Most coin flip decks I've ever seen are, well--- bad and just throw in all the coin flip cards with no thought. While these two commanders are basically impossible to build at a true CEDH level (a total CMC of 10 for both kills it in CEDH speeds or against Statis type decks) the deck should do well against some really strong decks you could see at whatever meta you play.
There are a couple of win-cons in the deck but it mostly falls on Okaun, Eye of Chaos's shoulders. His partner, Zndrsplt, Eye of Wisdom, is mostly just an enabler.
You flip a bunch of coins to make Okey big. It only takes 3 wins to make him commander damage lethal (24/24) and 4 wins (48/48) to win with non-combat damage.
Okaun can deal damage via becoming unblockable with either Rogue's Passage or Whispersilk Cloak. He can also just trample over folks (while gaining you an ungodly amount of life) by equipping him with Shadowspear. Who cares about "unblockable" when you have guy with 48+ power just stepping on everything in his path to smash a face in?
Another option with Okaun is to use Chandra's Ignition. Not only can you use this as a board wipe if you don't win enough flips, but at 4 flips it's a game win. If you win 3 flips before combat you can still wipe the board with Chandra and then swing for the kill at one opponent.
Fling works wonders on people. I've often had people try and kill Okaun during combat or before Chandra goes off. At that point I usually just get revenge by throwing Okaun at the person who targeted him. You can't react to the additional cost of sacrificing Okaun so that reduces their only options to preventing damage or countering Fling. It's also good for once one person is dead. You can kill one person with combat damage then Fling Okaun at the other person to end the game.
Zyndrsplt, Eye of Wisdom as said earlier, mostly just enables the deck and usually the first of the two you'll have out on the field. He can, however, win the game with one combo. Frenetic Efreet, unlike Frenetic Sliver, allows you to put infinite coin flips on the stack. Efreet will die or phase out on the first flip but all of the other flips still will be triggered. When Frenetic Sliver came out Wizards had actually errata'd the Efreet to work the same way, requiring a check to see if Efreet was still on the field. Not long after though Wizards decided to remove that errata and Efreet works like he did originally where you still do all of the remaining coin flips but their outcome just doesn't do anything. When combined with Laboratory Maniac and Zyndrsplt, Eye of Wisdom you get to just draw your whole deck by putting a million coin flips on the stack. 99% of people will agree that you're pretty likely to win the like 70~80 or so flips out of 1 million needed to win the game.
Some of the obvious breakdowns:
Muddle the Mixture is like 80% of the time going to be used to find Krark's Thumb or as a counterspell but it has some other worthwhile tutoring choices. Thought Vessel will keep you from discarding to hand size. Transmute Artifact and Reshape are 2CMC so you can tutor for a tutor with it. Swiftfoot Boots are also a good choice.
Drift of Phantasms may seem innocuous but as a tutor it is probably the most versatile. Here are some of the targets; Frenetic Efreet or Laboratory Maniac(whichever half of the combo you still need); Whispersilk Cloak to make Okaun get through defenses; Puppet's Verdict or Chaos Warp (for removal); Capsize (remove threats or bounce disabling effects on your stuff); Tribute Mage or Trinket Mage (tutor for a tutor); Propaganda (defense); Emry, Lurker of the Loch (graveyard recursion); Rhystic Study or Wheel of Fortune for card draw.
Tolaria West can search for any of your utility lands or duals. Very useful for getting Rogue's Passage or Reliquary Tower or simply getting color fixing with Command Tower. It can also snag Mana Crypt which gives you another coin flip engine as well as acceleration. Although it is 3 mana you can use it to grab one of the artifact lands to help transform Storm the Vault
if need be.
The deck runs Venser's Journal to counteract the self damage of the MANY 'pay life' or self damage effects the deck has (Mana Crypt, Mana Vault, Talisman of Creativity, Ancient Tomb, Prismatic Vista, Fiery Islet, Scalding Tarn, Shivan Reef, and City of Brass. The no max handsize is also key due to how many cards the deck draws once Zyndrsplt is out.
It's very easy to lose A LOT of health through self damage with this deck and the only ways to gain health in the deck are Shadowspear, Inventors' Fair and Venser's Journal so be careful.
Reshape and Transmute Artifact have good options in this. You can use either of the artifact lands or even the treasure tokens from Storm the Vault
or Tavern Scoundrel. It has good synergy with Goblin Engineer as it can help you put an artifact into your graveyard for swapping purposes.
Capsize may seem out of place but it's there because of times I've had issues with opponents enchantments or indestructible stuff. Early on an opponent put Darksteel Mutation on Okaun and it basically shut my deck off for quite a while. It's also good vs stuff like Aminatou, the Fateshifter's ult to help get your stuff back.
Gemstone Caverns is mostly there for luck flavor, but turn one 2 lands, Sol Ring, Mana Crypt into okaun certainly causes some eyes to bulge. If you play Whispersilk Cloak then equip him on the next turn many people will just scoop right there since he becomes unblockable and untargetable long before players can typically be ready for answers resource wise.
Tribute Mage basically falls into the same category as Muddle the Mixture. It's a body that you can search for Krark's Thumb with.
