Baccarat 3 Card Wins

3 Card Wins are a pair of side bets in baccarat at a table in the Gold Coast next to the Hippie Pit. They win if the chosen side wins with three cards. Player wins pay 4 to 1 and the Banker pays 5 to 1. For all the rules and analysis, please click the link I just left.

As usual, I welcome all questions, comments, and corrections.

The question for the poll is would you bet the 3 Card Wins if playing baccarat anyway? Multiple votes allowed.

Question for discussion: Are these countable? (shut up Wiz!)

Quote: Wizard

Are these countable?

Obviously countable. The "Dragon 7" count is almost certainly usable here, as it is correlated to 3-card final hands. (4,5,6,7 = -1, 8,9 = +2). However, there may be an even stronger count.

In the first sentence of the Analysis section at WoO, trade out "Banker" for "Player".

Quote: teliot

Obviously countable. The "Dragon 7" count is almost certainly usable here, as it is correlated to 3-card final hands. (4,5,6,7 = -1, 8,9 = +2). However, there may be an even stronger count.

I beg to differ, obviously it is not so countable, you can rest assured.

Fortunately, it is beatable with a very unique method . . .( shhh...)

Quote: teliot

Obviously countable.

I am just told the maximum bet is $25. Between that and one placement, I'm not going to fuss with it.

Quote: teliot

Obviously countable. The "Dragon 7" count is almost certainly usable here, as it is correlated to 3-card final hands. (4,5,6,7 = -1, 8,9 = +2). However, there may be an even stronger count.

100 million shoe simulation results :-

a) 96.6% penetration, BANKER 3 CARD WINS, EV/shoe = 0.014unit
b) 87.5% penetration, BANKER 3 CARD WINS, EV/shoe = 0.001unit
c) 96.6% penetration, PLAYER 3 CARD WINS, EV/shoe = 0.177unit
d) 87.5% penetration, PLAYER 3 CARD WINS, EV/shoe = 0.068unit

So it is not so countable, as per my prediction. Rest assured.

Quote: teliot

Obviously countable. The "Dragon 7" count is almost certainly usable here, as it is correlated to 3-card final hands. (4,5,6,7 = -1, 8,9 = +2). However, there may be an even stronger count.

(1) All popular side bets have been identified as countable by the Professor.
(2) Most gamblers only play the perceived "countable" games
(3) First figure out how much you can make per hour by counting
(4) Then get your bankroll ready and go bet.

Quote: ssho88

100 million shoe simulation results :-

a) 96.6% penetration, BANKER 3 CARD WINS, EV/shoe = 0.014unit
b) 87.5% penetration, BANKER 3 CARD WINS, EV/shoe = 0.001unit
c) 96.6% penetration, PLAYER 3 CARD WINS, EV/shoe = 0.177unit
d) 87.5% penetration, PLAYER 3 CARD WINS, EV/shoe = 0.068unit

So it is not so countable, as per my prediction. Rest assured.

The paytable has changed:

Banker 3 Card Win, 5,4,3,2,1 15 to 1
Banker 3 Card Win, 9,8,7,6, Push

Player 3 Card Win, 5,4,3,2,1 10 to 1
Player 3 Card Win, 9,8,7,6, Push

Countable?

Quote: UCivan

The paytable has changed:

Banker 3 Card Win, 5,4,3,2,1 15 to 1
Banker 3 Card Win, 9,8,7,6, Push

Player 3 Card Win, 5,4,3,2,1 10 to 1
Player 3 Card Win, 9,8,7,6, Push

Countable?

UCivan,


I get the following EV results for the new paytable:

Baccarat 3-Card Win: New Paytable
Result	Pays	Prob	Return
Banker Bet
Banker 3-Card Win with Total of 1-5	15	0.0528397212026086	0.792595818
Banker 3-Card Win with Total of 6-9	0	0.0999862425691615	0
Lose	-1	0.8471740362282300	-0.847174036
			-0.054578218
Player Bet
Player 3-Card Win with Total of 1-5	10	0.0682054873307859	0.682054873
Player 3-Card Win with Total of 6-9	0	0.1204224241038410	0
Lose	-1	0.8113720885653730	-0.811372089
			-0.129317215

Hope this helps!

