hi there,

hope someone would answer my doubts.
let's say i play 1000 hands.
how many occasions on average would it occur when player/banker wins more than 8 times in a row in a game of baccarat?
and also in BJ?(lose more than 8 times in a row)
TQ

On avg. 3 times for Bacarrat

For BJ?
Depends on the software and your betting patterns.
If you are looking at a double/triple up option, dont even try, cos you'll die.
(hey Im a poet!)
The people that run these places know about these options.

Find a better system, like discipline, EV, Basic Strategy, and hard work.

eek

Oh.

Dealers upcard should be a ten/face for 33% of the time.
Just thought you'd like to know.

eek

One baccarat 8-deck land casino shoe had 3-4 only of one thing, and the rest was the other. I can't remember whether banker or player was the stronger.

At land casino some just play banker continuously because over millions of hands banker should come up more often, hence the commission required and then are surprised when they lose.

But it happens regularly that player is far stronger in a particular shoe.

Originally posted by eek:
Dealers upcard should be a ten/face for 33% of the time.

Wouldn't it be more like 4/13? And actually a little less than that, if you take all your 2-card initial hand totals into consideration.

Originally posted by eek:
For BJ?
Depends on the software and your betting patterns.
Well, in theory at least, I don't think a streak is at all dependent on how much you bet or when you bet it. Of course the particular rules of the game would effect it but I don't see what the software has to do with it.
I guess you're implying that certain software is biased, especially with regard to the size & timing of your bets?

thanks 4 the advices.
by the way r there any casinos which allow u to deal cards without betting in the game of baccarat and/or BJ?

and also,to eek, what is EV?
TQ

Expected Value. http://www.omegamath.net/Data/d4.2.html

I play for fun and pleasure but serious players know all about this stuff.
Clayman for example, corrected me because I stated that a ten up was a third of the time, when in fact it is 4/13. (30.77%)

A serious player like Clayman knows these things like the back of their hand.

I made the "betting patterns" comment because I am guessing that the poster is looking at a double up type of system.

'how many occasions on average would it occur when player/banker wins more than 8 times in a row '

From my own experience, I would not recommend this sort of system at ecasinos.

hi eek
i played at reefclub.
this 1,2,4... strategy did me good in the beginning n i won $600.The day after i cashed in part,things crumbled.
8 occasions i had player/banker winning more than 9 times in a row.and all that in less than 1200 hands.incredible.
in a totally fair system, u can win with this strategy,i believe.

raje
then try mine:
bet on whatever happened in the last hand, then you would only lose when the hands go:
BPBPBPBPBPB
which means you win whenver there is streaks!

Originally posted by bonuslover:
On avg. 3 times for Bacarrat
OK - I've been in bed for a few days but when I first read this, I just kind of had a full-body shudder and hoped someone else would reply. The best I could muster was picking on poor eek for being off a couple % (sorry eek - I think I was coming down with something. And thanks for the valentine, BTW)

But now, 5 days later, I have to stop the nightmares in the middle of the night, and ask,

How in the WORLD did you come up with this stat?

and

are you going to graduate as a Stat major? :)

Clayman: It just came outta my mind! Just jokking. What I did was simple:

Let's say the chance of gettin' Banker or Player is the same at 48% (sorry I dont' have time to look up the correct values).
The chance of gettin' exactly 8 Bankers in a row is
0.48**8= 0.282%
In 1000 hands, you have 993 chances of hitting this streak. (You won't make a streak of 8 starting at hand 994). So I should expect to get this particular streak
0.282% x 993= 2.8 times.
Hence "On avg. 3 times for Bacarrat"

Of course if you want the chance of having any streaks of 8, regardless of Banker or Player, it should be
2.8 x 2=5.6 per 1000 hands

To be more precise, it should be:
0.48**7 x 993 = 5.83 per 1000 hands

I should stress one point: I am calculating for streaks of exactly 8. That means, we don't multiple count in streaks longer than 8. That is if you hit a streak of 9, it will be counted as only one 8-streak, not two. In hindsight, I could have used a binomial distribution to actually run down everything, but I am too busy for that. The method I used above should at least buy you a feel of how it should be.

Better ask KX to see if he agrees. :D

Clayman, I am still deciding.


[This message has been edited by bonuslover (edited 02-19-2003).]