Imperial Recruiter can fetch every creature in the deck except Karplusan Minotaur. This can easily allow you to fetch for another tutor or complete your Laboratory Maniac & Frenetic Efreet win combo.
Trinket Mage will let you search out a lot of useful cards though none quite on the power of Krark's Thumb. Trinket can let you get some ramp (Sol Ring; Mana Crypt; Mana Vault), no max hand size (Library of Leng), a land drop (artifact lands), or a win-con Shadowspear.
Note that if you have Library of Leng out and use Gamble you can choose to put the card on top of your library instead of into your graveyard. You will end up shuffling that card into your library but you wont lose it. In addition, if you put the card on top of your library you don't reveal it. This keeps the opponent from having information. Of course, if you have a way to recur the card, or if it's simply a land and you don't want to draw more land, it's best to toss it in the graveyard.
Goblin Engineer is great for searching for Krark's Thumb, obviously, but a really good alternative early on is to search for Mana Vault. Swapping the vault in and out of the graveyard with the engineer will let you essentially pay R to untap it instead of (4). Using Great Furnace to both pay the R and as the artifact you need to swap to put Mana Vault back into play is a big brain move. If you have Emry, Lurker of the Loch or Academy Ruins out you can use Goblin Engineer as just a straight artifact tutor. While Goblin Engineer can only swap artifacts with CMC 3 or less, he isn't restricted on CMC for the tutor effect. This means he can search for any artifact in your deck then you can use either Emry to cast it straight from graveyard or Academy Ruins to put it on top of your library. In a pinch Buried Ruin is an option, but the loss of a land +2 mana can really hurt. It effectively makes Goblin engineer's tutor effect cost 4R.
The deck has a good amount of recursion but it's pretty much limited to saving artifacts, which is important because of the need for equipment and krark's thumb. You've got Emry, Lurker of the Loch, Goblin Welder, Goblin Engineer, Academy Ruins, and Buried Ruin.
The deck runs a bunch of counter spells for protection though some of them are up for swapping. The main one that is on potential chopping block is the recently added Commandeer it's main advantage is that it deals with uncounterable stuff and also can be pretty easy to cast late game thanks to usually having a full hand. However mid game it's pretty weak.
For obvious reasons of recurring coin flips the recently released Tavern Scoundrel fits the deck very well. You often want to throw an artifact into the graveyard to use with Goblin Engineer for swapping and his ability to sacrifice a permanent is very useful there. It also lets you kill one of your commanders if somebody disables them. Lastly one of the bigger weaknesses of the deck is not being able to cast the cards you draw due to needing to keep mana open for counter spells. You can EASILY get 4+ treasures each combat phase if you have either commander out. That leaves you with mana for a counter spell & feeds Storm the Vaults.
There are a couple 'perfect hands' that can end the game on turn 1 or 2.
Gemstone Caverns, Mana Crypt, Mana Vault, Ancient Tomb, Swiftfoot Boots, Sol Ring and any other card.
That lets you cast Okaun and give him haste on turn 1. Win 3 coin flips and someone is dead from commander damage before their first land drop.
If you want a turn 2 full board win you can have this hand instead:
Gemstone Caverns, Mana Crypt, Sol Ring, Mountain, Chandra's Ignition and two random cards.
Zndrsplt, Eye of Wisdom you can do the same thing but unlike Okaun wins, which can be done with 5 cards + 2 randoms, this win requires keeping a very specific 7 card hand (which will never happen)
Ancient Tomb, Mana Crypt, Sol Ring, Izzet Signet, Frenetic Efreet, Laboratory Maniac, and any dual land that comes into play untapped.
Turn 1 you play the dual, mana crypt, sol ring, signet, and Efreet (in that order). Crypt pays for sol + floats 1, sol pays for signet, use floating 1 to make R/U from signet and tap dual to cast Efreet. Turn 2 play tomb and that gives you exactly the 6UU that is required to cast Zyndrsplt and Lab Man. Put infinite coin flips on the stack with Frenetic Efreet, draw your deck, start next game.
Tavern Scoundrel + Frenetic Efreet is an infinite mana combo that you can easily drop on turn 2 or 3. It also powers several cards such as allowing you to freely return artifacts with Goblin Engineer and Goblin Welder. You can also gamble with Chaos Warp on your own deck, but that's not really worth it. Transmute & Reshape lose all downsides.
Chance Encounter can also win you the game on turn 3 with this hand:
Chance Encounter, Frenetic Efreet, Mountain(or dual), Izzet Signet, Sol Ring, Mana Crypt, any other card.
You drop Efreet Turn 1 just like with the Zyndrsplt setup and then turn 2 chance encounter. Put a million coin flips on the stack and then next upkeep chance's win the game effect will trigger.
These are EXTREMELY unlikely scenarios but it's fun to imagine it happening.
While there is always luck to the deck with it being a coinflip based deck, other than Gemstone Caverns for flavor the deck tries to run as consistent as possible using lots and LOTS of tutors and counter spells. Like most competitive commander decks it also runs fairly low CMC at aprox 2.6 without the commanders.
Update--
Added: Imperial Recruiter, Inventors' Fair, Silverbluff Bridge, Yusri, Fortune's Flame, and Tavern Scoundrel