Dog Hand

Quote: DogHand

UCivan,


I get the following EV results for the new paytable:

Baccarat 3-Card Win: New Paytable
Result	Pays	Prob	Return
Banker Bet
Banker 3-Card Win with Total of 1-5	15	0.0528397212026086	0.792595818
Banker 3-Card Win with Total of 6-9	0	0.0999862425691615	0
Lose	-1	0.8471740362282300	-0.847174036
			-0.054578218
Player Bet
Player 3-Card Win with Total of 1-5	10	0.0682054873307859	0.682054873
Player 3-Card Win with Total of 6-9	0	0.1204224241038410	0
Lose	-1	0.8113720885653730	-0.811372089
			-0.129317215

Hope this helps!

Dog Hand

Thank U DogHand.

I was interested in countability? Easy to count?

Quote: UCivan

The paytable has changed:

Banker 3 Card Win, 5,4,3,2,1 15 to 1
Banker 3 Card Win, 9,8,7,6, Push

Player 3 Card Win, 5,4,3,2,1 10 to 1
Player 3 Card Win, 9,8,7,6, Push

Countable?

I will redo the simulations. What is the penetration ?

Quote: UCivan

Thank U DogHand.

I was interested in countability? Easy to count?

UCivan,

Well, to answer that, I first had to find the Effect of Removal of each rank on each of the sidebets. I did this by removing a single card of the given rank from the 8-deck shoe and then re-calculating the EV of each sidebet. From these EoR's, I selected tags to be used to count each sidebet. Here are those results:

Bac. 3-Card Win: EoR
Banker Bet	EV	EoR	Tag	Player Bet	EV	EoR	Tag
Full	-5.458%			Full	-12.932%
Remove 1				Remove 1
0	-5.649%	-0.191%	-1	0	-13.212%	-0.280%	-1
1	-5.664%	-0.206%	-1	1	-13.136%	-0.204%	-1
2	-5.712%	-0.254%	-1	2	-13.059%	-0.127%	0
3	-5.630%	-0.172%	-1	3	-12.978%	-0.046%	0
4	-5.391%	0.066%	0	4	-12.909%	0.023%	0
5	-5.373%	0.085%	0	5	-12.790%	0.142%	0
6	-5.155%	0.303%	2	6	-12.462%	0.470%	2
7	-5.222%	0.236%	1	7	-12.564%	0.368%	1
8	-5.043%	0.414%	2	8	-12.634%	0.298%	1
9	-5.166%	0.292%	2	9	-12.735%	0.196%	1

Using these tags for each system, I then ran a Baccarat simulation of 10-million 8-decks shoes. For each shoe, the number of cards cut off was 14+1 (the burn card)+(number of cards corresponding to the burn card, with A = 1, 2-10 = the pip value, and J,Q,K = 10), so the number cut off varied between 16 and 25. However, one more round was dealt AFTER the cut card appeared, in keeping with Baccarat tradition.


Here are the results for each sidebet as a function of the floored TC:

