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If Putin values his life more than victory, then he will, at each time, follow the path which minimizes the probability of his death as outcome, as estimated by him.
For the time being he can follow any of 3 possible paths: Withdrawal_before_Ukr, Conv_War_on_Ukr, and Tac_nukes_on_Ukr (kaboom).
The Conv_War_on_Ukr path has 2 possible outcomes: Victory or Defeat_by_Ukr.
The Tac_nukes_on_Ukr path has 2 possible outcomes: Victory or Conv_NATO_strike. After Conv_NATO_strike, Putin can follow any of 3 possible subpaths:
- Withdrawal_before_NATO,
- Conv_war_on_NATO (plus ongoing Tac_nukes_on_Ukr), with 2 possible outcomes: Victory (close to 0) or Defeat_by_NATO_Conv (close to 1),
- Tac_nukes_on_NATO (plus ongoing Tac_nukes_on_Ukr), with 2 possible outcomes: Victory (if NATO folds) or Strat_NATO_strike (KABOOM).
The Withdrawal and Defeat paths/outcomes have Putin's death as a possible outcome. KABOOM implies everyone's death with certainty.
The probabilities of Putin dying in each path are:
- Withdrawal_before_Ukr: P(I_die/Withdrawal_before_Ukr)
- Conv_War_on_Ukr: P(Defeat_by_Ukr/Conv_War_on_Ukr) x P(I_die/Defeat_by_Ukr)
- Tac_nukes_on_Ukr: P(Conv_NATO_strike/Tac_Nukes_on_Ukr) x
min({P(I_die/Withdrawal_before_NATO),
P(Defeat_by_NATO_Conv/Conv_War_on_NATO) x P(I_die/Defeat_by_NATO_Conv),
P(Strat_NATO_Strike/Tac_Nukes_on NATO)})
If Putin values victory more than his life, then he will, at each time, follow the path which minimizes the probability of Russian defeat as outcome, as estimated by him. In this case the Withdrawal paths vanish and the probabilities of Russian defeat in each path are:
- Conv_War_on_Ukr: P(Defeat_by_Ukr/Conv_War_on_Ukr)
- Tac_nukes_on_Ukr: P(Conv_NATO_strike/Tac_Nukes_on_Ukr) x
min({P(Defeat_by_NATO_Conv/Conv_War_on_NATO),
P(Strat_NATO_Strike/Tac_Nukes_on NATO)})
The above assumes that Putin perceives the KABOOM outcome as defeat. But if he perceives it as victory, then the Tac_nukes_on_NATO subpath leads always to victory, so that, as soon as Putin perceives that a Russian defeat by Ukraine in a conventional war has become likely, it is certain that he will follow the Tac_nukes_on_Ukr path, and that if NATO strikes Russian targets in response, he will then follow the Tac_nukes_on_NATO subpath.