big prize, and virtually all your remaining equity is your slim chance of sneaking into 9th, then folding everything is mathematically correct.

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