Thanks - I think I can sleep at night now.

I interpreted "lose more than 8 times in a row" as losing at least 9 times in a row. And the Banker chances are 45.87%, not 48%. So that would make it 1 in 510 for 8 Banker wins in a row and 1 in 1112 for 9 in a row. For Player, since it's 44.63%, it would be 1 in 635 and 1 in 1423. But you're doing the same thing with 48%. (1 in 355)

Even assuming they are both the same at 48%, I would think any streak of 8, regardless of Player or Banker, would just be the sum of the 2. (1 in 355 + 1 in 355= 2 in 355). In other words, I like your 5.6 better than your 5.83. Don't understand that one.

Given the actual probabilities of Banker & Player wins, I think the chances of getting ANY streak of exactly 8 of either Player/Banker is 3.53 out of a 1000. (1000/510+1000/635). Or once every 283 hands you'll get a streak of 8 of one or the other.

Now KX can correct us!

Anyway - looks like you're gonna graduate :)

THEN what are you gonna do?

Originally posted by Clayman:
THEN what are you gonna do?

Gambling..? :D :D :D


Thinking of Economics

Originally posted by Clayman:
In other words, I like your 5.6 better than your 5.83. Don't understand that one.

What you have done is multiplying 1/355 by 2 right?
See, if in my 8-streak, I don't care rather its a Banker or Player, then the first hand in that streak does not matter. Only the next 7 hands matter, agree?
Still assuming 0.48%, it would be
0.48%**7(not 8!) x 993
So I multiplied by 2.1 (1/0.48) instead of 2, hence the tiny difference.

Originally posted by bonuslover:
What you have done is multiplying 1/355 by 2 right?
See, if in my 8-streak, I don't care rather its a Banker or Player, then the first hand in that streak does not matter. Only the next 7 hands matter, agree?
Still assuming 0.48%, it would be
0.48%**7(not 8!) x 993
So I multiplied by 2.1 (1/0.48) instead of 2, hence the tiny difference.

Well actually I added 1/355+1/355, not multiplied.
I think if you pretend you are flipping a coin and look for 8 heads or 8 tails in a row, it has to come out to 1 in 128 or 7.8125 per 1000. I don't think your way will.

I said you were gonna graduate but I didn't say with an "A" :)

"I think if you pretend you are flipping a coin and look for 8 heads or 8 tails in a row, it has to come out to 1 in 128 or 7.8125 per 1000"


maybe i m wrong but shouldn't the calculation be like this:

let's say we flip a coin 8 times.(1 set).
probability of head or tail 8 times in a row is 1/2^8 + 1/2^8.
i.e. if we try 128 sets,1 in 128 it's going to be head or tail.(correct so far).

but each set of test consists of 8 flipping of coins.
shouldn't it be that the number of times u have to spin a coin is 128 x 8 = 1024 in order to have head or tail 8 times in a row?

but ofcourse u don't play in sets of 8 but continuously.still the calculation would be complex n involve multiplying by a cofactor inherent to that game.


anyway calculations aside,what do your experiences say?(in BJ and baccarat)

thank u.

Originally posted by raje:
1 in 128 it's going to be head or tail.(correct so far).
And correct, period.
If you flip a coin 1024 times, you can expect to have 8 sets of 8 in-a-row of either heads or tails.
Maybe thinking of 2 in a row with 4 flips would help you.
I gave you the probabilities for Player and Banker 8 & 9 streaks above. You can relate your experience to that.

Let me join this Math Seminar. :)

The way you guys calculate is correct, but the input data not quite.

Yes, baccarat appears to have 3 events: Banker, Player, Tie. And,
P(Banker) = 45.84%; P(Player) = 44.61%; P(Tie) = 9.54%

Since Tie events neither affect Banker/Player Bets nor Streaks, hence in actual sense, we can disregard all Ties.

Having ignored all Ties, the picture now looks:
P(Banker) = 45.84%/(45.84 + 44.61) = 50.68%
P(Player) = 44.61%/(45.84 + 44.61) = 49.32%

The prob. of 8-Banker streak:
0.5068**8 = 1 in 230 games = 4.4 in 1000 games.

The prob. of 8-Player streak:
0.4932**8 = 1 in 286 games = 3.5 in 1000 games.

