While doing the stranger mission "Lights, Camera, Action" you will be tasked with winning a deed from a guy playing liars dice in thieves landing. Use your property in thieves landing to save your game then go to the saloons liars dice table, If there is more then 1 player there reload your save and try again until you get just the 1 player ( the guy for the mission ). it took me 5 reloads before i got just the one player.
Once you start playing the best tip would be to not bluff unless you have to. The AI wasnt to smart and it took me just a few minutes to beat him, get the deed for the mission and unlock the achievement.
Also, On a side note. the following is from Red Dead Wiki:
Each round of Liar's Dice in Thieves' Landing during "Lights, Camera, Action" will cost everyone at the table a whopping $200 -- ten times the normal ante amount. Because you can ante indefinitely, this is the single most profitable opportunity in the game. You can spend real hours amassing a ridiculous fortune. (Playing for the better part of the day yielded this editor over $50,000.) To maximize your profits, the best strategy is to ensure that you're playing one-on-one with deed holder Lyle Mouton. Chances are another man might be at the table, so if you save before entering the saloon and keep reloading that save, you'll eventually be able to land a match with Mouton alone. You may periodically get up from the table to engage Autosave to preserve your growing earnings, and Lyle will stay seated for you to repeatedly join him at that $200 ante. As long as you don't leave the saloon and save elsewhere, Lyle (and his awful AI strategy) is there for the taking, indefinitely! Once Lyle leaves the table and the mission enters the Spatchcock phase, antes return to normal.
Hope this helps