Tuesday, November 07, 2006

One card

No new poker here as we had a get together last night at Filadelfio's a local, slightly upscale, neighbourhood bar and grill, which actually does a pretty good job of emulating the real thing (just to choose an example I happen to be familiar with). One item on the pizza menu there, is a ‘Canadian’ pizza. Now what toppings do you suppose that has? I almost don't want to spoil the suspense, and force you to follow the link instead, but I'll give in: salmon, sour cream, gherkins (that is, dill pickles, for the linguistically challenged). As many poker players have so eloquently put it in the chat boxes of a myriad of poker sites: WTF????? I have a peculiar fascination with this pizza, rather like Steinbeck's character Doc in Cannery Row who was obsessed with the idea of a beer milkshake. Some day, I suspect, I'll just have to break down and have one.

Rooder left a comment on yesterday's post (thanks for that!) which leads me to suspect that I didn't make the point I was trying to make as effectively as I might have (alas, it was ever so). I was trying to fight my training and not present a simplified example (as in the mathematician of joke number 6) but, in light of the comment, and a failure of any other sort of inspiration, here we go.

Dad puts $1 on the table, and also gives $1 each to his twin sons Billy and Bobby. He then shuffles the 13 hearts from a standard deck of cards, and deals one card to each boy. The game is ‘One card hold'em’. Billy can bet $1, whereupon Bobby can fold or call; or Billy can check, whereupon Bobby can bet or check, and if he bets, Billy can choose to fold or call. In the event of a show down, higher card wins (ace is high).

Billy, who must act first, receives the J♥. He must decide to bet or check. Since Bobby is his twin brother, Billy knows how Bobby will respond to each action. If Billy bets, Bobby will fold any card 8 or under, and call with 9 or better. If Billy checks, Bobby will bet any card 8 or better, and also with a 2, as a bluff. No claim is being made that these strategies are in any way optimal, just that they are what they are.

Under these conditions it is clearly correct (do the math yourselves!) for Billy to play passively. The short reason is that Bobby is betting with more hands than he's calling with, and the extra hands that he bets with are ones that Billy beats.

The real hold'em situation was meant to mirror this. The key ingredients are: heads up play; a good hand, which is a decent favourite against your opponent's range; a very dry board that gives your opponent few outs if he's behind; and an aggressive opponent who is likely to bet more hands than he would call.

One purpose of aggressive play out of position at hold'em is to buy information. If the information given by a call is something you would rather not have paid for, it might be time to consider playing passively instead.

Edit: Oh yes, in the real hand, I was the TAG player in MP and held AK. I might have chosen to check the turn, since I guessed that I was well behind to a pair of jacks, but there are a lot of players out there who routinely call apparent continuation bets with air, but fold to a second bullet. Further, I thought that there was some chance I might actually fold a jack worried about an overpair, or more reasonably a middle or bottom pair hand (people do call raises from the BB with Ax sometimes). BB's call on the river shows that he wasn't thinking along the lines I've been describing, but it occurred to me as I went over the hand (as I tend to do when I've put nearly half my stack in behind) that up to that point, there was little to criticise in his play.

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