Some thoughts on Baccarat

Back in late January ('15) I started the following thread:


In short I ran a computer simulation against the 250k shoes of Baccarat decisions supplied by Michael at WOO, with the results showing an average win of just over 3 units per shoe.
Since nobody answered my questions asking about refining the method and since I don't think there is anything in the method that is revolutionary I've decided to set the method free and see if any of you can make anything of it.

The method is based on two basic observations:
1. That the Banker bet has a built-in advantage and 2. that given an event with a .5 probability, that event will (on average) occur twice in no more than five trials.
{edit} That should read: 2. that given an event with a .5 probability, that event should (based on probability theory) occur twice in no more than five trials about 83% of the time.

So I got the results posted in the previous thread by 1. always betting Banker, and betting the following sequence 2,3,5,8,13 (which you all recognize as a Fibonacci sequence), starting a new sequence when either two wins are recorded or the fifth bet bet has lost without two wins.

Have fun playing with this and please report back with any insights you may gain.

Cheers,

Insights? Hmmm...1. There is no player advantage on the banker bet. 2. The probability of a banker win is not .5.

Here are the possible results, and the probabilities (out of 32) in which they happen:

Result	Profit	Times out of 32	Profit in 32
WW	+5	8	+40
WLW	+4	4	+16
WLLW	+2	2	+4
WLLLW	-1	1	-1
WLLLL	-27	1	-27
LWW	+6	4	+24
LWLW	+4	2	+8
LWLLW	+1	1	+1
LWLLL	-25	1	-25
LLWW	+8	2	+16
LLWLW	+5	1	+5
LLWLL	-21	1	-21
LLLWW	+11	1	+11
LLLWL	-15	1	-15
LLLLW	-5	1	-5
LLLLL	-31	1	-31

As you can see, if you add up the numbers in the last column, you get zero. Those runs where you end with a loss are killers.

Of course, this assumes a 50/50 game that pays even money. Baccarat is not 50/50, and while the bank does win more than the player does, that's why you pay a commission when you bet on the bank (sometimes you pay it up front, so, in effect, the payoff is 20-21; sometimes you only pay when you win, so it's 19-20).

Remember, one of the casino's best friends is when people throw the phrase "on average" around.

Very interesting thread! Especially considering I just returned home from a local casino after 4 hours of playing Baccarat!
I was wondering is someone can answer a silly question from a beginner: The general consensus seems to be that you can't beat the Casino at Baccarat. Most materials I have read state that the house has an advantage of 1.06%. Pretty clear. However, is there a competitive advantage using comps? How long do I have to play and how much to wager to get a free meal every visit? Have you guys done any calculations on this? Thanks!

And yet, after 250k shoes this "system" shows a profit. (I put system in quotes because I make no claims that it is a viable system.)

That's why I find playing Baccarat an interesting diversion. (That it often pays for the weekend I spend playing it is an added bonus.)

May I ask a really silly question??
I often go to the local casino with my dad. He plays at the Baccarat table and I am just standing there watching. There are often other people standing around the table and watching too.
What if I always get in when there is a streak of 4 "bankers" or "players" and play a simple Martingale strategy? From what I understand, it rarely goes beyond 7... With this strategy (getting in only at a streak of 4 otherwise just watching Dad) would I come out in profit every time?
I understand some people may say it's "no fun", my question is only about mathematics/statistics. Thank you!

The cards have no idea how long the streak is. Why do the hands you don't play matter?

Seems to me it is akin to praying for positive variance in life.

Alas, wishing doesn't make it so.

The universe is chaos, robed in a bit of symmetry.

Quote: Kendig

And yet, after 250k shoes this "system" shows a profit.

If you bet on coin tosses, here are two "systems":
(a) Always bet heads.
(b) Always bet tails.
After 250,001 tosses, one of the two will show a profit.

Quote: ThatDonGuy

If you bet on coin tosses, here are two "systems":
(a) Always bet heads.
(b) Always bet tails.
After 250,001 tosses, one of the two will show a profit.

You assume that the game is fair; casinos rarely offer fair games.

I have a simple rule when it comes to observing a streak unfold in any (approximately) even chance game (Bac. / craps): Bet that the streak will continue or don't bet at all.

My reasoning is simple. If you bet that the streak will continue and you lose, you will have lost one bet. If you bet that the streak will end and the streak continues you can lose a lot (especially with a Martingale. I have personally witnessed streaks longer than 20 four times and streaks longer than 10 more times than I can recall.

What has this to do with casino games? There is no casino game that pays true odds as your example does.

Quote: Kendig

I have a simple rule when it comes to observing a streak unfold in any (approximately) even chance game (Bac. / craps): Bet that the streak will continue or don't bet at all.

My reasoning is simple. If you bet that the streak will continue and you lose, you will have lost one bet. If you bet that the streak will end and the streak continues you can lose a lot (especially with a Martingale. I have personally witnessed streaks longer than 20 four times and streaks longer than 10 more times than I can recall.

Kendig,
Thanks for your reply. I am afraid I don't fully get it. At my casino, they display history on the screen and show not only numbers but Banker % and Player % for the game. I have seen a situation where Banker was 70% and Player was 30% and not only that but there was a streak of 4 bankers in a row. Statistically, aren't there huge chances of winning a wager on "player" under this specific scenario?

