Games: Backgammon
Here's a difficult problem which many players would get wrong over the board. In fact many players would get the wrong answer to both halves of the question: should Black double; should White take?
Let's look at the double first. On the downside, Black is on the bar facing a 5-point board. Otherwise his position is excellent: he has a five-point prime blockading two of White's men, one of which is not even at the edge of the prime, and there is another White blot on the mid-point which is vulnerable to attack. All he has to do to realise the potential of his position is to enter from the bar. Even if he doesn't come in this roll, White's position will self-destruct if he doesn't roll a six soon. For example, look at the effect of White rolling 55. This is a very volatile position, and Black may well miss his market if he doesn't double now. He should do so.
How about the take? White has four blots, two of which are stuck behind Black's 5-point prime. Many players would see the loss of a gammon as imminent and drop in an instant. However, White has two things in his favour: he has a 5-point home board, and he leads in the race by 97-133. Never forget that backgammon is essentially a race and if White can free his back men he will win not only the race, but also a high percentage of gammons. Finally, White will have some very powerful redoubles after certain sequences.
In practice, many players wouldn't double as Black, preferring to enter from the bar first; and those same players would drop as White, fearing a gammon loss. You simply cannot play winning backgammon with attitudes such as this; you must be prepared to speculate to accumulate.
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