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21 + 3
Version 1 of 21+3 I noticed at the Las Vegas Hilton in April, 2001. The side bet pays based on the player's first two cards and the dealer's up card. If the three cards equal a flush, straight, straight flush, or three of a kind the side bet pays 9 to 1. The following table shows the probability of each hand in a six-deck game,as played at the Hilton.
21+3 — 6 decks
|Straight flush||10368||0.002068||9 to 1||0.018613|
|Three of a kind||26312||0.005248||9 to 1||0.047236|
|Straight||155520||0.031021||9 to 1||0.279192|
|Flush||236736||0.047221||9 to 1||0.424993|
|Pair+flush||56160||0.011202||9 to 1||0.100819|
|Pair (no flush)||977184||0.194918||Loss||-0.194918|
The house edge under these rules is 3.24%.
At the Regent (now known as the Rampart) in Las Vegas all hands listed above, plus a pair, pay 5 to 2. I'll call this version 2. Two decks are used in this version. The following table shows a house edge under these rules of 2.78%.
21+3 — 2 decks
|Straight flush||384||0.002109||2.5 to 1||0.005272|
|Three of a kind||728||0.003998||2.5 to 1||0.009994|
|Straight||5760||0.03163||2.5 to 1||0.079076|
|Flush||8768||0.048148||2.5 to 1||0.120371|
|Pair||34944||0.19189||2.5 to 1||0.479726|
I have an unconfirmed report that Internet casinos using Wagerworks software use the following pay table, which I will call "Version 3."
21+3 — Version 3 — Six Decks
|Suited three of a kind||100||1040||0.000207||0.020745|
|Three of a kind||33||25272||0.005041||0.166352|
Although Wager Works only uses six decks in their blackjack game, as far as I know, here is the house edge for 3 to 8 decks.
21+3 — Version 3 — 3-8 Decks
This version, with a 30-20-10-5 pay table, is known as "21+3 Xtreme." The following return table shows the house edge for six decks is 13.39% (ouch!).
21+3 — Version 4 — Six Decks
|Three of a kind||20||26,312||0.005248||0.104968|
If you happen to see it with other than six decks, here is the expected value for various number of decks.
21+3 — Version 4 -- 1 to 8 Deck Summary
The Caesars Entertainment Blog mentions that the xtreme version of 21+3 can be found in the Party Pit at the Paris casino in Las Vegas. I had to chuckle at their sense of humor with this remark,
"We would calculate the odds of hitting these side bets, but being in Vegas isn't about math, it's about having fun. And just never-you-mind that this is the blog of a casino company. Check out the new Ooh La La Party Pit at Paris Las Vegas the next time you’re in the neighborhood.
Hey, it is about the math everywhere, even in the Party Pit!
I saw this version at an Internet casino using live dealers from Evolution Gaming. Following is the return table, based on eight decks.
21+3 — Version 5 — 8 Decks
|Suited three of a kind||100||2,912||0.000244||0.024446|
|Three of a kind||25||61,568||0.005169||0.129213|
Following is the house edge for this pay table for various numbers of decks.
- 4 decks: 8.78%
- 5 decks: 7.81%
- 6 decks: 7.14%
- 7 decks: 6.29%
Written by: Michael Shackleford