😥 🅰🅱🅰🅱🅰🅱
1/6 ⚫⚫⚪⚪⚪⚪
1/6 ⚪⚫⚫⚪⚪⚪
1/6 ⚪⚪⚫⚫⚪⚪
1/6 ⚪⚪⚪⚫⚫⚪
1/6 ⚪⚪⚪⚪⚫⚫
1/6 ⚫⚪⚪⚪⚪⚫
🅰🔫
◻️ 💥➡️🅰⚰️
◻️ ❌➡️🔄
🅰🔫🅱
◻️ 💥➡️🅰⚰️
◻️ ❌➡️🅰🔪🅱➡️🅱⚰️
❌❌❌❌❔ (🅰)
1/1 ⚪⚪⚪⚪⚫⚫
🅰🔫
◻️ 1/1 💥➡️🅰⚰️
🅱🔫🅰
◻️ 1/1 💥➡️🅱⚰️
✔️🅱🔫🅰➡️💯🅱⚰️
❌❌❌❔ (🅱)
1/2 ⚪⚪⚪⚫⚫⚪
1/2 ⚪⚪⚪⚪⚫⚫
🅱🔫
◻️ 1/2 💥➡️🅱⚰️
◻️ 1/2 ❌➡️💯🅱⚰️
🅰🔫🅱
◻️ 1/2 💥➡️🅰⚰️
◻️ 1/2 ❌➡️🅰🔪🅱➡️🅱⚰️
✔️🅰🔫🅱➡️1/2🅰⚰️➕1/2🅱⚰️
❌❌❔ (🅰)
1/3 ⚪⚪⚫⚫⚪⚪
1/3 ⚪⚪⚪⚫⚫⚪
1/3 ⚪⚪⚪⚪⚫⚫
🅰🔫
◻️ 1/3 💥➡️🅰⚰️
◻️ 2/3 ❌➡️1/2🅰⚰️➕1/2🅱⚰️
🅱🔫🅰
◻️ 1/3 💥➡️🅱⚰️
◻️ 2/3 ❌➡️🅱🔪🅰➡️🅰⚰️
✔️🅰🔫/🅱🔫🅰➡️2/3🅰⚰️➕1/3🅱⚰️
❌❔ (🅱)
1/4 ⚪⚫⚫⚪⚪⚪
1/4 ⚪⚪⚫⚫⚪⚪
1/4 ⚪⚪⚪⚫⚫⚪
1/4 ⚪⚪⚪⚪⚫⚫
🅱🔫
◻️ 1/4 💥➡️🅱⚰️
◻️ 3/4 ❌➡️2/3🅰⚰️➕1/3🅱⚰️
🅰🔫🅱
◻️ 1/4 💥➡️🅰⚰️
◻️ 3/4 ❌➡️🅰🔪🅱➡️🅱⚰️
✔️🅱🔫➡️1/2🅰⚰️➕1/2🅱⚰️
❔ (🅰)
1/6 ⚫⚫⚪⚪⚪⚪
1/6 ⚪⚫⚫⚪⚪⚪
1/6 ⚪⚪⚫⚫⚪⚪
1/6 ⚪⚪⚪⚫⚫⚪
1/6 ⚪⚪⚪⚪⚫⚫
1/6 ⚫⚪⚪⚪⚪⚫
🅰🔫
◻️ 1/3 💥➡️🅰⚰️
◻️ 2/3 ❌➡️1/2🅰⚰️➕1/2🅱⚰️
🅱🔫🅰
◻️ 1/3 💥➡️🅱⚰️
◻️ 2/3 ❌➡️🅱🔪🅰➡️🅰⚰️
✔️🅰🔫/🅱🔫🅰➡️2/3🅰⚰️➕1/3🅱⚰️
❌2/3🅰⚰️
✔️1/3🅱⚰️
I'll call the player who goes first A and the one who goes second B.
On the fifth turn it's A's move. If the game reaches this point, A
knows that a round is chambered, so he will always opt to shoot B.
On the fourth turn it's B's move. At this point the odds that a round
is chambered is 1:1 even. B knows if he fires at himself he will
either die now or in the next round, so he opts to fire at A, where
his odds of survival are 1:1 even.
On the third turn it's A's move. At this point the odds that a round
is chambered is 2:1 against. It makes no difference what A does: if
he fires at himself he dies now with probability 1/3, or dies in the
next round with probability 1/2, leading to an odds of survival of 2:1
against. If he fires at B his odds are the same, 2:1 against.
On the second turn it's B's move. At this point the odds that a round
is chambered is 3:1 against. If B fires at himself he dies now with
probability 1/4, or dies in a subsequent round with probability 1/3,
leading to an odds of survival of 1:1 even. If he fires at A his odds
are 3:1 against, so he chooses to fire at himself.
On the first turn it's A's move. At this point the odds that a round
is chambered is 2:1 against. It makes no difference what A does: if
he fires at himself he dies now with probability 1/3, or dies in a
subsequent round with probability 1/2, leading to an odds of survival
of 2:1 against. If he fires at B his odds are the same, 2:1 against.
Thus B has the higher chance of survival, with odds of 2:1 on.