[tylerdurden]

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I believe they dig a trench. FLoat the barge in from the Mississippi and then fill in the trench. The barge is therefore on Miss river water.

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This is correct. The barges can be "detached" from the main buildings on land and floated down the river, in theory at least - some of them have very seamless-looking construction and would require quite a bit of effort to detach from the land-based structures.

I'm not sure exactly how filled-in the trenches can be, but the barges definitely can be relocated down the river. Several of the original Tunica casinos at Mhoon Landing (President and Lady Luck IIRC) were moved downriver as well as the Tresure Bay, which is now on the Gulf.