Riddles, brain puzzles and mathematical problems

**BAndrew** · 12-09-2012, 06:30 PM

Correct! OK, your turn.

**Bridge** · 12-09-2012, 07:05 PM

Checkmate in 2

**BAndrew** · 12-09-2012, 07:14 PM

(12-09-2012, 07:05 PM)Bridge Wrote:

Checkmate in 2

Have I the black or the white?

**Bridge** · 12-09-2012, 07:20 PM

(12-09-2012, 07:14 PM)BAndrew Wrote:
(12-09-2012, 07:05 PM)Bridge Wrote:

Checkmate in 2
Have I the black or the white?

White to move. Generally in chess puzzles the board is flipped according to the pieces you control.

**Froge** · 12-09-2012, 08:55 PM

Qf7
Nxf7
Ne6

**Bridge** · 12-09-2012, 09:02 PM

Yeah.

**Froge** · 12-09-2012, 09:38 PM

Coins

Last week, Kman and failedALIAS played a gambling game. In the first part of this game, ALIAS tosses three coins and Kman tosses two. If ALIAS obtains more heads than Kman, then he receives $6. If Kman obtains more heads, then ALIAS has to pay $10. But if both obtain the same number of heads, then ALIAS has to pay $2. They play this for four rounds.

Just before the second part of the game starts, ALIAS finds out that Kman cheated and used biased coins, each of which had a 60% chance of obtaining heads. As retribution, Kman is forced to pay ALIAS $5.

In the second part of the game, ALIAS again tosses three coins and Kman tosses two (these are fair now). Whoever has more heads wins the game and gets an extra $11. But if both obtain the same number of heads, they continue playing until someone obtains more heads in one round. How much is ALIAS' expected winnings, theoretically, at the end of the whole game?

**Bridge** · 12-09-2012, 10:03 PM

In the second part only one game is played?

Edit: nvm

**BAndrew** · 12-09-2012, 10:09 PM

hmmm 1?

I don't expect that to be correct, but anyway that was my first thought.

**Bridge** · 12-09-2012, 10:10 PM

According to my calculations his expected "winnings" are -2.4725 dollars.

EDIT: These are my notes if anybody is curious:

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