Appendices
1: Total dependent expected return table for an infinite deck
2a: Probabilities of dealer blackjack after peek
2b: Probabilities of dealer blackjack before peek
3a: Exceptions to single-deck S17 basic strategy
3b: Exceptions to double-deck S17 basic strategy
3c: Exceptions to single-deck H17 basic strategy
4: Blackjack standard deviation details
5: Infinite deck expected return by player hand and dealer upcard
6: Fine points of when to surrender
7: Effect of card removal
8: Analysis of blackjack side bets
9: Composition-dependent expected returns for 1 to 8 decks
10: Continuous shuffling machine vs. cut card
11: Value and strategy for 678 and 777 bonuses
12: Risk of ruin statistics
13: Probabilities in the first four cards
14: Value of each initial player card
15: House edge using total-dependent vs. composition-dependent basic strategy
16: Basic strategy when dealer exposes both cards
17: The Ace-Five card counting method
18: Basic strategy exceptions for three to six cards
19: Blackjack splitting strategy when a back-player is betting
20: Blackjack doubling strategy when doubling after splitting aces is allowed
21: Details on the Wizard\’s Simple Strategy
Miscellaneous
My comments on the movie "21"
Australian Blackjack
Introduction to Card Counting
Rule Variations
Blackjack "Charlie" Rule
Rummy (Blackjack variant popular in Costa Rica)
External Links
Macau Blackjack rules
Simple Blackjack Explanation
Bet the Set Progressive
Introduction
I noticed this variation of Bet the Set on April 19, 2013 at the Red Rock casino in Las Vegas. It was dealt from a six-deck game. The bet wins if the player has a pair for his initial two cards, more if they are suited. Unlike the normal Bet the Set, if the player has a pair he has a chance for big wins if the dealer also has a pair of the same rank.
If the player gets a colored four of a kind not only is he paid 250 to 1, but also wins a progressive jackpot. In addition, there are envy bonuses if another player gets a colored four of a kind. The minimum bet to qualify for the jackpot and envy bonuses is $1.
Rules
The following analysis is based on six decks. I suppose any number could be used.
If the four cards, consisting of the player's and dealer's initial two cards, consist of a colored four of a kind, then the player's wager shall win 250 to 1, plus the amount in the progressive jackpot.
Otherwise, if the four cards, consisting of the player's and dealer's initial two cards, consist of a four of a kind of both red and black, then the player's wager shall pay 100 to 1.
Otherwise, if the player's two cards form a suited pair, then the player's wager shall pay 20 to 1.
Otherwise, if the player's two cards form a non-suited pair, then the player's wager shall pay 5 to 1.
Otherwise, the player must have two cards of different ranks, which loses.
If any player gets a colored four of a kind then every other player at the table who made the Bet the Set wager shall win an envy bonus of $50.
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Rack card. Click on either image for a larger version.
Analysis
The following table shows the odds for a six-deck game, before considering the jackpot and envy bonuses. The lower right cell shows a house edge of 27.74%.
Bet the Set — Progressive — Six Decks
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Colored four of a kind | 250 | 77,220 | 0.000033 | 0.008308 |
| Four of a kind | 100 | 751,608 | 0.000323 | 0.032346 |
| Suited pair | 20 | 37,177,920 | 0.016000 | 0.319993 |
| Pair | 5 | 133,840,512 | 0.057599 | 0.287993 |
| Loser | -1 | 2,151,826,560 | 0.926045 | -0.926045 |
| Total | 2,323,673,820 | 1.000000 | -0.277405 |
The following table shows the expected value per each $1,000 in the meter and each additional player by the bet amount. Remember that the progressive and envy bonuses are flat awards, thus the benefit is inversely proportional to bet size.
Value per $1000 in Meter and Additional Players
| Wager | Value per $1000 in Meter |
Value per Additional Player |
|---|---|---|
| $1 | 3.323% | 0.166% |
| $5 | 0.665% | 0.033% |
| $10 | 0.332% | 0.017% |
| $25 | 0.133% | 0.007% |
The following table shows the expected value per each $1,000 in the meter and each additional player by the bet amount. Remember that the progressive and envy bonuses are flat awards, thus the benefit is inversely proportional to bet size.
Value per $1000 in Meter and Additional Players
| Wager | Breakeven Point |
|---|---|
| $1 | $8,347.58 |
| $5 | $41,737.88 |
| $10 | $83,475.76 |
| $25 | $208,689.39 |
When I saw this bet on April 20, 2013 the meter was at $7,817.44.