	Banker				Player
TC	TCDist	SBPush	SBWin	SBEarn	TCDist	SBPush	SBWin	SBEarn
15	7,714,005	730,819	598,265	2,589,054	3,237,345	379,343	390,690	1,439,588
14	1,842,853	178,388	125,902	349,967	999,335	118,294	101,987	240,816
13	1,777,361	172,035	119,035	299,234	932,350	109,887	93,347	204,354
12	3,301,499	321,622	215,993	476,011	2,002,354	236,948	192,593	353,117
11	3,322,676	323,068	214,221	427,928	1,984,491	235,191	185,191	287,801
10	4,580,157	447,158	290,674	517,785	2,902,061	343,935	262,442	328,736
9	5,644,117	552,764	349,114	494,471	3,701,078	439,241	326,123	325,516
8	7,764,370	763,410	472,449	558,224	5,343,113	634,001	454,900	294,788
7	9,609,805	945,775	574,549	528,754	6,802,509	809,225	565,377	225,863
6	13,562,514	1,336,643	796,957	525,441	10,154,075	1,207,806	819,353	66,614
5	17,922,702	1,769,443	1,034,339	396,165	14,013,054	1,671,613	1,099,149	(250,802)
4	26,223,936	2,598,921	1,485,978	150,633	21,991,179	2,621,434	1,680,152	(888,073)
3	35,953,829	3,568,299	2,003,702	(326,298)	32,022,653	3,830,548	2,382,868	(1,980,557)
2	54,913,429	5,462,100	3,011,912	(1,260,737)	53,512,894	6,407,886	3,876,721	(4,461,077)
1	81,875,272	8,163,128	4,420,180	(2,989,264)	87,916,629	10,548,621	6,208,874	(9,070,394)
0	148,708,524	14,855,087	7,882,451	(7,734,221)	183,412,736	22,059,772	12,582,731	(22,942,923)
-1	116,576,166	11,661,275	6,090,490	(7,467,051)	137,623,593	16,583,601	9,230,607	(19,503,315)
-2	82,777,653	8,305,564	4,247,496	(6,512,153)	88,672,118	10,706,522	5,768,761	(14,509,225)
-3	52,834,845	5,311,580	2,659,058	(4,978,337)	51,269,217	6,200,838	3,241,030	(9,417,049)
-4	36,364,504	3,664,107	1,796,887	(3,950,205)	32,647,127	3,960,485	2,003,519	(6,647,933)
-5	99,542,092	10,126,548	4,572,229	(16,259,880)	71,672,398	8,785,389	3,978,788	(19,120,341)

On this table, the TC=15 row is actually 15 and up, while the TC=-5 row is actually -5 and below.

From these results, we see the Banker SB becomes +EV at a Banker-TC of +4, while the Player SB becomes +EV at a Player-TC of +6. If we bet each SB only when it is +EV, we get these results:

SB	Banker	Player
Pays	15	10
Trigger	4	6
Play%	12.70%	4.68%
Hit%	6.08%	8.91%
EV%	7.08%	9.90%

So, the Banker SB is +EV on 12.7% of the rounds, with an average edge of just over 7%. When we play it, it wins just over 6% of the time.

The Player SB is +EV on just under 4.7% of the rounds, but with an average EV of nearly 10%. When we play it, it wins just under 9% of the time.

Just as a check, here are the overall statistics for the 10-million shoes:

Baccarat
Shoes	10,000,000
Decks	8
Cut Off	14
Rounds	812,812,309
Banker	372,732,698	45.86%
Player	362,723,121	44.63%
Tie All	77,356,490	9.52%

So, to answer your query: yes, it is easily countable, but with a $25 max bet, you won't get rich doing so ;-)

Hope this helps!

Dog Hand

Yes, indeed. Thanks.

Quote: UCivan

Yes, indeed. Thanks.

My simulation results for BANKER 3 CARD WIN(1 pay 15), RC method, penetration = 87.5%, the ev/shoe = 0.43 units, bet when RC >= xx .

If penetration = 96.6%, the ev/shoe = 0.75 units.

Unbalanced Running Count system tag values from Ace to T ( -1, -1, -1, 0, 0, +2, +2, +2, +2, -1)

How to post an image files ?

Edited, your EORs match with mine . . .

My EORs(BANKER 3 CARD WIN 1 pay 15) . . . .

