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Robert Fischer
02-17-2015, 08:26 PM
I was reading about "the law of independent trials". Can anyone tell me with a "yes" or a "no" whether these 4 games are subject to
"the law of independent trials"? Thanks

Roulette
Poker
Horse Racing
Blackjack

example:

Roulette YES
Poker YES
Horse Racing YES
Blackjack NO

tucker6
02-17-2015, 08:40 PM
I was reading about "the law of independent trials". Can anyone tell me with a "yes" or a "no" whether these 4 games are subject to
"the law of independent trials"? Thanks

Roulette
Poker
Horse Racing
Blackjack

example:
Can a horse lose so badly to another horse repeatedly where the beaten horse is influenced in future races between them? Some horses like sandy tracks. Some like mud. Are they still independent trials?

Robert Fischer
02-17-2015, 08:45 PM
Can a horse lose so badly to another horse repeatedly where the beaten horse is influenced in future races between them? Some horses like sandy tracks. Some like mud. Are they still independent trials?

Interesting ideas. I don't know. What do you think?
How about the other games in question, does shuffling and surveillance make them all 'independent trial' games?

tucker6
02-17-2015, 08:48 PM
To me, only roulette would be independent each spin. I can see the other games as not independent from event to event.

Robert Fischer
02-17-2015, 09:06 PM
To me, only roulette would be independent each spin. I can see the other games as not independent from event to event.
so
Roulette YES
Poker NO
Horse Racing NO
Blackjack NO
?

I'm not the card player that many of you are.
Also, quite interesting that you refer to Horse Racing as an "interdependent" game, Tucker.

098poi
02-17-2015, 09:23 PM
I think poker would be a yes also. Every time the cards are dealt what happened previously has no effect on this hand. If 4 hands were dealt and in each hand one player was dealt 4 of a kind before any draw the 5th hand would have the exact same odds of another 4 of a kind being dealt.

Searching the web does mention craps and roulette but not poker so maybe I am in error

ReplayRandall
02-17-2015, 09:48 PM
I was reading about "the law of independent trials". Can anyone tell me with a "yes" or a "no" whether these 4 games are subject to
"the law of independent trials"? Thanks

Roulette
Poker
Horse Racing
Blackjack


Is this a question of the trial outcomes of the game, or the winnings from each trial?

therussmeister
02-17-2015, 09:53 PM
I think poker would be a yes also. Every time the cards are dealt what happened previously has no effect on this hand. If 4 hands were dealt and in each hand one player was dealt 4 of a kind before any draw the 5th hand would have the exact same odds of another 4 of a kind being dealt.

Searching the web does mention craps and roulette but not poker so maybe I am in error
Which cards are dealt is independent, but how the hand is played is quite dependent on past events.

Robert Fischer
02-17-2015, 10:03 PM
Is this a question of the trial outcomes of the game, or the winnings from each trial?
Whichever one you could make a case for.

ReplayRandall
02-17-2015, 10:14 PM
Whichever one you could make a case for.
Unless you have identified a biased wheel in roulette, then it's the only game I say "yes".....BTW, where are you going with this?

Robert Fischer
02-17-2015, 10:27 PM
BTW, where are you going with this?

good feedback and new ideas

tucker6
02-17-2015, 10:32 PM
Yes, roulette would be the only true independent game listed imo. The other three are influenced by past events from a gaming perspective.

Robert Fischer
02-17-2015, 11:19 PM
Can a horse lose so badly to another horse repeatedly where the beaten horse is influenced in future races between them? Some horses like sandy tracks. Some like mud. Are they still independent trials?
Could consecutive races on the same day's 'card' be dependent upon each other (interdependent) in any ways?

thaskalos
02-17-2015, 11:41 PM
Roulette.....,,...YES
Poker........,,...YES
Horse Racing....YES
Blackjack..... NOT YET :)

ReplayRandall
02-17-2015, 11:45 PM
Roulette.....,,...YES
Poker........,,...YES
Horse Racing....YES
Blackjack..... NOT YET :)
Poker and horse racing, yes?......A little explanation, if you will....

thaskalos
02-18-2015, 12:01 AM
Poker and horse racing, yes?......A little explanation, if you will....

Poker hands and horse races are "individual trials"...with their own, unique, peculiarities and characteristics. What happens in one "trial" has no bearing on the outcome of a latter one. Yes...horseplayers are fond of their ability to identify "biases"...but my own opinion is that they are mistaken much more often than not. Poker players too think that they are capable of identifying "betting patterns" which, supposedly, affect the play of future hands...but they too are mistaken much more often than not.

