During the 12th World Chess Championship, Magnus Carlsen, the current World Chess Champion, offered draw to his competitor Caruana. This offer has been widely criticised, also by many former World Champions, because Carlsen's position was better.
However, according to Peter Wakker, Professor of decisions under uncertainty at Erasmus School of Economics, the offer of Carlsen was completely rational. He explains this with the help of behavioural economics and risk-theory.
'This wide criticism can be attributed to the fact that people do not understand risk-theory',
says professor Wakker. AlphaZero - a computer programme developed to master the games of chess, shogi and go - showed that the winning odds of playing on would be 3:1 for Carlsen. However, taking the ELO rating (rating of the player's agility) in rapid games of Carlsen and Caruana into account, the winning probability of Carlsen in one rapid game would have been the same as his winning probability if he would have played on in the 12th game.
Nevertheless, the tiebreak against Caruana involved 4 rapid games, instead of one, which, as a result, gives the stronger player a bigger chance of winning overall. Calculations show that the chances of an even score were 27 percent. If the game resulted in such a tie, a blitz game would have followed. Again, taking the ELO ratings into account, the remaining odds would have been more favourable to Carlsen: his overall probability of winning the tiebreak exceeded 80%.
However, the match was a zero sum game, which means that what is good for the one player can only be bad for the other player. As such, the fact that Carlsen offered draw should have alarmed Caruana as to declined the offer.
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You can find the entire article in New in Chess, May 2019, attached.