Pretty close with Clay's coin example. A larger discrepancy with BL's answer due to he "lazily" (quote) assumed P(Banker/Player) = 48%.

My calculation accords with my record sheets I collected previously in Macau B&M casinos. I kept about 260 shoes, about 15,600 games, of Baccarat real deals.

Originally posted by HKGambler:
Having ignored all Ties, the picture now looks:
P(Banker) = 45.84%/(45.84 + 44.61) = 50.68%
P(Player) = 44.61%/(45.84 + 44.61) = 49.32%

So does this mean, if event P and Event B each won 10% of the time with 80 % of results being ties, the odds of getting a streak of 8 of either P or B would be:

.1/(.1+.1)=.5 etc.

and therefore end up being the same as the odds of 8 heads or tails using a coin flip?
Somehow, I don't think so.

Actually, Baccarat is like flipping a thick coin, where the prob. of the coin standing on the edge is 9.54%. In case of the coin standing on the edge, a re-flip is required for those who bet on H/T to see until it lands on H/T.

In that case, the casino can still accept stakes on a coin standing on the edge to pay the odds 1:8. Does this side bet affect the odds of H/T? No, the odds of H/T is still 1:1.

In Baccarat, the difference being that B has a slight advantage over P (50.68% vs 49.32%), while H/T has equal chances in coin flipping.

The problem on your mind might have been why we could/should disregard Ties, in calculating the B/P probabilities. Since T is only a side bet which does not affect the win or lose of B/P bets. As illustrated by the thick coin example above.

Another look. As we all know the HA of B & P is 1.06% & 1.23% respectively. With 5% comm. charged on Banker & no comm. on Player, this closely matches with their prob. being 50.68% & 49.32% to make it a fair game.

How could that possible for B/P's prob. = 45.84%/44.61% to yield a low HA of 1.06% & 1.23%?

Originally posted by HKGambler:
How could that possible for B/P's prob. = 45.84%/44.61% to yield a low HA of 1.06% & 1.23%?
Thanks for trying to straighten out my thinking. Keep trying. I will too.

I think the HA of 1.06%, or any HA, comes from at what odds a bet is paid and not simply the frequency with which the hands occur. So using the Wiz's frequencies it's pretty easy to see how he gets to the HA. But the HA has nothing to do with how often something will occur or how many times in a row it will occur. The odds of getting 8 ties in a row are what they are no matter how they are paid off or what HA is attached to it. If blackjack's got paid off 10-1, they wouldn't occur any more or less often.

Anyway that leads me to ask, again, how would you determine the probability in my example of a coin that comes up heads and tails 10% of the time each but has a really thick edge that comes up 80% of the time coming up 8 times in a row heads?
Using the same methodology that you used in the Baccarat example seems to yield an impossible result. In other words I just don't see how the ratio of heads to tails occuring to each other is relevant. The only thing that matters is simply how often they actually occur. You can't just pretend ties don't happen, as you seem to suggest.


[This message has been edited by Clayman (edited 02-22-2003).]

"I think the HA of 1.06%, or any HA, comes from at what odds a bet is paid and not simply the frequency with which the hands occur....But the HA has nothing to do with how often something will occur or how many times in a row it will occur."

I see your point. Casinos can offer different odds, e.g. on baccarat ties, some 1:8, some 1:9, thereby different HA.

But casinos base on the chance of success (true odds) to determine the payoffs (casino odds), otherwise the game will be far from feasible, ie. either casinos or players will go broke in minutes. That's why we can never find one casino which offers BJ payoff 1:10. I admit that I should have specified true odds & casino odds to make my point clear in my last post, since true odds is easily confused with casino odds.

In Baccarat, with the existence of Ties, the chance of occurance is not equal to the chance of success (winning). Whereas in most other games, the two is equal.
The chance of OCCURANCE of a banker/Player Event = 45.84%/44.61%.
The chance of SUCCESS of a Banker/Player Bet = 50.68%/49.32%.
Therefore, 50.68%/49.32% is used to calculate B/P streaks.

Below examples are considered to be 8-Banker streaks. Unless you don't think so.
- BBBTBBTBBB
- BTTBBBBBBB
- BBBBTBBBB

"How would you determine the probability in my example of a coin that comes up heads and tails 10% of the time each but has a really thick edge that comes up 80% of the time coming up 8 times in a row heads?"