Quote: Kendig

What has this to do with casino games? There is no casino game that pays true odds as your example does.

There is no casino that offers even money on betting on the banker in baccarat, either, but that is what I am reading from your
initial post - the fact that the banker "has an advantage" (50.68244%) is negated by the fact that it pays 19-20.

Here is what the table looks like if you bet with the banker in baccarat, assuming 5% commission on win (i.e. if you bet 20 and win, you gain 19)

Result	Profit	Probability	Prob x Profit
WW	4.75	0.256870953	1.2201370265
WLW	3.65	0.1266824913	0.4623910932
WLLW	1.5	0.0624767161	0.0937150741
WLLLW	4.25	0.0308119931	0.1309509708
WLLLL	-27.1	0.0299822273	-0.8125183604
LWW	5.6	0.1266824913	0.7094219512
LWLW	3.45	0.0624767161	0.2155446705
LWLLW	0.2	0.0308119931	0.0061623986
LWLLL	-25.15	0.0299822273	-0.7540530171
LLWW	7.35	0.0624767161	0.4592038632
LLWLW	4.1	0.0308119931	0.1263291719
LLWLL	-21.25	0.0299822273	-0.6371223306
LLLWW	9.95	0.0308119931	0.3065793318
LLLWL	-15.4	0.0299822273	-0.4617263008
LLLLW	-5.65	0.0299822273	-0.1693995844
LLLLL	-31	0.0291748071	-0.904419019

The sum of the "probability x profit" column is -0.0088030605, or an expected loss of 0.88% of each bet that does not end in a tie.

Your profit over 250K shoes can be explained with one word: luck.

In fact, I simulated the 2-3-5-8-13 method ("don't call it a system") over 20 million shoes (note that I reset at the beginning of each shoe), betting on the bank with 5% commission on win (i.e. a bet of 20 results in a gain of 19), and got a profit in 48.1% of the shoes. On the other hand, without the 5% commission, 54.9% of the shoes turn a profit.

Quote: ThatDonGuy

Your profit over 250K shoes can be explained with one word: luck.

and OP bets Banker every round...
no way a profit of what he says in another thread
maybe without a comm, sure

Quote: ThatDonGuy

In fact, I simulated the 2-3-5-8-13 method ("don't call it a system") over 20 million shoes (note that I reset at the beginning of each shoe), betting on the bank with 5% commission on win (i.e. a bet of 20 results in a gain of 19), and got a profit in 48.1% of the shoes. On the other hand, without the 5% commission, 54.9% of the shoes turn a profit.

and did you average, what, 3 units win per shoe over that simulation?

i doubt (without even looking)

neither did the OP over the Wizards shoes

I be willing to bet the OP $3.76 (I will pay in CASH)

he did not play out the Wizards shoe collection (sounds funny - his wife says so too)
correctly
as would be done in a real casino with real commissions or even at EZ Bacc

Sally

Quote: mustangsally

and did you average, what, 3 units win per shoe over that simulation?

i doubt (without even looking)

Actually, it was more like 4.9 units/shoe, assuming the initial bet was 2 units.

Remember, I'm talking about a version of baccarat where there is no commission on bank wins (and no special rules to make up for it, like it pays only 1-2 if the banker wins with a hand value of 6). I have a feeling the OP was doing it this way as well.

Follow the trend, loose the last one when it falls off, simple. Play for it to cut and you will be wrong most of the time. If it is chopping, play with the chop, once again, same as a trend. Chuckle, chuckle.

Thank you: Being lucky is perfectly acceptable.
Also, thank you for running the simulation for 20 million shoes. I had a hypothesis and you proved it wrong (and saved me money to boot); time to move on.

Cheers

Quote: MikeWise

Thanks for your reply. I am afraid I don't fully get it. At my casino, they display history on the screen and show not only numbers but Banker % and Player % for the game. I have seen a situation where Banker was 70% and Player was 30% and not only that but there was a streak of 4 bankers in a row. Statistically, aren't there huge chances of winning a wager on "player" under this specific scenario?

Umm no. The challenge in gambling is that the statistics of any particular game is based on theory and demonstrated by tabulating a very large number of trials. The problem faced by the person sitting at the Baccarat table is that a shoe will generate only around 80 trials (8 decks). Do a search for the term "random walk" for more insight into the probability of the improbable.

Also, do your own investigation. Wander around your local casino and note the scoreboard at (or near) the end of each shoe and compare the actual results to the expected results. Let us know if you are surprised by the outcome. While you are scoreboard watching, note the percentages after 20, 40, and 60 hands and at the end. Did the numbers change much? (Beware that the number of ties will affect the percentages.) What did you learn (if you did this)?

I've been playing Baccarat for almost 30 years now, and I'm very much a "go with the flow" kind of guy. I've often been happily playing (and winning) while favoring the Player bet (because the shoe has been favoring Player) when someone will come to the table, look at the scoreboard, bet heavily on Banker and then leave in a huff when Player continues to dominate. Of course the small still voice in the back of my is constantly saying: "Beware! This is a statistical outlier." and I'm ready to switch over to betting Banker. Again, refer to your notes if you do the 20, 40, 60, end of shoe observations.

Remember: Get lucky and quit while you are ahead.

Bon Chance!