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Possibly the last thing you would think of doing when faced with a tough greenside bunker shot would be to get your putter on it, but it can be a very effective option under the right circumstances. You will need the sand to be firm and compact for starters. If you attempted this when the sand is the slightest bit soft then you will be asking for trouble. Your ball also needs to be lying in a good spot so when you make your stroke, you can get the entire putter face on the ball at impact.
The next thing you need before attempting this shot is for the bunker to have no lip, or worst-case scenario a very small lip. If you try to putt out over a lip that is more that an inch high then you will be playing at least another shot from this bunker. If all of these conditions are not present then putting out of the bunker is definitely not an option.
If you have the conditions working in your favor then you need to set up to the ball as if you were on the green, keeping your weight central across your feet. Take your standard putting grip with the difference of gripping down one inch. This will prevent you from catching the sand during the stroke. Place the ball just behind the centre of your stance so you can hit the ball a little on a downward angle to avoid hitting the sand first.
Your ball will roll a little bit like it is on the green before it pops up over the lip and on to the green. Make sure you hit your putt a little harder than normal, as the potential bounce up over the lip will take the sting out of the ball. With a little practise, you can be very effective from hard compact bunkers if the conditions are in your favor.
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For the most part and for 98% of your golfing life, you will never putt out of a bunker, in fact you will never really need to. Yet in the winter when the sand in the bunker is hard and compact due to the rain, using your putter can be an effective weapon, especially if you are prone to blading the ball across the green.
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When the sand is too hard and compact then the option to putt out of the bunker can be a good one, but only if the ball is lying well. No matter how hard the sand is, if your ball is in a bad lie then you need to play a more traditional bunker shot with a sand wedge or lob wedge.
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No matter where the hole is cut on the green, and to a point what is on the other side of it, if you can play a traditional bunker shot then you should. The control you have over the impact and spin of the ball will make it easier to get the ball closer to the hole than if you used your putter.