Looks like your coin is a Canadian Nickel 5 inches thick. :) This is a good example to illustrate how we should differentiate the chance of occurance with the chance of success once again. Here, the chance of occurance of a H/T Event = 10%, the chance of success a H/T Bet = 50%. True odds = 1:1, not 1:9. Exactly my point. Remember, this game rules that the 80% chance landing on the thick edge does not disqualify your H/T Bet. Of course in reality no one designs such crazy games. Thus, we can ignore all ties & use 50% (P(success)) to calculate streaks.

sorry to bother u guys again,but in my newbeeish mind i'm thinking:

is it not that 1 set consists of 8 hands?
n the the chances of 8 P/B win in a row is 1 in 128 sets and not hands?
n therefore the chances of a 8 P/B wins in a row is 1 in 128x8 hands?

but since HKGambler says your calculations correlate with actual experience, u guys must be right.
but i couldn't help wondering.

Originally posted by HKGambler:
Below examples are considered to be 8-Banker streaks. Unless you don't think so.
- BBBTBBTBBB
- BTTBBBBBBB
- BBBBTBBBB
I was thinking after my last post that this maybe has been our problem all along.
Whenever I read stuff like "what are the chances of 8 wins in a row" or "I lost 10 times in a row", etc I always exclude ties in my mind. So, no, I don't (or wasn't) consider those to be streaks of 8 banker wins. I call them "no-lose" streaks :)

And, if we are going to include ties as not ruining a win streak, I'm still not convinced your way is right. Sticking with our Baccarat %'s, let's jump down to a win streak of 2, as opposed to 8. It seems you would say the odds of this happening are .5068^2=1 in 3.9 hands (as opposed to .5068^8). But the odds of
BTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTB
occurring are not the same as
BTB,
or even
BB
even though all would be win streaks of 2 in your definition and apparently likely to occur on average every 3.9 hands by your calculations.
Just as the odds of getting 8 "B"'s and 2 "T"'s (your first 2 examples) and getting 8 "B"'s and 1 "T" (your 3rd example) can't both be 1 in 230 hands like you say.
I think including ties as not ruining a "win" streak is a whole different question and would have to be analyzed in a different way entirely.

"is it not that 1 set consists of 8 hands?
n the the chances of 8 P/B win in a row is 1 in 128 sets and not hands?
n therefore the chances of a 8 P/B wins in a row is 1 in 128x8 hands?'

raje- I don't know whether your concept "1 set consists of 8 hands" really matters. I am talking about the prob. of WINNING a Banker Bet = 50.68%. And that how many Ties OCCUR in between do not affect a winning streak.


"Below examples are considered to be 8-Banker streaks. Unless you don't think so.
- BBBTBBTBBB
- BTTBBBBBBB
- BBBBTBBBB"

Clayman- I know where the problem is. You don't think they are 8-Banker streaks. I think in actual sense they are.

HKGAMBLER
It must have cost you a fortune to play that many hands in Lisboa...I am not talking about the theoretical house edge if you know what I mean :D

You mean the other expenses: hydrofoils, hotels, dinners, night clubs, and so on?

Nah, I used to rent a room (HK$1500/month, cheap, eh?) & stayed for 2~3 days per trip. Hydrofoils cost about HK$300 each round. And I didn't chase after women, no interest! :eek: So, no big money to cost. :eek:

Do you know why I lingered in the casinos for so long? I wanted to test out a betting system & finally found out it didn't really work. :(

Actually, the Baccarat shoes were not all played by me, many of them I collected from adjacent tables. But I made sure the records are complete & accurate, for the sake of doing statistics myself.

Originally posted by HKGambler:
And that how many Ties OCCUR in between do not affect a winning streak.
How many ties occur in between certainly does effect the answer of how OFTEN, in terms of 1 in x number of hands, a win streak will occur.

At the risk of beating a dead horse, and to show what I think is the fallacy of the logic you used in the Baccarat example with P/B/T %'s of 45.84,44.64, & 9.55 my point is, if we do use this 50% probability of success for my 5 inch thick Canadian nickel (I like that!), employing your logic, we get an absurd answer of .5^8=1 in 256 games, do we not?

