Accepted for publication in the International Journal of Combinatorial Number Theory.

**ISSN/ISBN:** Not available at this time.
**DOI:** Not available at this time.

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**Abstract:** We study the following two-player game involving
players A and B. Let n be a positive integer known to both
players. The player A (B) chooses an n-digit integer a (b). They
do this without the knowledge of the other player’s choice. Then
the numbers are revealed and the product ab is computed. If the
leading digit (i.e., the first digit from the left) of ab is 1, 2 or 3,
then player A wins, else player B wins. Since six digits favor B
and only three favor A, a naive reasoning would suggest a 2 to 1
advantage for player B. The reality is nearly the opposite. More
precisely, let p_{n} be the probability that A wins when both players
play optimally. We show the somewhat surprising result that
lim_{n→∞} p_{n} = log_{10}4≈0.6020599913. We also determine the odds
in favor of the players when they use some non-optimal strategies.
Our analysis of optimal play involves the scale invariance
of the well-known Benford distribution.

**Bibtex:**

```
@misc{,
title={A simple multiplication game and its analysis},
author={Ravikumar, Bala},
journal={Int J Comb Numb Theory},
year={2009}
}
```

**Reference Type:** Journal Article

**Subject Area(s):** Applied Mathematics