Vivien’s Arkbow looks like a fun cube card that will act in a Birthing Pod like manner. It enables the trading up of resources similar to Pod. In Birthing Pod, a creature is traded for a better creature that can be tutored. Vivien’s Arkbow does not have the tutoring ability, costs more, and has the potential to miss. However, it does gain by being instant speed and, more importantly, allows the exchange of non-creature cards into creature cards. These two factors are huge. It is improbable that the Arkbow will be a better card, certainly not in constructed where decks of sixty cards can pack many one offs and tutoring is incredibly powerful. Cube is a different story. There are less cards to go through and games play out differently. This should indicate that the power of the Arkbow will hinge on how reliable it is at finding a creature every time. The table below shows how likely it is for a creature with a converted mana cost equal to or lower than X to be found versus how many creatures in the deck satisfy that condition.
Consider a reasonable curve for a pod deck. Usually 1-3 one drops, 3-5 two drops, 4-7 three drops, 3-5 four drops, and 1-3 five drops. So, pick 2-4-5-3-2. Then, the odds for the first six values of X are: 5.0%, 28.1%, 63.0%, 83.6%, 93.5%, and 96.5%. This means that already when X is six, the odds are over 95%. When X is four and five, the odds will be more than worth it considering that often it is a land that is being exchanged for a creature at instant speed. Going past six does not really affect the odds, but will allow more cards to be seen which does allow for better creature selection when multiple hits occur. A glaring fact that can be seen from the table is that hitting above 95% for X below five is going to be impossible as decks rarely have more than eighteen creatures in cubes. However, most pod style decks will have fourteen or more creatures, meaning, that for X at six, the percentage is already at 94% or better. That makes activations of six mana or more of the Arkbow reliably output great results. Alternatively, it also means that for x at four or less, the Arkbow will not give reliable results.
The table does not consider odds after the first successful activation though. Once a successful activation occurs, the creature density of the deck will decrease and make future activations less reliable. This is offset a bit by players having access to more mana in future turns and the chosen X values increasing as the density decreases. However, the Arkbow encourages players not to play their lands, so activations of more than seven will probably be rare and after three or four activations of six mana, the deck will already have been cycled through once and the creatures that will be found will not only be rarer but worse than before as the best have already been taken.
The last thing to consider between the differences from Pod to the Arkbow is that the latter does not ask for a creature to be on the battlefield. That is a glaring difference in the late game when Pod decks have run out of gas and are subject to whatever is at the top of the library or have to come back from a boardwipe. This also indicates that having Pod and the Arkbow in the same deck makes the case of drawing both in the same game good, while drawing two Pods in the same game is often quite bad unless the opponent removes one.
Overall, the lessons from the math is that Arkbow players should be happy activating it for x more than or equal to six, almost never activating for x less than or equal to three, knowing that five will result in misses a little too often, and that sometimes four will be necessary even if unreliable. Considering all else, cubes that are currently running three Pods should definitely remove one and give the Arkbow a try. Cubes that were running three Pods but changed one for Prime Speaker Vannifar, should probably change another for Arkbow and run one of each or add the Arkbow and run two-one-one. Cubes that run two Pods should probably just add the Arkbow alongside the Pods. Lastly, cubes that do not run Pod, might want to try the Arkbow a try and see if it is more to their tastes as it looks like a promising card.