Sobriety is a crutch. Monks that have chosen the way of the drunken fist are not usually those still belonging to monasteries. Often they are nomads, outcasts, wanderers, and ronin that have chosen to pursue indulgence over endless discipline. Don't be fooled however by their drunk appearances, Monks that have devoted themselves to this tradition have become masters of improvised combat, turning themselves into unpredictable hurricanes of martial combat. 

Drunken Boxing

When you choose this tradition at 3rd level, you embrace being drunk, and the benefits it provides. Due to your practiced control over your drunken stumbling, you have +2 AC while you are poisoned. You also add your Dexterity and Wisdom modifiers to your attack rolls to counteract the disadvantage gained from being poisoned. Lastly, as a bonus action, you may spend 1 ki point to poison yourself for one minute as long as you have the means to do so.

In addition, your confidence allows you to use alternate weapons to display your diverse skills. Improvised weapons count as monk weapons for you while poisoned, as long as the weapon is not considered heavy. You are proficient with the weapon and you may use your monk dice for the damage rolls with that weapon.

My Kung Fu is Superior

At the 11th level, your drunken confidence and cockiness heighten your skills in lone combat. While in combat, if no friendly creatures are within 10 feet of you and if you are poisoned, you may add an additional damage die equal to your current unarmed strike damage die in the relevant damage of a melee attack you make. Also, enemy creatures cannot gain an advantage against you in combat due to positioning.

Numbness of Body

At 6th level, your drunkenness numbs your body, allowing you to shrug off some of the damage you receive. When you become poisoned, you gain temporary HP equal to 2x your monk level. This HP disappears when you are no longer poisoned. You cannot use this ability again until you finish a short or long rest.

The Drunken Master

By 17th level, you have mastered the ability to transfer your drunken flow into other creatures. Whenever you successfully deal damage to a creature, you may spend 4 ki. If you do, that creature takes 4d12 poison damage and must make a Con save with a DC of 8 + your Wisdom modifier + your proficiency. If the creature fails the save, it dies. 

In addition, because you have adapted to being drunk so often, being poisoned no longer causes you to make ability checks with disadvantage.