In gambling, it's dangerous to think that you know something...when you really don't.

ReplayRandall
02-18-2015, 01:00 AM
Poker hands and horse races are "individual trials"...with their own, unique, peculiarities and characteristics. What happens in one "trial" has no bearing on the outcome of a latter one. Yes...horseplayers are fond of their ability to identify "biases"...but my own opinion is that they are mistaken much more often than not. Poker players too think that they are capable of identifying "betting patterns" which, supposedly, affect the play of future hands...but they too are mistaken much more often than not.

In gambling, it's dangerous to think that you know something...when you really don't.
Subjectively, I see your points. However, I believe the OP was asking for an objective opinion, based on the "law" of independent trials......I could be wrong.. :eek:

tucker6
02-18-2015, 09:07 AM
Poker hands and horse races are "individual trials"...with their own, unique, peculiarities and characteristics. What happens in one "trial" has no bearing on the outcome of a latter one. Yes...horseplayers are fond of their ability to identify "biases"...but my own opinion is that they are mistaken much more often than not. Poker players too think that they are capable of identifying "betting patterns" which, supposedly, affect the play of future hands...but they too are mistaken much more often than not.

In gambling, it's dangerous to think that you know something...when you really don't.
So if horse #1 was fast early speed in previous races, would not jockey of horse #2 use this info to his advantage? Horse racing is interdependent in some respects and independent in others. However, as long as some aspects are interdependent, the answer to the OP question is NO imo. If there was no interdependence, then TimeformUS would not exist to assist in predicting outcomes.

With poker, the very fact that there are 'tells' in the game indicates that hands are interdependent.

thaskalos
02-18-2015, 12:28 PM
So if horse #1 was fast early speed in previous races, would not jockey of horse #2 use this info to his advantage? Horse racing is interdependent in some respects and independent in others. However, as long as some aspects are interdependent, the answer to the OP question is NO imo. If there was no interdependence, then TimeformUS would not exist to assist in predicting outcomes.

With poker, the very fact that there are 'tells' in the game indicates that hands are interdependent.
Well...I disagree. IMO...what "independent trials" means isn't whether or not prior jockey tactics can be used in the handicapping of future events. It's whether or not prior results INFLUENCE subsequent results...as in the case of blackjack...where the exclusion of certain cards seriously affects the composition of the deck...and greatly influences the player's future play. In the example that you've provided...yes, the presence of a given amount of early speed in a race is a handicapping concern, but it's "influence factor" is uncertain. Your jockey on horse #2 may indeed try to make use of his "knowledge" of the tactics employed by jockey #1...but who's to say if by so doing he will directly influence the result of this particular race? And, yes...TimeformUs assists in predicting outcomes. But PREDICTING doesn't mean INFLUENCING.

I play poker quite seriously, and have done so for a number of years. Are "tells" really a factor which would lead me to believe that poker as a game defies the "law of independent trials"? I would have to say, NO. Tells make for interesting poker movie fodder...but they don't actually amount to much in the scheme of things. And they certainly don't influence the future. There are no Mike McDermotts out there...in my opinion at least. :)

tucker6
02-18-2015, 12:35 PM
Well...I disagree. IMO...what "independent trials" means isn't whether or not prior jockey tactics can be used in the handicapping of future events. It's whether or not prior results INFLUENCE subsequent results...as in the case of blackjack...where the exclusion of certain cards seriously affects the composition of the deck...and greatly influences the player's future play. In the example that you've provided...yes, the presence of a given amount of early speed in a race is a handicapping concern, but it's "influence factor" is uncertain. Your jockey on horse #2 may indeed try to make use of his "knowledge" of the tactics employed by jockey #1...but who's to say if by so doing he will directly influence the result of this particular race? And, yes...TimeformUs assists in predicting outcomes. But PREDICTING doesn't mean INFLUENCING.

I play poker quite seriously, and have done so for a number of years. Are "tells" really a factor which would lead me to believe that poker as a game defies the "law of independent trials"? I would have to say, NO. Tells make for interesting poker movie fodder...but they don't actually amount to much in the scheme of things. And they certainly don't influence the future. There are no Mike McDermotts out there...in my opinion at least. :)
I look at tells as tendencies. Just like in football, a team will have a tendency to call a certain play in a certain situation. Poker is somewhat similar due to the nature of the player. Over time, a player will tend to play a certain hand in a similar manner. If I know an opponents tendencies, then as an opposing player, is that not an influence on how that hand is played and won/lost? I know what you are saying, and I can agree to that part of the discussion, but there is an interdependent part to the game as well. Poker isn't about who has the best hand. It is about who is left in the game with the best hand.