Is this not the answer your methodology would yield?
If not, what answer does your methodology yield in terms of 1 in x games?

And, with the same coin, for a win streak of 2, your meyhodology would yield .5^2=1 in 4 hands. And since 80% of the hands will be ties, this can't possibly be right.

Originally posted by HKGambler:
You mean the other expenses: hydrofoils, hotels, dinners, night clubs, and so on?
No...that's not exactly what I am talking about. I am interested in that $1500 room though...I am talking about the *extra* commission. Maybe you haven't won enough to experience it :D

HKgambler,

"raje- I don't know whether your concept "1 set consists of 8 hands" really matters. I am talking about the prob. of WINNING a Banker Bet = 50.68%. And that how many Ties OCCUR in between do not affect a winning streak."


i couldn't care less about those ties thing.
it's a push anyway.
but what i do care is how many times there is a streak of more than 8 times in 1000 hands.
if it's less than twice, than u could walk away a rich man using Martingale strategy.

but since your experience suggests otherwise,i rest my case.

(n yes, PBTTBBBBBBBP IS 8 times in a row as far as this strategy is concerned)


clayman,
"5^8=1 in 256 games, do we not?"
don't u mean 2^8?

Originally posted by raje:
i couldn't care less about those ties thing.
it's a push anyway.
but what i do care is how many times there is a streak of more than 8 times in 1000 hands.
clayman,
"5^8=1 in 256 games, do we not?"
don't u mean 2^8?

You should care about the number of ties that will occur because that effects how often you will be able to get win streaks for any given number of hands. I'm guessing you mean how often will the streaks occur per every 1000 times a win or loss occurs, no matter the number of hands it will take to get the 1000 decisions.

I meant what I said which was 0.5^8. That's one-half. I think you missed the decimal point.

Good luck with your Martingdale Strategy. There's always the chance of a long streak wiping you out. Sounds like you have already discovered that.

Originally posted by HKGambler:

Since Tie events neither affect Banker/Player Bets nor Streaks, hence in actual sense, we can disregard all Ties.

Having ignored all Ties, the picture now looks:
P(Banker) = 45.84%/(45.84 + 44.61) = 50.68%
P(Player) = 44.61%/(45.84 + 44.61) = 49.32%

The prob. of 8-Banker streak:
0.5068**8 = 1 in 230 games = 4.4 in 1000 games.

The prob. of 8-Player streak:
0.4932**8 = 1 in 286 games = 3.5 in 1000 games.



Clayman, read my first post above.

The games I referred to are only the games having each & every ties ignored, as if they are non-existent. You have been neglecting this important concept.

i.e. When I said 4.4 in 1000 games above, it meant 4.4 in 1000 no-tie-games.

That is why you have been disagreeing all along. :)

Using Binomial Distribution to run down everything (as BL mentioned earlier), you'll discover that your methodology will converge to mine.

I can do the rundown, later when I have more time.

And raje- having cleared things up with Clayman, I am confident that you can trust my figures (based on the ignoring all Tie games concept).

Also, don't ever believe there are less than two 8-streaks in 1000 games. Simply not true. Moreover, you won't get rich with Martingale.

Originally posted by HKGambler:
When I said 4.4 in 1000 games above, it meant 4.4 in 1000 no-tie-games.
Yes, exactly. I just think it's an important distinction to make. Otherwise one might think it will happen 4.4 times after $1000 in wagers rather than the reality you will have to wager more than $1000 to make it happen.
Exactly how much more? I'll let you tell me :) I'm worn out!




[This message has been edited by Clayman (edited 02-25-2003).]

yes,yes
i won't use martingale though it's very tempting.

but i notice that the more variety there is in a game,the less volatile it is.
e.g. BJ has less streaks than baccarat n baccarat less than craps n craps less than roulette.
(by volatile, i mean longer n more frequent streaks)

raje- FYI, the longest streaks I encountered was 13-B in B&M & 11-B online. I played relatively much fewer games online. And 8-B/P streak to me was not unusual. Nice to hear you heed our advice.

Clayman- 1000 no-tie-games = 1105.5 overall games.

OK, let me start doing the rundowns now. You guys must be lazier than me.

I'm progressed in Baccarat analysis thru the discussions with you guys. Thanks.

Rundowns: Using Clayman's Counting Ties Methodology.

