You have to save an awful lot of dollars to make up for just once mistakenly throwing the best hand in a $100 pot for a $1 bet.
There was a player who was absolutely convinced that no one would be dumb enough to bluff for his last chip. Say the pot contains $80. You might have $11 left after having put $40 so far into the pot. He has a good hand, but not the absolute nuts. He bets $10, and you put in all of your chips, that is, you raise your last $1. Most poker players would sigh and then call that last minuscule raise. Most poker players also always end up losing that last chip nearly every time. He wanted to show he was too smart for that, and saved that dollar. He would never throw a pot away if the player was about to buy more chips, and was just trying to get rid of those last chips. If the player would be going home after losing the pot, though, that was when he wouldn’t call.
A few players caught on to his habit, however, and, perhaps as a desperation play once in awhile would take a chance on their last chips, and go all in as a bluff. They would never do it against any other player, knowing that any other player would resignedly toss in the extra chip.
Did this player outsmart himself? He didn’t think so. He thought he was very clever not to lose that last dollar. The pot has $100 in it, he’d reason. Let’s say he’s in that situation 100 times. He throws away his hand each time. Let’s further say he’s right 99 of those times, so he saves $99. On the hundredth play someone bluffs his case money in desperation. Our friend loses the $100 in the pot that he could have had for calling the dollar. That’s a net loss of $1 for the 100 plays, or about 1 cent per play. Not much of a loss per play when you figure it that way, right?
Here’s what’s wrong with that reasoning.
First, the situation probably wouldn’t come up 100 times in any one player’s lifetime.
Second, even if the precise situation did come up 100 times, that one bluff per 100 would be only a guess. Even if it was a good one, it would still be an average. Statistical analysis would show that this is an awfully small sample. Some runs of 100 situations he would be right every time. Some runs he’d be wrong as many as 10 times. Over thousands of runs it all might average out, but what if the next 100 is the run he gets bluffed 10 times? He saves a buck 90 times, plus $90; he loses $100 10 times, minus $1000. Net loss, $910. Not such a good play anymore.
Third, once smart players see that he might fold sometimes for an extra buck, they might well make the play.
Never throw away a moderate-sized or larger pot for a tiny fraction of that pot, even if the chances are practically nil of being bluffed. I adopted this maxim years ago, right after one player and I got into a raising war in a straight $2-limit (Northern California style, same bet both before and after the draw) lowball game. I was drawing to 6-4-joker-ace, with an extra 6; he wanted to gamble, and so showed me his whole hand, king-6-3-2-ace, and then kept reraising me each time I raised him. I wasn’t going to quit, because the joker made mine the better draw. Finally, after 20 bets apiece, he stopped raising. We each drew a card. He was first to bet, and came right out swinging. I paired fours, and disgustedly dumped my hand.
He showed me his pair of sixes, and gave me the horselaugh as he took the pot. Since then, if a pot had as few as 10 bets, I usually called the last bet, even if I had hardly any chance of winning, and even if proper poker strategy said it was a bad play. No, I wasn’t like the guy who had lost his farm calling every bet, but, by God, no one had bluffed him. I just wasn’t going to give up any pot for one bet that represented only a small part of the pot.
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