Ask the Wizard #109
- 5- place $5
- 6- place $6
- 8- place $6
- field- $5
- total= $22
They claim the house edge is 1.136%. How is that possible if every individual bet made has a higher house edge?
Good question. To confirm their math I made the following table, based on a field bet paying 3 to 1 on a 12. The lower right cell does shows an expected loss of 25 cents over $22 bet. So the house edge is indeed .25/22 = 1.136%.
Mensa Anything but Seven Combo
|Number||Probability||Field||Place 5||Place 6||Place 8||Win||Return|
The reason the overall house edge appears to be less than the house edge of each individual bet is because the house edge on place bets is generally measured as expected player loss per bet resolved.
However, in this case the player is only keeping the place bets up for one roll. This significantly reduces the house edge on the place bets from 4.00% to 1.11% on the 5 and 9, and from 1.52% to 0.46% on the 6 and 8.
For you purists who think I am inconsistent in measuring the house edge on place bets as per bet resolved (or ignoring ties) then I invite you to visit my craps appendix 2 where all craps bets are measured per roll (including ties).
What I meant was that images of cards on the screen had to be statistically fair. For example if you took a tally of each card observed in the initial hand of video poker or video blackjack you would see the distribution approaching a flat line over time, much as you would in a hand dealt game. However there is no law that the standard rules of blackjack must be followed. The machine can legally offer horrible rules like the player losing on ties. The only caveat is that the theoretical return must be at least 75%.
Yes, I interpreted the question that the place could after the second card was dealt to the split aces. If the player could double on each ace alone then that would reduce the house edge by 0.21% (based on infinite decks). With an ace alone the player should opt to double against any dealer up card.
What I meant was half of one person, or one person for every two casinos. However you were not the only person I confused so I reworded my original answer to say half on one person, not half of everyone playing.
Thanks. I just asked a dealer and he confirmed that the house would win that hand because the joker would be used as a king. The general rule is the joker can substitute for any specific card not already in the same hand as long as it completes a straight, flush, or straight flush. Otherwise it is treated as a fifth-suit ace, thus allowing for the possibility of five aces.
The probability all numbers will be different is (5/6)*(4/6)=20/36. So the probability at least two numbers will be the same is 1-(20/36) = 16/36 = 44.44%.
Baccarat (at the big tables) is the only casino game in which players are allowed to damage the cards. An explanation I heard is that Asian players bend the cards anyway as they slowly peak at them that they only use each card once. Therefore as long as the dealer is replacing the cards after one usage the casino may as well let the players do anything with them. Being able to identify cards is of little value to baccarat players anyway because the dealer doesn't take a hole card (as the dealer does in blackjack) and the player has no choice as to whether to hit or stand. However, there are also gaming regulations that stipulate that the tapes must show all the cards in case of a dispute, which isn’t possible if the player tears them up first. In the show you mention the player didn’t know this and I think both parties handled it badly, which led to the hard feelings that the show captured. Had I been the casino manager I would have explained what I just said and then asked the player to lay the card face-up on the table before ripping it into tiny pieces.
On a related note yours truly will be on The Casino sometime this season. The story is some college students try to parlay $1000 into $5000 as quickly as possible. They seek my advice on how to do achieve this goal.
Update: That episode never aired. Probably because of me.
Thanks for the compliment. This theory is called card clumping and would make for good fertilizer if it could be bagged. No legitimate blackjack writer puts any stock in it at all.