Robert Fischer
02-18-2015, 12:53 PM
Subjectively, I see your points. However, I believe the OP was asking for an objective opinion, based on the "law" of independent trials......I could be wrong.. :eek:

I'm happy with any contributions that Thaskalos is willing to offer on the subject.

The answer he gave is probably the commonly accepted answer , (with only blackjack being known for it's 'interdependence', thus the storied efforts of scammers, card-counters and 'teams', who have tried to beat the system, and the sophisticated surveillance employed by casinos in order to thwart those efforts).

In horse racing it depends upon how you define 'interdependence'.
Clearly 'form' of individual horses, and even 'key races' from 'past performances' is an accepted form of 'interdependence', although in the traditional gaming sense of 'consecutive trials' that Thaskalos seems to be referring to, Horse Racing would generally be considered subject to the Law of Independent Trials.

I have some ideas, and some specific interest in any ambiguity involved with Horse Racing and consecutive trials (consecutive races), and also a general interest in the topic at large.

thaskalos
02-18-2015, 12:59 PM
I look at tells as tendencies. Just like in football, a team will have a tendency to call a certain play in a certain situation. Poker is somewhat similar due to the nature of the player. Over time, a player will tend to play a certain hand in a similar manner. If I know an opponents tendencies, then as an opposing player, is that not an influence on how that hand is played and won/lost? I know what you are saying, and I can agree to that part of the discussion, but there is an interdependent part to the game as well. Poker isn't about who has the best hand. It is about who is left in the game with the best hand.
Tells are not clear cut tendencies...they are often just incidental occurrences. And they don't always mean the same thing. Nor do we ever get to know the other player well enough to form a picture of his "tendencies" in our mind. During the online poker phase...there were ways to keep track of a players betting tendencies over time...but player tendencies change. And players sometimes let other friends play on their accounts.

Yes...you can make "predictions" based on prior observations...but, as I said before, "predicting" that something would happen, and INFLUENCING it to happen...are not the same thing.

therussmeister
02-18-2015, 02:08 PM
Tells don't have to be real to influence the outcome of a hand. There only has to be a player that thinks they are real, and acts accordingly.

thaskalos
02-18-2015, 02:12 PM
Tells don't have to be real to influence the outcome of a hand. There only has to be a player that thinks they are real, and acts accordingly.
If you misidentify a mannerism of mine, and you mistakenly call my bet instead of folding your hand...have you really influenced the outcome of the hand in any way?

thaskalos
02-18-2015, 02:25 PM
Seeing that people whom I respect are disagreeing with me...I am starting to think that I have made a mistake in my interpretation of the "Law of Independent Trials". I took the term "interdependent" to mean that the results of prior events directly influenced the results of UPCOMING events...as in making the upcoming events more likely to occur as a consequence of what preceded them. I wasn't talking about whether or not these prior events influence people to PLAY differently during the upcoming events.

We all know that the past does not predict the future in roulette...and yet, past results FREQUENTLY affect the way that most roulette players make their future bets. If black comes up 7 times in a row in roulette, then the play at the wheel is DEFINITELY affected...whether players bet for the streak to end, or to continue. But this altered play of the players can hardly be considered an interdependent occurrence.

Robert Fischer
02-18-2015, 02:33 PM
Seeing that people whom I respect are disagreeing with me...I am starting to think that I have made a mistake in my interpretation of the "Law of Independent Trials". I took the term "interdependent" to mean that the results of prior events directly influenced the results of UPCOMING events...as in making the upcoming events more likely to occur as a consequence of what preceded them. I wasn't talking about whether or not these prior events influence people to PLAY differently during the upcoming events.

We all know that the past does not predict the future in roulette...and yet, past results FREQUENTLY affect the way that most roulette players make their future bets. If black comes up 7 times in a row in roulette, then the play at the wheel is DEFINITELY affected...whether players bet for the streak to end, or to continue. But this altered play of the players can hardly be considered an interdependent occurrence.

Thaskalos, I agree with you 100%. I also find your perspective here to be consistent with the traditional academic perspective.

