Hell of a problem to have, really.
The left-hander demonstrated his class with a wonderful undefeated knock of 99 against Australia in the opening T20 in Christchurch on Monday evening.
It was the third time in as many innings the finishing post had pipped an impending milestone.
Last week he guided Wellington to a five-wicket win against Canterbury in the Super Smash final. He stroked 93 not out from 63 deliveries in a masterful display.
Earlier this month he slapped 91 not out from 58 balls in another match-winning effort in the Super Smash.
And while we are counting, late last month he scored 69 not out in a T20 against Central Districts.
The 29-year-old has scored 352 runs without being dismissed.
Canterbury’s Matt Henry was the last player to pick up his wicket and Conway hit 50 in that game.
What makes his astonishing run so remarkable is that it is just not that remarkable — for Conway, that is.
He is a regular fixture at the top the domestic run-scoring lists.
Last summer he was the leading scorer in Plunket Shield, Ford Trophy and the Super Smash.
His record for Wellington since joining the province in 2017-18 is staggering.
He has scored 2008 runs at 69.24 in first-class cricket, 1227 at 47.18 in list A games and 1526 at 56.51 in T20s.
Conway has been utterly dominant at domestic level, so it certainly has not been a surprise to see him succeed at international level.
In seven T20 games for the Black Caps he has scored 273 runs at an average of 91 and a strike rate of 156.89.
Wellington and Black Caps team-mate Jimmy Neesham has no doubt Conway would be an asset in the test or one-day line-up as well. But he is not surprised Conway has not had a run yet.
‘‘I think it is the case at the moment, which is a bit of a rarity in New Zealand cricket, where we have a number of high-quality batsmen vying for those spots.
‘‘I’m sure whatever teams he is picked for and whatever team he makes the XI for, he will be scoring runs.
‘‘But while he is not playing for those teams for New Zealand, we are more than happy to have him at Wellington churning the runs out.’’
‘‘He is a unique kind of batsman,’’ Neesham said.
‘‘Sometimes he sort of looks like he is not that comfortable at the crease and looks like he is not timing the ball that well. But then you look at the scorecard and he is 50 off 40 and putting in a real good performance for the team.
‘‘I think the best thing about him . . . is he does not give it away that often. He really grinds through those tough patches and, as we saw [Monday night], it probably took him 30 or 40 balls before he started timing the ball really nicely.
‘‘But after that he really opened the game up for us.’’
Conway whacked 27 off his last nine legal deliveries, so he does have a power game. But he is more of a finesse player who likes to gap the ball and generate a decent run rate through rotating the strike.
Leaving him out of the next test line-up would be like reaching for a Krispie when there are Toffee Pops on offer.
They are both good but one is much, much better.
