Probability of winning in Blackjack
Introduction
Doublet Blackjack is a blackjack game created by Gamesys N.V., a provider of software for Internet casinos. It features a unique set of rules that I thought made it worthy of its own page.
Rules
- Six decks.
- No dealer hole card. If the player doubles or splits, and the dealer gets a blackjack, then the player loses his total amount bet.
- Dealer stands on soft 17.
- Player may double on any two cards, including after a split.
- Player may re-split to four hands, including aces.
- No surrender, except after doubling (see next rule).
- Double Down Rescue is allowed. This means that the player can surrender after doubling, except if the double causes the player to bust.
Strategy
The following table shows the basic strategy.
The double down rescue strategy is as follows:
- Surrender 16 or less against an 8, 9, 10, or ace.
- Surrender 17 against an ace.
Analysis
According to my analysis, the house edge in Doublet Blackjack is 0.38%.
Side Bets
There are two side bets, as follows.
The first is simply on a player blackjack and pays 19 to 1. The probability of winning is 4.75% and the house edge is 5.02%.
The second is titled "Sevens" and pays according to the number of consecutive sevens the player gets. The sevens must start with the first card. Splitting two sevens will pay as two sevens, regardless of the next card. The following table shows the the probability and return of each event. The lower right cell shows a house edge of 4.09%.
The table assumes the player will always hit two sevens and does not consider the cost of deviating from basic strategy in doing so against a dealer 2 to 7, when the player should split.
Sevens
| Event | Pays | Permutations | Probability | Return |
|---|---|---|---|---|
| Three sevens | 250 | 12, 144 | 0.000404 | 0.100931 |
| Two sevens | 40 | 158, 976 | 0.005285 | 0.211405 |
| One seven | 2, 142, 720 | 0.071234 | 0.569874 | |
| No sevens | -1 | 27, 766, 080 | 0.923077 | -0.923077 |
| Total | 30, 079, 920 | 1.000000 | -0.040867 |
Zero House Edge
There is also a so-called "Zero House Edge" version of the game. The only difference is that a winning blackjack in spades pays 2.5 instead of 1.5. The probability of this is 0.30%, which is also the reduction in house edge. So, I put the house edge of this version at 0.38% - 0.30% = 0.08%.
As with all Gamesys "Zero House Edge" games, the player must pay a 10% commission on any net gambling win per session. A "session" ends after not making a bet for an hour or 24 hours, whichever happens first.
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