Also very interesting, is that in your description of some of the ambiguity in our forum consensus, you've touched on some of the basic concepts, that make up the tip of the iceberg, of the idea, I have regarding consecutive trials/events/races within the context of the parimutuel system.

tucker6
02-18-2015, 04:38 PM
Seeing that people whom I respect are disagreeing with me...I am starting to think that I have made a mistake in my interpretation of the "Law of Independent Trials". I took the term "interdependent" to mean that the results of prior events directly influenced the results of UPCOMING events...as in making the upcoming events more likely to occur as a consequence of what preceded them. I wasn't talking about whether or not these prior events influence people to PLAY differently during the upcoming events.

We all know that the past does not predict the future in roulette...and yet, past results FREQUENTLY affect the way that most roulette players make their future bets. If black comes up 7 times in a row in roulette, then the play at the wheel is DEFINITELY affected...whether players bet for the streak to end, or to continue. But this altered play of the players can hardly be considered an interdependent occurrence.
Poker winning/losing is affected by more than just the cards, and so independence is lost. The cards themselves are independent, but winning/losing is not.

Here is a definition of the Law of Independent Trials:

"What do dice rolls, the spin of roulette wheels, and the spin of slots reels have in common? All of these are subject to what we call the law of independent trials. Simply put, each of these things, like the dice rolls you make in craps for example, are completely independent of any other event. So it doesn't matter how many times you shoot the dice, the next toss will not be affected by the previous toss.
By abiding by the law of independent trials casinos make a lot of profit. Casinos make their money through their house edge not to mention that some games or bets have lopsided odds. Games like roulette and slots are pure games of chance subject to the law of independent trials. It is interesting that slots is a major contributor to a casino's profit since many people play them. It is either that many players are unaware of the law of independent trials or are just ignoring the potency of this law and are caught up in their game.
Fortunately, there are casino games that are not subject to the law of independent trials. One prime example of such a game is blackjack. In blackjack, you have a fixed number of decks though the total number of decks used at a table varies. As the game progresses the type of cards that will be dealt later is influenced by what cards have already been dealt earlier. If a lot of low numbered cards were dealt earlier in the game then you can expect to find more high numbered cards showing up later.
The rules of the game also help make things work for players in blackjack. Doubling down, splitting, get paid three to two when you get a blackjack makes this game more favorable for players compared to games of pure chance. It is interesting to note that these rules weren't there when blackjack was first introduced. The house edge back then was about seven percent or even a lot higher. The addition of the said rules lowered the house edge and made the game more player friendly.
Players can take advantage of the absence of the law of independent trials in blackjack by improving their playing skills. They can make the house edge go down even further using basic strategy. It is a player's skill not the law of independent trials that has a direct effect on the outcome of a game.
Another important tool that any blackjack player can put to good use is card counting. If a player is able to tell if there are more high valued cards left on the deck then that player has the advantage. Learning to count will take some time however. The absence of the law of independent returns, and its effects, in blackjack is an advantage no one should miss."


The bolded area is what I refer to when describing the limitations of independence in some games. Is it about the role or the card, or is it how you use strategy in order to win? In blackjack it is card counting. In poker, it is playing the opponent. Roulette and craps are purely independent games because each spin or roll are independent AND there is no ability to influence winning beyond the spin and roll.

thaskalos
02-18-2015, 05:27 PM
The bolded area is what I refer to when describing the limitations of independence in some games. Is it about the role or the card, or is it how you use strategy in order to win? In blackjack it is card counting. In poker, it is playing the opponent. Roulette and craps are purely independent games because each spin or roll are independent AND there is no ability to influence winning beyond the spin and roll.

In theory, you are right. Poker is a PEOPLE game, played with cards. But that's not how the game is actually played by the vast majority of the people in this country today.

I walk in the poker room, and sit down to play no-limit holdem for 5-7 hours. I recognize no one at the table...and I know from the get-go that I will not see enough of their starting hands to make any accurate determinations about their playing "tendencies". You'd be surprised how rarely a good no-limit player will actually have to show down a starting hand...and there is no way to determine his playing style without seeing a fair number of his starting hands.

So...what do I do upon sitting at the table? I count on the fact that my playing "philosophy" will overcome the general playing philosophy of the players that I usually see. It's not player vs player; it's philosophy vs philosophy. What else can it be? I never played against the players that I am playing against today...and it's unlikely that I'll ever play with them again. Even if I can make some accurate assumptions about their play by the end of today's game...what good will it do me in the future? Will I ever see the same players again?

THAT'S the climate under which most of the players play today...whether they admit it or not. Poker isn't like boxing...or even fencing. It isn't a "personal" thing.

