Entering a Pot to Take it All
In Poker, a maneuver technically known as 'sandbagging', should be kept for 'tough' games.
It is frowned upon in many clubs, and one loses more by ignoring their 'climate of opinion' than one is likely to gain by flouting it.
Let us assume, therefore, that we are playing a game in which 'sandbagging' plays no part; a player who has openers will open, unless he is first or second to speak and has nothing better than a pair of Knaves.
On what principles should those who follow him a) play, and b) double?
A player who has a pair of Kings or better should, of course, enter the arena. With a pair of Knaves, or even a pair of Queens, a good player will think twice.
It is almost certain that his hand is not as good as the opener's, and he is therefore competing at a disadvantage. The determining factor is the odds which the pot offers.
If it has not been sweetened, there are 14 chips in it, and the opener's initial bet (four chips) raises the amount to be won to 18 chips.
One should not, therefore, put up four chips unless one's chances of winning against the opener are shorter than four and a half to one.
Now, if a player holds a pair, the odds against his finishing with a better hand than the opener's are theoretically four to one. If, therefore, one is last to speak and has any pair in one's hand, it is just worth while to compete in the pot.
But, unless one is last to speak, it isn't worthwhile. For there are one or more players who still have a chance of coming in, and one's chance of wining the pot is pro tanto lessened.
Hence, a player who is sitting in B's seat is likely to be on a losing proposition if he comes in on a pair of Queens or Knaves where A has opened the pot, and it's longish odds against his winning if he comes in on a smaller pair.
Admittedly they have one chance in nine of making threes, but what guarantee is there that the opener--- or some other player--- will not also produce threes or maybe a still better hand?
It is often seen as many as four out of the six players who follow the opener play on a small pair. The fourth of them sees--- if the opening bet has not been raised--- that there are 30 chips to be played for.
He is therefore being offered odds against his winning of 30 to four, i.e., seven and a half to one. But he is now up against four competitors, and as likely as not his is the worst of the competing hands.
He must inevitably lose heavily in the long run. Moreover, it is always possible, unless he is last to speak--- that the opening bet will be doubled.
Suppose that everyone comes in for the double. Now each of the players who started with a small pair can see that there are 54 chips to be played for (40+14).
The odds which it offers to each player who has put up 8 chips are 54 to eight, or less than seven to one.
But, since we must assume that the doubler stands a better chance than the original opener of winning, the odds against the player with a small pair of beating both of them are proportionately enhanced.
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