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# A Side Bet

Best Answer bonanova, 27 January 2013 - 08:21 PM

Spoiler for Revised payoff schedule

Go to the full post

6 replies to this topic

### #1 Prime

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Posted 27 January 2013 - 07:54 AM

Mr. Gamble and Mr. Prude went to the Brain Den Casino, which offered the following game:

A customer bets on a number on a die (1 through 6). The dealer rolls a single die. If the customer’s number comes up, he is paid 4 times his bet, if not - customer loses his bet.

Without delay, Mr. G makes his mind to play 5 rounds betting \$1 on number “1” each time. Mr. P, believing the game is in favor of the house offers a side bet, whereby if after 5 rolls Mr. G ends up behind he must pay \$5 to Mr. P, otherwise Mr. P pays \$5 to Mr. G.

After 5 rounds, what is the average payoff to:

1) BrainDen Casino?

2) Mr. Gamble?

3) Mr. Prude?

Results may be rounded to the nearest cent. Calculators are allowed.

Answers obtained by way of computer simulations may not claim the “best answer” spot.

• 0

Past prime, actually.

### #2 bonanova

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Posted 27 January 2013 - 01:50 PM

Mr. Gamble and Mr. Prude went to the Brain Den Casino, which offered the following game:
A customer bets on a number on a die (1 through 6). The dealer rolls a single die. If the customers number comes up, he is paid 4 times his bet, if not - customer loses his bet.
Without delay, Mr. G makes his mind to play 5 rounds betting \$1 on number 1 each time. Mr. P, believing the game is in favor of the house offers a side bet, whereby if after 5 rolls Mr. G ends up behind he must pay \$5 to Mr. P, otherwise Mr. P pays \$5 to Mr. G.

After 5 rounds, what is the average payoff to:
1) BrainDen Casino?
2) Mr. Gamble?
3) Mr. Prude?

Results may be rounded to the nearest cent. Calculators are allowed.
Answers obtained by way of computer simulations may not claim the best answer spot.

Spoiler for For starters

• 0

Vidi vici veni.

### #3 bonanova

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Posted 27 January 2013 - 03:11 PM

Spoiler for To finish it off...

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Vidi vici veni.

### #4 Prime

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Posted 27 January 2013 - 07:24 PM

A note of clarification:

BrainDen Casino table games are set in a typical way. When a guest wins, he keeps his bet too. E.g., in this single die roll game, if you bet \$1 and your number is rolled, you get \$4 and keep your \$1 bet.

• 0

Past prime, actually.

### #5 bonanova

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Posted 27 January 2013 - 08:21 PM   Best Answer

Spoiler for Revised payoff schedule

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Vidi vici veni.

### #6 Prime

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Posted 27 January 2013 - 08:46 PM

Spoiler for Revised payoff schedule

That is a good solve! Exact and exhaustive proof.

Complexity could be reduced just a bit, though.

Spoiler for simplified perspective

• 0

Past prime, actually.

### #7 witzar

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Posted 29 January 2013 - 04:27 AM

Spoiler for simple solution

Edited by witzar, 29 January 2013 - 04:28 AM.

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