Card	EOR
Ace	-0.205995
2	-0.253708
3	-0.172030
4	0.066330
5	0.085137
6	0.302564
7	0.235779
8	0.414440
9	0.291926
T	-0.191111

James

Quote: DogHand

UCivan,

Well, to answer that, I first had to find the Effect of Removal of each rank on each of the sidebets. I did this by removing a single card of the given rank from the 8-deck shoe and then re-calculating the EV of each sidebet. From these EoR's, I selected tags to be used to count each sidebet. Here are those results:

Bac. 3-Card Win: EoR
Banker Bet	EV	EoR	Tag	Player Bet	EV	EoR	Tag
Full	-5.458%			Full	-12.932%
Remove 1				Remove 1
0	-5.649%	-0.191%	-1	0	-13.212%	-0.280%	-1
1	-5.664%	-0.206%	-1	1	-13.136%	-0.204%	-1
2	-5.712%	-0.254%	-1	2	-13.059%	-0.127%	0
3	-5.630%	-0.172%	-1	3	-12.978%	-0.046%	0
4	-5.391%	0.066%	0	4	-12.909%	0.023%	0
5	-5.373%	0.085%	0	5	-12.790%	0.142%	0
6	-5.155%	0.303%	2	6	-12.462%	0.470%	2
7	-5.222%	0.236%	1	7	-12.564%	0.368%	1
8	-5.043%	0.414%	2	8	-12.634%	0.298%	1
9	-5.166%	0.292%	2	9	-12.735%	0.196%	1

Using these tags for each system, I then ran a Baccarat simulation of 10-million 8-decks shoes. For each shoe, the number of cards cut off was 14+1 (the burn card)+(number of cards corresponding to the burn card, with A = 1, 2-10 = the pip value, and J,Q,K = 10), so the number cut off varied between 16 and 25. However, one more round was dealt AFTER the cut card appeared, in keeping with Baccarat tradition.


Here are the results for each sidebet as a function of the floored TC:

	Banker				Player
TC	TCDist	SBPush	SBWin	SBEarn	TCDist	SBPush	SBWin	SBEarn
15	7,714,005	730,819	598,265	2,589,054	3,237,345	379,343	390,690	1,439,588
14	1,842,853	178,388	125,902	349,967	999,335	118,294	101,987	240,816
13	1,777,361	172,035	119,035	299,234	932,350	109,887	93,347	204,354
12	3,301,499	321,622	215,993	476,011	2,002,354	236,948	192,593	353,117
11	3,322,676	323,068	214,221	427,928	1,984,491	235,191	185,191	287,801
10	4,580,157	447,158	290,674	517,785	2,902,061	343,935	262,442	328,736
9	5,644,117	552,764	349,114	494,471	3,701,078	439,241	326,123	325,516
8	7,764,370	763,410	472,449	558,224	5,343,113	634,001	454,900	294,788
7	9,609,805	945,775	574,549	528,754	6,802,509	809,225	565,377	225,863
6	13,562,514	1,336,643	796,957	525,441	10,154,075	1,207,806	819,353	66,614
5	17,922,702	1,769,443	1,034,339	396,165	14,013,054	1,671,613	1,099,149	(250,802)
4	26,223,936	2,598,921	1,485,978	150,633	21,991,179	2,621,434	1,680,152	(888,073)
3	35,953,829	3,568,299	2,003,702	(326,298)	32,022,653	3,830,548	2,382,868	(1,980,557)
2	54,913,429	5,462,100	3,011,912	(1,260,737)	53,512,894	6,407,886	3,876,721	(4,461,077)
1	81,875,272	8,163,128	4,420,180	(2,989,264)	87,916,629	10,548,621	6,208,874	(9,070,394)
0	148,708,524	14,855,087	7,882,451	(7,734,221)	183,412,736	22,059,772	12,582,731	(22,942,923)
-1	116,576,166	11,661,275	6,090,490	(7,467,051)	137,623,593	16,583,601	9,230,607	(19,503,315)
-2	82,777,653	8,305,564	4,247,496	(6,512,153)	88,672,118	10,706,522	5,768,761	(14,509,225)
-3	52,834,845	5,311,580	2,659,058	(4,978,337)	51,269,217	6,200,838	3,241,030	(9,417,049)
-4	36,364,504	3,664,107	1,796,887	(3,950,205)	32,647,127	3,960,485	2,003,519	(6,647,933)
-5	99,542,092	10,126,548	4,572,229	(16,259,880)	71,672,398	8,785,389	3,978,788	(19,120,341)

On this table, the TC=15 row is actually 15 and up, while the TC=-5 row is actually -5 and below.

