21+3

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Scooter

Member
New to counting. Have done lots of research, and looked to see what is out there on other games, Spanish 21, Baccarat, etc.

Has anybody done any work on 21+3? It seems ripe for counting. Especially with such a high payoff. A small change in the underlying probabilities should result in big player advantage. I think the count would have to be of suits though since flushes represent most of the payoff.

Anybody know of any work. I have some C++ skills, but would rather just review someone else's work than spend time reinventing the wheel.
 
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Scooter

Member
21+3 is a simple side bet. The player's first two cards and the dealer's up card form a three card poker hand. If this hand forms three of a kind, flush, or straight, the bet pays 9:1. All combinations of the three (straight flush, three of a kind flush) pay just 9:1.

The house edge on a fresh six deck game is 3.24%. I did a little work on this since posting. I ran analysis on a few thousand random decks from 52 to 311 cards. The player has a positive expected value about 5% of the time. Some of these are very substantial >10%. A very few were 50%+.

I still haven't identified a count that might work for finding these opportunites, but will keep working.

I would really rather hear from someone who has done the work already.
 
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gross

Member
blackjack sidebets

Here is a link to a mathematically sound analysis of available blackjack side bets such as 21+3. Because of the house odds on this bet I almost never play it. However, I believe in very high counts this bet can be advantageous due to the likelihood of making high card straights or 3 of a kind with high cards. I don't see any way the likelihood of a flush could be tracked. Flush, straight or 3 of a kind all pay the same 9:1 which sounds nice but leaves the house with a big take. Remember that any time the house offers you an additional bet on a game they are finding a way to make more money! Good Luck.

http://wizardofodds.com/games/blackjack/bjapx8.html
 
S

Scooter

Member
21+3 Can be Beat

Though it will take team play.

Here is a condensed version. When the normalized difference between the most common suit and the least common suit is 6 or greater, the player has a positive edge. This is in the case when the penetration is to the 104th card. When penetration is to the 52nd card, the index is 7.

How to implement this? If you can keep four running counts great. Count each suit as it comes out. Take the difference between the largest running count and smallest running count and divide by the number of decks remaining. If it is 7 or greater, make the bet.

If you can't keep four running counts, pick any two suits, say Clubs and Diamonds. Count one suit +1 and the other suit -1. Get a true count by dividing your running count by the number of decks remaining to be dealt. If it is greater than 7 (or less than -7), take the bet. Since there are six combinations of the four suits, this will only alert you to 1/6th of the profitable opportunities.

This is where team play comes in. Six players each track a seperate combination of suits. If any true count exceeds 7, that player makes the bet. All the other players would thus be alerted to the profitability of the bet and make it as well. Ideally, there would be a seventh player keeping the count for blackjack purposes.

It is ugly, but this bet can be incredibly profitable. Here are the player's advantages and frequencies at various true counts (penetration to 52nd card):

Point Frequency Advantage
6 3.63% -1.4%
7 2.19% 0.2%
8 1.37% 2.4%
9 0.72% 4.6%
10 0.40% 7.6%
11 0.20% 10.1%
12 0.11% 13.3%
13 0.05% 17.2%

Being new to counting, I do not know any other counters, so I cannot implement this strategy myself. Keeping a single count and betting only 1/6th of the opportunities isn't as profitable as a simple Hi Lo, so I will stick with that.

I imagine no casino is aware that this side bet can be beat, so huge bets would not be questioned. Likely they would be welcomed as this game has an overall house edge of 3.24%.

If anyone would like the gorry details or if you actually implement this strategy, please let me know.
 
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Scooter

Member
Better Count for 21+3

I keep working this problem.

My first count for the 21+3 side count required 6 counts, or catching only 1/6th of the profitable opportunites. This count is better. It requires 4 counts, or catches 1/4th of the profit.

The 21+3 side bet is profitable when the suits in the deck are out of balance. It should be obvious that if the deck consisted entirely of a single suit, the player would win with 100% certainty as any three card combination is a guaranteed flush. Imagine, a 900% expected return. SWEET

Here are the mechanics. Pick a suit. I recommend watching the first round and picking the suit that has the fewest cards dealt. Count each card of that suit as a -1. And count every four cards dealt (regardless of suit) as a +1. The best opportunities occur when the deck is heavy in a suit, this is why I recommend picking the suit with the fewest cards dealt on the first round.

Divide your running count by the remaining decks to get your true count. If your true count is -5 or less, or +4 or greater, take the 21+3 side bet.

With a four counter team, each member could count an assigned suit. This would find every "findable" profitable opportunity. But even a lone counter can track a single suit as a side count. The opportunities this count finds are much more profitable than any additional information an ace side count provides. Also, this count is a great cover. Imagine dropping a purple chip on what the pit boss thinks of as a sucker's bet. You may have a 10%+ advantage, but he will never bother you again.

Here are the counts, frequencies, and player advantages assuming penetration to the 52nd card:

Count____________Freq_____________Advantage
+4_______________2.47%____________1.26%
+5_______________0.90%____________5.13%
+6_______________0.34%____________9.19%
+7_______________0.13%___________14.13%
-5_______________2.23%____________1.82%
-6_______________0.76%____________4.87%
-7_______________0.24%____________8.44%
All Profitable counts
_________________4.06%____________3.65%
 
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