Ask the Wizard #112
- 6 decks.
- Dealer hits soft 17.
- All ties push, except player wins tied blackjack.
- Player can double on hard 9 to 11 only.
- Player can re-split, including unlike tens, to four hands.
- Double after split allowed.
- Draw to split aces allowed.
This must have a player advantage, can you tell me what it is?
As I'm sure you know this game is offered by Lucky Chance casino. Using the appropriate basic strategy for these rules the player advantage is 7.2%! Wait it gets even better. You can bet three hands at once of $5 or more each and if you get a blackjack on all three you win a progressive jackpot that is currently at $18095. The probability of getting three blackjacks in three hands is 1 in 10552. So the progressive is worth an extra $1.71 per hand. On two days while I played they also offered 15% rebate on losses, calculated whenever you exited the game. So I simply exited after every hand, except on a push.
However I'm suspicious if the player advantage is too high. I checked Winner Online and found they allegedly used to offer a video poker game with a 120% return, although they use a normal pay table now. That is two red flags. Lucky Chance offers a 100% immediately bonus up to purchases of $500, so I put them to the test. It was my goal to either make a fortune on their Double Exposure game or prove the game was not fair. Following are my results:
- 313 of single hands: net win of 32 units.
- 1959 hands of 3 spots at once: net loss of 29 units.
- 2272 total hands: net win of 3 units.
Given a 7.2% advantage my expected win was 163.6 units. The probability of only winning 3 or less is 12.4%. This is using a standard deviation of 1.17 for a single hand and 2.68 per hand for playing three at time. My source of the 1.17 is a random simulation using Stanford Wong's Blackjack Count Analyzer and I multiplied that by 2.28 for 3 hands, based on the standard deviations for regular blackjack for 1 and 3 hands as found in my blackjack appendix 4.
This certainly does not rise anywhere near enough to make any accusations. In addition I recorded results all sorts of ways but every test came out looking normal. I would have played longer but the game play is extremely slow and I went broke. The reason I went broke is I did worse on larger bet sizes and my first few hours I didn't record results but they were not good.
So I failed on both my goals. I was too skeptical to deposit again and already wasted several hours on the game. However, if you wish to take a crack at it then be my guest.
I have some questions on tipping etiquette...
Blackjack: Can I double, split or take insurance for the dealer?
Caribbean Stud Poker: Can I (or do I have to) raise also for the dealer?
Let It Ride Poker: Can I place more than one bet for the dealer (what happens if I decide to take back one of my bets and there was a tip)?
Craps: Can I play a tip everywhere I can play (odds and props included)?
Roulette: Can I play on numbers for him?
As a general rule, you can make any bet for the dealer in any game. In general you should tell the dealer which bets are his, except blackjack where its common practice that any bet outside the betting circle is for the dealer.
Blackjack: Yes to all three. The usual way to bet for the dealer in blackjack is to put the tip on the edge of the betting circle. If you split or double most people also split or double the dealer’s bet, although it is not required.
Caribbean Stud Poker: I asked a dealer and he said raising for the dealer is optional. I haven't studied it but I think this would result in the tip having an advantage.
Let it Ride: I'm told that the player should put out three tips initially but must pull them back in the same manner that they pull back their own bets. Bets that are pulled back go to the player, not the dealer.
Craps: Yes, you can make any bet for the dealer. The most common ones are the yo-11 and the hard ways. If you make a line bet for the dealers and back it up with the odds it is implied the odds are a tip too.
Roulette: As in craps you can make any bet for the dealer. Just tell them in advance.
Risk of ruin questions are mathematically complicated. Unless it is a simple win/lose game I would recommend doing a random simulation on a computer.
Betting on the horses is one of my weakest areas when it comes to gambling. I have heard that "bridge jumper" bets (a bet on a huge favorite to show) can sometimes be a good bet due to the guaranteed $2.20 minimum return on a $2 bet. However I know of no way to have a consistent edge or any person who is successful as a professional racetrack bettor. Yet I don’t deny the track can be beat. In the book Gambling Wizards author Richard Munchkin tells the story about one professional gambler’s success at the racetracks in Hong Kong, where the track cut is less than in the United States.
Any legitimate game maker has the double up feature as a truly fair bet with a 100% return. So you have a 50/50 chance of winning any given bet (not counting ties) regardless of the amount bet or the results of past bets.
I think this would put a small dent in the house edge, assuming you know how to make the correct strategy adjustments, but will not come anywhere close to overcoming it.
There are some casinos that treat A2345 (known as "the wheel") as the lowest straight but most still treat it as the second highest straight. I will make a note that this rule is a generality and not always the case.