I recently purchased my home and as you can see in the photo I have a patio that needs a little help. The crack in the patio isn't a concern at this time, but the standing water is really bothering me. The grass hits the patio slightly higher so any water that is on the patio just stands on the last 3 feet of the patio instead of draining away. Is there anything I can do in my yard (digging, certain landscaping, adding rock, or anything) that will help the water drain away? Also as you can see in the photo, the grass has died right where the patio and yard meets so it's all dirt - and when the patio is wet it carries mud all over it. At this time I do not plan on changing the patio or repaving it - I'm looking for something I can do on the yard side that might solve this issue. Thanks!

- Editing to add --- where that one landscaping stone is in the center is there because we had an old gas pipe, 4" around, that we recently cut out, but it sticks up still about 1" out of the ground with sharp edges. I have that there so the kids dont step on it right now before I get a cap for it.