Given the prob. of occurance (Po): Banker = 45.84%; Tie = 9.55%; Player = 44.61%

(A) The prob. of WINNING a Banker Bet,
= Po(B+TB+TTB+TTTB+TTTTB+¡K+¡K.)
= 0.4584 + 0.0955*0.4584 + 0.0955^2*0.04584 + 0.0955^3*0.4584 +¡K.+¡K.)
= tending to 0.5068
= My Methodology Excluding all Ties, that is 0.4584/(0.4584 + 0.4461)

(B) The prob. of WINNING a 8-Banker Streak, where their prob. of occurance (Po) with:
- (0 Tie in between) i.e. BBBBBBBB = 0.4584^8
- (1 Tie in ./.) e.g. BBTBBBBBB = 8*0.0955*0.4584^8
- (2 Ties in ./.) e.g. BTBBBTBBBB =36*0.0955^2*0.4584^8
- (3 Ties in ./.) e.g. BBTBBBTTBBB = 120*0.0955^3*0.4584^8
- (4 Ties in ./.) e.g. BBBTTTBBBTBB = 330*0.0955^4*0.4584^8
- (5 Ties in ./.) e.g. BBTBTTBBTBTBB = 792*0.0955^5*0.4584^8
and so forth.....

The summation is tending to 0.004352
= My Methodology Excluding all Ties, that is 0.5068^8

Two Different Approaches match up! Wonders of Maths!

Originally posted by HKGambler:
I'm progressed in Baccarat analysis thru the discussions with you guys. Thanks.
Me too . And thank you. These simple questions aren't always so easy.
Never played Bacarat but I was wondering why you (or anyone) like to play it. To me it seems like you just sit there, pretty much picking heads or tails with absolutely no "skill" involved whatsoever. Is there ANYTHING to actually think about?
I guess it seems I would just sit there placing Banker bet after Banker bet and let the 1.06% eat me alive. Why play a game twice as bad (or more) as BJ?
Sounds like BL and raje like the game because they hope to catch a "streak". I guess I can see how a Martingale-like betting scheme would be tempting given you have a ~50% chance of getting your loses back on the next bet. But, overall it sounds boring as can be. Not so? Less HA than craps & roulette anyway. Do you play less/more than BJ?
Would it have more or less variance than BJ?
You know I'm a wimp compared to you guys, going for lowest HA as I do.

hkgambler
"- FYI, the longest streaks I encountered was 13-B in B&M & 11-B online"

13 seems to be a magic number.i checked with my gambling friends.their longest streak is also 13 in B&M casinos.
my personal experience in online casinos is also 13 in about 7000 hands.

clayman,
"I guess I can see how a Martingale-like betting scheme would be tempting given you have a ~50% chance of getting your loses back on the next bet. But, overall it sounds boring as can be."

boring?yes boring.
but when u get to $16 tension creeps up on u.
at $32 u sensethe spine tingling
at $64 u feel the adrenalin rush.
at $128 ur heart threatens to leap out.
at $256 u lose all sanity.

that's why i stop at $128.
u only grow a shade greyer,
only a little more clever,
but all the more wiser,
only to go back allover,
n grow a shade greyer. :)

Originally posted by raje:
at $128 ur heart threatens to leap out.

Especially when it's followed by 4 ties :)

Love your description

I hope I am not too late for the seminar ;)
The charm of baccarat is that it's a simple game, easy to analyze and offer a reasonable payout. For bonus hunters, this game is more stable than BJ because there is no double or split to raise your bet. Hence in the long run, you are less likely to bust your bank roll if you play baccarat although you will earn less bonus. Too bad most casinos won't let us play baccarat nowadays :(
As for the analyze part, there are only 3 outcomes for baccarat which make it easier to analyze the probability of busting based on your bet size (flat bet). I am temped to put down the equations here but they won't allow me to put factoria or summation signs here...

