7-14-21

Introduction

I first encountered the table game 7-14-21 during the summer of 2011 at the Palms. It had previously been offered at the Grand Biloxi towards the end of 2010.

It's quite challenging to draw a direct comparison between 7-14-21 and other games. If I had to, I would say it's reminiscent of a mixture between pai gow poker and blackjack. The game's strategy is straightforward, it moves at a leisurely pace, and the risks involved are minimal. When played with optimal strategy, the house edge stands at a mere 0.54%, which is quite low for a relatively new game. For those seeking a simple game where their funds last a while, 7-14-21 is tough to top.

Rules

1. A single 52-card deck is used.
2. All cards scored as in blackjack.
3. The player places three equal bets along with an optional Bonus Bet.
4. Player and dealer each get six cards.
5. The player arranges their cards into three hands, each composed of two cards, labeled as 7, 14, and 21.
6. The aim of each hand is to achieve a score that is as close to the specified point total as possible without exceeding it.
7. Once players finalize their hands, the dealer will configure his hand following the house rules.
8. The player's 21 hand is evaluated against the dealer's 21 hand, with the closer one to 21 declared the winner.
9. Next, the player's 14 hand is compared with the dealer's hand. The winner is the one who has 14 points, provided neither goes over. If both exceed, the dealer wins.
10. For the player's 7 hand, it's again a comparison with the dealer's 7 hand, where the closest to 7 wins without exceeding it. If both exceed, the dealer takes the win.
11. The scoring for the 14 and 7 hands follows the same rules as the 21 hand.
12. Wins pay even money, and ties push.
13. In a situation where the player achieves a 'perfect hand,' consisting of exactly 7, 14, and 21 points, they automatically receive a payout of 4 to 1 on all three bets, regardless of what the dealer has.

House Way

The dealer first constructs the optimal hand for 21, and then builds the best possible hand for 14. If multiple combinations result in 14 points, the dealer will opt for the one that includes the fewest aces.

Bonus Bet

The table below outlines the payout structure for the Bonus Bet. All wins are presented on a 'to one' basis, implying that the player receives their initial Bonus Bet back if they win.

Example

Here is an example from the 7-14-21 free demo game I placed $25 bets on the 7, 14, and 21 hands, and an additional $5 on the Bonus Bet.

I won my '7' wager since the dealer exceeded 7, while I did not. The '14' bet resulted in a push, as both of us accumulated exactly 14 points. On the '21' wager, I lost, as my total of 20 was beaten by the dealer's 21. Additionally, I lost my Bonus Bet. In total, my $80 investment yielded $75 back, translating to a net loss of $5. It's not uncommon to experience a mix of wins, pushes, and losses in this game.

Rack Card Strategy

The strategy card suggests the following tactics, ranked by significance:

1. Bust as few hands as possible.
2. Maximize value of \"7\" hand.
3. Maximize value of \"14\" hand.

If this strategy is followed to the letter, it results in a house edge of 7.78%. Savvy players might make slight modifications when aces are involved to extract an extra 10 points from an ace.

Power Rating Strategy

The table below illustrates the frequency with which the dealer achieves various totals in each hand. Notably, the dealer achieves the top hand 35% of the time for '21' and 36% for '14.' This highlights the importance of aiming for the best hands when possible.

The next table converts the probabilities mentioned earlier into a power rating ranging from 0 to 10 for each score across all hands. To determine the optimal way to handle any specific hand, refer to all available play options, choosing the one that provides the highest points. In cases where multiple options yield the same score, prefer the one maximizing the '21' first and then the '14.'

An example hand is provided below, demonstrating the use of the power rating table.

According to the strategy card, a player would take 7-12-20 for a total of 10+3+4=17 power rating points. However, the combination of 5-14-20 maximizes power ratings with 8+8+4=20 points. In this instance, sacrificing two points on the '7' hand results in a significant advantage on the '14' hand. Ultimately, this was a beneficial choice. Regardless, I would have won the '7' and pushed on '21,' but improving from 12 to 14 on the '14' transformed a potential loss into a victory. Overall, the house edge associated with the power rating strategy is 0.59%.

Optimal Strategy

Besides spreadsheets that outline all possible 4,915 hands, no one has formally documented the optimal strategy, to my knowledge. However, considerable data exists regarding its effectiveness. The subsequent three tables present the probabilities and returns for the 7, 14, and 21 hands, assuming the optimal strategy is employed without the Bonus Bet. The figures in the bottom right indicate a player advantage of 10.61% on the '7' bet, 5.55% on '14,' and -17.78% on '21.'

The following table summarizes the odds for the three bets based on optimal strategy, neglecting the Bonus Bet. The lower right cell reveals an overall house edge of 0.54%.

Next is a table depicting the probability and expected return for each event related to the Bonus Bet, under optimal strategy and with the Bonus Bet equating to any of the three 7-14-21 wagers.

Interestingly, in the game of 7-14-21, the player's decisions primarily influence the outcome of the Bonus side bet, unlike many other table games. In some borderline scenarios, this could lead the player to deviate from the optimal strategy of the primary game. The higher the ratio of the Bonus Bet in relation to the 7, 14, and 21 bets, the more the player will be inclined to pursue the Bonus Bet at the expense of the others.

The table below illustrates the anticipated returns for all four bets depending on the ratio of the Bonus Bet to any single 7, 14, or 21 wager. The left column lists the ratio. For instance, if a player wagers $5 on each of the 7, 14, and 21 bets, and $1 on the Bonus Bet, the ratio becomes $1/$5=0.2. This row indicates a combined house edge of 0.547% on the 7-14-21 bets and 0.690% on the totals.

House Edge Summary

The table below encapsulates the house edge associated with the three strategies discussed earlier, assuming no deviations in strategy stemming from the Bonus Bet.

Rack Card

Acknowledgements

I would like to extend my gratitude to the individuals who contributed to this page.

• Special thanks to Stroll Enterprises, the developers of the game, for providing their gameplay insights, photos, and imagery.
• Thanks to miplet and CrystalMath for their work on the dealer probabilities table and for most of the development behind the Power Rating strategy.

Outside Links

• Official7-14-21 The official website from the game creators features outstanding resources.free demo game .
• Forum discussion on 7-14-21 at WizardOfVegas.com.

Written by: Michael Shackleford