From these results, we see the Banker SB becomes +EV at a Banker-TC of +4, while the Player SB becomes +EV at a Player-TC of +6. If we bet each SB only when it is +EV, we get these results:

SB	Banker	Player
Pays	15	10
Trigger	4	6
Play%	12.70%	4.68%
Hit%	6.08%	8.91%
EV%	7.08%	9.90%

So, the Banker SB is +EV on 12.7% of the rounds, with an average edge of just over 7%. When we play it, it wins just over 6% of the time.

The Player SB is +EV on just under 4.7% of the rounds, but with an average EV of nearly 10%. When we play it, it wins just under 9% of the time.

Just as a check, here are the overall statistics for the 10-million shoes:

Baccarat
Shoes	10,000,000
Decks	8
Cut Off	14
Rounds	812,812,309
Banker	372,732,698	45.86%
Player	362,723,121	44.63%
Tie All	77,356,490	9.52%

So, to answer your query: yes, it is easily countable, but with a $25 max bet, you won't get rich doing so ;-)

Hope this helps!

Dog Hand

With a nominal 52-card cutoff, I get these results for a 10-million-shoe simulation:

SB	Banker	Player
Pays	15	10
Trigger	4	6
Play%	10.25%	2.68%
Hit%	5.95%	8.62%
EV%	5.12%	6.71%

Comparing these results to the 14-card-cutoff results posted earlier in this thread dramatically illustrates the value of penetration when counting this sidebet.

Hope this helps!

Dog Hand

Vegas casinos cut one and 1/4 decks, about 65 cards.

Quote: UCivan

Vegas casinos cut one and 1/4 decks, about 65 cards.

UCivan,

Is that an 8D game?

Dog Hand

Quote: DogHand

UCivan,

Is that an 8D game?

Dog Hand

yes

UCivan,

With a nominal 65-card cutoff, my sim gives these results:

SB	Banker	Player
Pays	15	10
Trigger	4	6
Play%	9.48%	2.19%
Hit%	5.93%	8.56%
EV%	4.78%	6.09%

Once again, as the number of cards cut off increases, the advantage gained by counting decreases... no surprise!

On an EV/shoe basis, using 71 rounds/shoe with 65 cut off, these correspond to 0.32 units/shoe on the Banker sidebet, and 0.095 units/shoe on the Player sidebet: combined, with the $25 max, you'll earn about $10/shoe... I think the casino can relax.

Hope this helps!

Dog Hand

Quote: DogHand

UCivan,

With a nominal 65-card cutoff, my sim gives these results:

SB	Banker	Player
Pays	15	10
Trigger	4	6
Play%	9.48%	2.19%
Hit%	5.93%	8.56%
EV%	4.78%	6.09%

Once again, as the number of cards cut off increases, the advantage gained by counting decreases... no surprise!

On an EV/shoe basis, using 71 rounds/shoe with 65 cut off, these correspond to 0.32 units/shoe on the Banker sidebet, and 0.095 units/shoe on the Player sidebet: combined, with the $25 max, you'll earn about $10/shoe... I think the casino can relax.

Hope this helps!

Dog Hand

I could follow your math and logic clearly until you said 71 hands make $10/shoe. How did you get 0.32 units/shoe, 0.095 unit/shoe? Thank you

Quote: panda1314

<snip>I could follow your math and logic clearly until you said 71 hands make $10/shoe. How did you get 0.32 units/shoe, 0.095 unit/shoe? Thank you

dated

panda1314,

Well, if you get 71 hands per shoe, and you play the Banker sidebet on 9.48% of them, you'll play (71 hands/shoe)*(0.0948 Banker sidebets/hand) = 6.73 Banker sidebets/shoe.

