Gambling Guide
Ask the Wizard #300
On Monday night, a servant steals three cups from the barrel and replaces them with three cups of water.
On Tuesday night another servant steals three cups from the now diluted barrel of wine and replaces them three cups of water.
On Wednesday night yet another servant steals three cups from the now-more diluted barrel of wine and replaces them three cups of water.
On Thursday morning the barrel is 50% wine and 50% water.
How much wine was initially in the barrel?
"Anonymous" .
Here is the answer and solution (PDF).
For discussion about this problem, please visit my forum at Wizard of Vegas.
matiX
Here is the answer and solution (PDF).
For discussion about this problem, please visit my forum at Wizard of Vegas.
Blony1789
This bug is equivalent to getting an extra unit every time the dealer has a blackjack with an ace up. That will happen 2.37% of the time. The house edge would be 0.72% without this bug. With it, the player advantage is 2.37% - 0.72% = 1.66%.
For further discussion on this question, please see my forum at Wizard of Vegas.
"Anonymous" .
I'm never offended by a healthy degree of skepticism. To satisfy those skeptics, I created this follow-up video. Enjoy.
"Anonymous" .
Before I answer, I'd like to remind everybody that the number of ways to choose k out of n items, with replacement, is combin(n+k-1,k) = (n+k-1)!/((n-1)!×k!).
That said, here are the following types of seven-card hands and the number of distinct ways to make each:
- 7 cards of one suit: combin(13,7)=1,176.
- 6 cards of one suit and 1 of another: COMBIN(13,6)×13 = 22,308.
- 5 cards of one suit and 2 of another: COMBIN(13,5)×combin(13,2) = 100,386.
- 5 cards of one suit and 1 each of another two: COMBIN(13,5)×combin(13+2-1,2) = 117,117.
- 4 cards of one suit and 3 of another: COMBIN(13,4)×combin(13,3) = 204,490.
- 4 cards of one suit, 2 of a second, and 1 of third: COMBIN(13,4)×combin(13,2)×13 = 725,010.
- 4 cards of one suit and one each of another 3: COMBIN(13,4)×combin(13+3-1,3)×13 = 325,325.
- 3 cards of two different suits and one card of a third suit: 13×((COMBIN(13,3)×(COMBIN(13,3)-1)/2+COMBIN(13,3))) = 533,533.
- 3 cards of one suit and two cards each of two other suits: COMBIN(13,3)×(COMBIN(13,2)×(COMBIN(13,2)+1)/2) = 881,166.
- 3 cards of one suit, 2 cards of a second, and one card each of the two other suits: COMBIN(13,3)×COMBIN(13,2)×COMBIN(13+2-1,2) = 2,030,028.
- 2 cards each of three suits and 1 from the fourth: ((COMBIN(13,2)×(COMBIN(13,2)+1)×(COMBIN(13,2)+2)/6) = 1,068,080.
The sum of those combinations is 6,009,159. Compared to the combin(52,7)= 133,784,560 ways to pick 7 cards out of 52, that is a 95.5% reduction in hands analyzed.
For more discussion on this question, please see my forum at Wizard of Vegas.
Donald Trump Jr. from New York, NY
For more discussion on this question, please visit my forum at Wizard of Vegas.
