The game is 8 ball. I have ended up on both ends of this situation in the past. So far it has been a contest where someone has ball in hand. Let's say it is the 14 ball player. That often is the result of either the 14 ball player shooting everything else in or the 8 ball player intentionally fouling by shooting the stripes in to force this situation.
The common strategy with ball in hand for the stripes is to put the cue ball behind the 14 and bump it to create separation. It is the same thing in reverse for the 8 ball player if he gets first shot at it. The hope is to get ball in hand, put the cue ball between the 8 and 14 on the next shot, then shoot one ball one way and the 8 the other, or for the 8 ball player, just the 8. The defense for this seems to be for the 8 ball player to use a bad hit to push the 14 back up to the 8 to prevent this. It then becomes a contest to see who can keep this up until the 8 ball either goes in the pocket by accident, costing the stripes player to lose, or one of the balls is right in front of the pocket and it is not possible to hit the other one any longer without pushing the opponent's ball into the pocket so the player does a long rail kick. The outcome than depends on the result of that attempt. It can go either way.
I am not sure if I mixed things up in my description. It can also be the 14 ball that ends up in front of the pocket. It all depends on who starts things. One player is making a good hit each time trying for separation. The other player is making a bad hit to close the gap and giving up ball in hand each time. The ball in hand player doesn't HAVE to keep this up but they never seem to think of anything better to do.
What I am wondering is if there is a better ball in hand strategy for whoever has the first attempt. I am thinking of things like setting up an angle to bank whichever ball I have (8 or 14) away from the rail and leave the opponent a long shot to a frozen ball with no chance to cut it. this would force a return safety or a difficult bank. Let's say I am shooting the 8 and get first chance at this with ball in hand. My goal (I assume) could be to bank the 8 out somewhere it would be very hard to safety back and leave the cue ball at the other end of the table with no angle for a cut shot.
This is not incredibly common but it does happen from time to time. Someone mut have a great escape shot here.
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