Hit or Miss (Roll Call)

The rules of this game can be found here.

Hit or Miss is not a game you will win very often: the odds are just 1-in-531! You have about one chance in four of finishing with ten cards or fewer.

The most common result is to end up with 13 cards, which happens about one game in six. The distribution of how many cards are left at the end of the game, is pretty wild (as shown below):

As you can see, there are spikes of losses that occur whenever the length of the deck is an even multiple of 13 cards. Note that in these cases, if you fail to get a "hit" during the first pass, you are guaranteed not to get one during the second pass either (the same ranks will be called out for each card).


The worst case scenario of Hit or Miss, when you fail to get a single hit and finish with all 52 cards, happens about one game out of 62. This situation is actually the same as a win in the game Frustration (which is played similarly as Hit or Miss, but with the aim of not getting any hits).

Super Hit or Miss

I also tested the variation known as "Super Hit or Miss", in which you get unlimited redeals regardless of hits. Of course, this results in a much higher win rate (over 60%). You don't win every game, because you can still get blocked whenever you have an even multiple of 13 cards left with no hits.

Ultimate Hit or Miss

I tested "Ultimate Hit or Miss" as well (same as Super Hit or Miss, but with a second deck of cards shuffled together). While the second deck of cards may make the game take longer to play, it does little to make the game harder to win (the win rate drops by just 1.2%).

Hit or Miss and variants,
one billion deals each
Rate %
Hit or Miss1,884,2790.188
Super Hit or Miss606,362,55360.6
Ultimate Hit or Miss594,439,78059.4

Any comments are welcome, please send to Mark Masten at:

Last modified February 2, 2022

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