Originally posted by hhcfreebie:
I hope I am not too late for the seminar ;)
The charm of baccarat is that it's a simple game, easy to analyze and offer a reasonable payout. For bonus hunters, this game is more stable than BJ because there is no double or split to raise your bet. Hence in the long run, you are less likely to bust your bank roll if you play baccarat although you will earn less bonus. Too bad most casinos won't let us play baccarat nowadays :(
As for the analyze part, there are only 3 outcomes for baccarat which make it easier to analyze the probability of busting based on your bet size (flat bet). I am temped to put down the equations here but they won't allow me to put factoria or summation signs here...
Never too late!
I don't know - it would sort of seem with the higher HA one would be more likely to bust out.
Any chance you know the variance for baccarat?
Aw - you can put the fornmulae here - I thought a factorial sign was just an exclamation point and you can always just use the word "Sigma".
Thanks for your insight on the game.

hhc- "The charm of baccarat is that it's a simple game, easy to analyze and offer a reasonable payout. For bonus hunters, this game is more stable than BJ because there is no double or split to raise your bet. Hence in the long run, you are less likely to bust your bank roll if you play baccarat although you will earn less bonus. Too bad most casinos won't let us play baccarat nowadays"

Exactly.

Clayman- "I don't know - it would sort of seem with the higher HA one would be more likely to bust out.
Any chance you know the variance for baccarat?'

I think both- higher HA & higher variance- would be more likely to bust out. Of course, shallower pockets would too. :)

The variance of Baccarat can be estimated (quite close) using normal approximation, where:

SD = SQRT(npq)

Suppose for 100 no-tie-games, then,

SD= SQRT(100*0.5068*0.4932) ~= 5, which is obviously lower than that of BJ.


BTW- I have been unable to access WOL for the last 3 days. I'm now loading WOL thru safeproxy.net. Some guys in HK I know couldn't either. I hope Max knows what is happening.

Originally posted by HKGambler:
SD= SQRT(100*0.5068*0.4932) ~= 5, which is obviously lower than that of BJ.
Thanks HKG
Hope your acess problems clear up. I get periodic VERY slow page-loads but at least I have access.

I am taking my time off on gambling cause of a bad loosing streak. :(
Anyway I am more interesting in analyze games instead of playing.
Now lets get started with something simple: flip coins.
In case you forgot what factoria is, n factoria is equal to n x (n-1) x (n-2) ... x 1 so 3 factoria is equal to 3 x 2 x 1 = 6. I'll use the note F as factoria. Noted that 0 F = 1 instead of 1 (tricky isn't it? :D)
so if you flip a coin n times, assuming both side has equal chance of showing, what's the odds of m face showing?
the combination for m faces is:
nF/((n-m)F * mF)
for example, if you throw 3 times, the combination of face showing twice is:
3F/((3-2)F * 2F) = 3x2x1 / (1x2x1) = 3
To calculate the chance, you need to know what ALL combination is, that is, the combination of face showing 0,1,2,3 times and they can be calculated from the above equaltion. so the total combination is (1+3+3+1) = 8, then the chance of face showing on 3 rolls is:
3/8 = 37.5%
the chance of face showing "at least" 2 times is:
(3+1)/8 = 50%

I'll stop here and continue on next post ;)


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Online Casino Newbie.

ok! have you all done your homework today? ;)
I'll discuss what happened when the coin is in favor of one side to reflect the house edge.
Suppose the chance of showing face is 49% and chance of tail is 51% (house edge 2%), what will happen?
Lets started with general equation. For n trials of events and face shows m times, if chance of face showing is of chance x, the combination is:
nF / ((n-m)F * mF) * (1-x)^(n-m) * (x)^m
for example, 3 throw and face shows twice, and face have 49% chance of showing, the combination is:
3 * 0,51 * 0.49^2 = 0.36735
To calculate the chance of face shows twice, we need to know the summation of ALL combination, let me calculate them for ya!
0.13265+0.37485+0.36735+0.11765=0.9925
so the chance of face showing twice is:
0.36735/0.9925 = 37 %
and the chance of face showing at least twice is:
(0.36735+0.11765)/0.9925 = 48.87%
now you can see, with 2% house edge, if you divide your bet in three you only have 48.87% chance to get even.
what if we decrease our bet size? the trials (n) will increase and it's less likely to loose them all.you can use exactly the same equation to calculate your chance if you are playing a game called (coin flipping with 2% house edge).
As for buracate, there are 3 events, win loose and tie so the equation is slightly more complicated. You can calculate tie event aside. ;)
I'll stop for now. Let's see if anyone else are really interested in this kinda of topic :)

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Online Casino Newbie.