Below is a spoiler for the MontyHallVariant
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The numbers are 1/5 ( two times 1/10 ) versus 2/5 from (1-1/5)/2.
Your chances of winning double if you switch.
You have a 2 in 10 chance of picking the right card at the start, so you have a 20% chance to win if you don't take the option to switch cards. Since you have a 20% chance at the start, the host has an 80% chance of having the winning card at the start. If you take the option to switch to one of the host's cards, you then have a 50% chance of picking the correct one, if he has it.
- Odds if you don't switch = 20% chance of winning.
- Odds if you do switch (both 80% and 50%) = 40% chance of winning. -- JasonWilson
Several other correct responses were received.