John Tromp

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John Tromp [1]

Johannes (John) Theodorus Tromp,
a Dutch mathematician and computer scientist with a Ph.D. in 1993 on algorithms and complexity from University of Amsterdam under advisor Paul Vitányi. His research interests include artificial intelligence and board games such as Connect Four, Chess and Go, complexity, algorithmic information theory, distributed computing, and computational biology. His recreational interests include playing Go and chess. Along with Álvaro Begué, John Tromp is co-author of the Go playing program Dimwit [2].

Number of Positions

John Tromp has researched on counting the number of legal positions in Go and reachable chess positions, and gives an upper bound of 7728772977965919677164873487685453137329736522 (about 10^45.888 or ~ 2^152.437) on the number of chess positions, but states, like the bound of ~10^46.25 published by Shirish Chinchalkar [3], that it requires better documentation to be considered verifiable [4]. On January 20, 2016, the number of legal positions on a standard size Go board was determined to be [5]:

```L19 = 208168199381979984699478633344862770286522453884530548425639456820927419612738015378525648451698519643907259916015628128546089888314427129715319317557736620397247064840935
```

or more compact

```2081681993819799846
9947863334486277028
6522453884530548425
6394568209274196127
3801537852564845169
8519643907259916015
6281285460898883144
2712971531931755773
6620397247064840935
```

The approximation

```L19 ~ 2.081681994 * 10^170
```

has been known since 2006. So what took 10 years to nail it down to the last digit? [6]