21 + 3

Version 1

In April 2001, I noticed Version 1 of 21+3 at the Las Vegas Hilton. The side bet is determined by the player's first two cards along with the dealer's up card. A three-card combination yielding a flush, straight, straight flush, or three of a kind pays out at 9 to 1. The table below outlines the probabilities for these outcomes in a six-deck game, as played at the Hilton.

The following details the house edge associated with 4, 6, and 8 decks.

• 1 deck — 13.30%
• 2 decks — 7.26%
• 4 decks — 4.24%
• 6 decks — 3.24%
• 8 decks — 2.74%

Version 2

At the Regent, now called the Rampart in Las Vegas, all winning hands listed here, including a pair, pay out at 5 to 2. I refer to this as version 2, which utilizes two decks. The table below indicates that the house edge under these conditions is 2.78%.

Version 3

I have heard an unofficial report that online casinos utilizing this software provide the following payout structure, which I will label as 'Version 3.' Wagerworks Notably, Wager Works employs six decks in their blackjack offerings, but from what I know, here’s the house edge calculated for 3 to 8 decks.

This version, which offers a 30-20-10-5 payout structure, is recognized as '21+3 Xtreme.' The return table indicates that with six decks, the house edge stands at 13.39%, which is quite steep.

Version 4

Should you encounter this game with a different number of decks, here's the expected value for a range of deck counts.

According to the Caesars Entertainment Blog, the xtreme variant of 21+3 can be found in the Party Pit at the Paris casino in Las Vegas. Their humorous comment made me chuckle: 'We would typically calculate the odds of these side bets, but being in Vegas is more about the experience than math. And don't worry that this is a casino blog. Make sure to check out the new Ooh La La Party Pit at Paris Las Vegas on your next visit.'

Mathematics indeed plays a role everywhere, even in the Party Pit!

I observed this version at an online casino featuring live dealers from Evolution Gaming. The return table provided here is based on play with eight decks.

The following outlines the house edge for this payout structure, considering various deck counts.

Version 5

I have received an unofficial tip that the Ameristar in Kansas City employs the following pay table using two decks.

The next table presents the house edge associated with the Version 6 payout table across different deck counts.

• 4 decks: 8.78%
• 5 decks: 7.81%
• 6 decks: 7.14%
• 7 decks: 6.29%

Version 6

This payout table is reportedly utilized by Evolution Gaming's live dealer casinos, which use eight decks.

Here’s the breakdown of house edge for both four and six decks.

Version 7

I believe I spotted this variant at the Global Gaming Expo, though I'm not entirely sure. It's noteworthy for offering a progressive jackpot for hitting three suited aces. Here’s the complete payout table, which pays on a 'to one' basis.

The next table provides my analysis based on a six-deck game setup.

• Four decks: 6.39%
• Six decks: 3.70%

Version 8

The lower right corner of the analysis indicates a house edge of 33.44% prior to factoring in jackpot values. For a minimum bet of $1, each $1,000 in the jackpot reduces the house edge by 1.60%. If the starting bet is $5, each $10,000 in the jackpot lowers the house edge by 3.19%.

The points at which the house edge balances to zero are calculated as $27,016.90 for a $1 wager and $135,084.50 for a $5 wager, based on the six-deck format.

On January 29, 2021, I came across this version at the Rampart casino in Las Vegas. It's similar to version 8, except a suited three of a kind from queens to aces is necessary to qualify for the jackpot, placing it as a $1 'red light' bet that pays 'for one'. The payout table follows.

The bottom right cell shows an expected return of 47.54%, excluding jackpot considerations. Each $1,000 added to the jackpot boosts returns by 4.79%. For instance, during my observation, the jackpot stood at $3,886.15, resulting in an expected return of 66.15%.

Version 9

The break-even point, where there is no house edge, emerges at a jackpot value of $10,957.37.

The points at which the house edge balances to zero are calculated as $27,016.90 for a $1 wager and $135,084.50 for a $5 wager, based on the six-deck format.

Concept Gaming, which creates games for online casinos, offers a bet known simply as the 'poker' bet. Their setup employs six decks and features a payout structure of 100-35-20-15-5, with wins calculated 'for one'. The following table reflects a player return of 95.14%. However, the help file states a return of 95.11%. It's your choice whom to trust.

Accurate mathematical strategies and information to enhance your gameplay for casino offerings like blackjack, craps, roulette, and numerous others.

Version 10

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Written by: Michael Shackleford