On each Banker sidebet, the average EV is 4.78%, so (6.73 Banker sidebets/shoe)*(0.0478 units/Banker sidebet) = 0.32 units/shoe for the Banker sidebet.

Similarly, for the Player sidebet, you get (71 hands/shoe)*(0.0219 Player sidebets/hand)*(0.0609 units/Player sidebet) = 0.095 units/shoe for the Player sidebet.

Adding these together (because you're keeping both the Banker and Player counts) and multiplying by $25/bet gives $10.38/shoe, which I rounded to $10.

Hope this helps!

Dog Hand

Got it. In real life, you cannot just bet $100 for 6-7 hands per shoe and none for other 64/65 hands. If high% of ur bets win, u get kicked out soon.

Thanks a lot though.

Quote: panda1314

Got it. In real life, you cannot just bet $100 for 6-7 hands per shoe and none for other 64/65 hands. If high% of ur bets win, u get kicked out soon.

Thanks a lot though.

panda1314,

I have a confession to make: although I regularly play blackjack, I've never played baccarat. Perhaps you (or others with experience here) could answer some procedural questions for me.

First, earlier in the thread I wrote: "For each shoe, the number of cards cut off was 14+1 (the burn card)+(number of cards corresponding to the burn card, with A = 1, 2-10 = the pip value, and J,Q,K = 10), so the number cut off varied between 16 and 25. However, one more round was dealt AFTER the cut card appeared, in keeping with Baccarat tradition." Is that an accurate description of the dealing procedure?

Second, can you just play the sidebet, or must you also wager on the "main game" as well?

Third, if a main wager is required to be able to play the sidebet, can the sidebet wager be larger than the main wager?

I suppose I was anticipating that the player would place minimum wagers on Banker or Player every 2-3 rounds, and then pop out a max sidebet wager when appropriate.

Thanks in advance!

Dog Hand

I'm a little confused. What does it all mean?

I don't play baccarat myself, but I watch it a lot.

First, earlier in the thread I wrote: "For each shoe, the number of cards cut off was 14+1 (the burn card)+(number of cards corresponding to the burn card, with A = 1, 2-10 = the pip value, and J,Q,K = 10), so the number cut off varied between 16 and 25. However, one more round was dealt AFTER the cut card appeared, in keeping with Baccarat tradition." Is that an accurate description of the dealing procedure?

shuffle 8 deck, cut off 65 cards, open 1st card, look at pip value, burn pip cards, start play

Second, can you just play the sidebet, or must you also wager on the "main game" as well?

different casino has different rules. e.g., let you play sides alone iff the total side bets amount to be >$25 at $25-$2,000 table. difficult to put this into analysis.

Third, if a main wager is required to be able to play the sidebet, can the sidebet wager be larger than the main wager?

yes, allowed. but most players do not

I suppose I was anticipating that the player would place minimum wagers on Banker or Player every 2-3 rounds, and then pop out a max sidebet wager when appropriate.

yes, mostly this is the case. But, like Panda says, if you bet main $1,000 and bet side $100, and hit a high % of side, you are escorted out.

I welcome corrections to my answers from other members

Hi DogHand,

What is your simulation results for OLD paytable ? Please note that OLD paytable : Player wins pay 4 to 1 and the Banker pays 5 to 1



Just want to prove that it is NOT countable for OLD paytable. My 100 million shoe simulation results based on OLD paytable :-

a) 96.6% penetration, BANKER 3 CARD WINS, EV/shoe = 0.014unit
b) 87.5% penetration, BANKER 3 CARD WINS, EV/shoe = 0.001unit
c) 96.6% penetration, PLAYER 3 CARD WINS, EV/shoe = 0.177unit
d) 87.5% penetration, PLAYER 3 CARD WINS, EV/shoe = 0.068unit

James