With this post...I will respectfully bow out of this discussion...because I don't want to turn this thread into a Thaskalos-against-Everyone affair. I know that my position on this issue is unpopular...but it is what it is. When it comes to gambling, there is "theory"...and then there is "practice". And the two are seldom in agreement.

tucker6
02-18-2015, 06:07 PM
In theory, you are right. Poker is a PEOPLE game, played with cards. But that's not how the game is actually played by the vast majority of the people in this country today.

I walk in the poker room, and sit down to play no-limit holdem for 5-7 hours. I recognize no one at the table...and I know from the get-go that I will not see enough of their starting hands to make any accurate determinations about their playing "tendencies". You'd be surprised how rarely a good no-limit player will actually have to show down a starting hand...and there is no way to determine his playing style without seeing a fair number of his starting hands.

So...what do I do upon sitting at the table? I count on the fact that my playing "philosophy" will overcome the general playing philosophy of the players that I usually see. It's not player vs player; it's philosophy vs philosophy. What else can it be? I never played against the players that I am playing against today...and it's unlikely that I'll ever play with them again. Even if I can make some accurate assumptions about their play by the end of today's game...what good will it do me in the future? Will I ever see the same players again?

THAT'S the climate under which most of the players play today...whether they admit it or not. Poker isn't like boxing...or even fencing. It isn't a "personal" thing.

With this post...I will respectfully bow out of this discussion...because I don't want to turn this thread into a Thaskalos-against-Everyone affair. I know that my position on this issue is unpopular...but it is what it is. When it comes to gambling, there is "theory"...and then there is "practice". And the two are seldom in agreement.
No reason to bow out. My blood pressure is still hopefully 120/80. Just a discussion. I agree with your philosophy vs philosophy take, but when you say that, it tells me that it is no longer just about the cards, and therefore poker is no longer independent. That's my point. I understand where you are coming from. I really do. I probably just take matters one step further than you.

thaskalos
02-18-2015, 06:19 PM
No reason to bow out. My blood pressure is still hopefully 120/80. Just a discussion. I agree with your philosophy vs philosophy take, but when you say that, it tells me that it is no longer just about the cards, and therefore poker is no longer independent. That's my point. I understand where you are coming from. I really do. I probably just take matters one step further than you.

Poker can't be just about the cards...because we all get the same cards in the long run. But it's about how you PLAY those cards...and how close you can keep to your ideal game. If you play with basically the same nucleus of opponents all the time, then you can taylor your game to the play of individual opponents. But that's quite a luxury these days...

thaskalos
02-18-2015, 06:34 PM
No reason to bow out. My blood pressure is still hopefully 120/80. Just a discussion. I agree with your philosophy vs philosophy take, but when you say that, it tells me that it is no longer just about the cards, and therefore poker is no longer independent. That's my point. I understand where you are coming from. I really do. I probably just take matters one step further than you.

Let's take a gambling game which also requires skill...but doesn't involve as much "personal interaction". Sports betting, for instance. The sports games are the same for all...and yet, the results of the bettors differ in accordance with their skill level. It's no longer "just about the games"...but the games themselves remain "independent trials".

Robert Fischer
02-18-2015, 07:12 PM
If black comes up 7 times in a row in roulette, then the play at the wheel is DEFINITELY affected...whether players bet for the streak to end, or to continue. But this altered play of the players can hardly be considered an interdependent occurrence.

how about if that altered play remained constant, yet the roulette was being offered at parimutuel odds?

Would predictable, 'altered' irrational betting behavior in a parimutuel system be considered 'interdependent'?

(I understand that this is a question which could only exist in a hypothetical format, but play along)

therussmeister
02-18-2015, 07:29 PM
If you misidentify a mannerism of mine, and you mistakenly call my bet instead of folding your hand...have you really influenced the outcome of the hand in any way?
Yes, but I influence the outcome more if I mistakenly fold.

Robert Fischer
02-23-2015, 06:51 PM
So in this fictional construct we are playing roulette...
And instead of a 2.7% house advantage with standard rules, we are instead playing a Parimutuel version, where the house takes it's 2.7% off the top, and the winners split the remaining moneys.
And black has now come up 7 times in a row.

This now presents a new dynamic.

The old Roulette Rules in the real world featured fixed odds. Thus, the predictable, irrational betting that was made following 'streaks' while amusing, remained an 'independent' betting trial of the previous spin.

the new Fictional Parimutuel Roulette Rules present a different dynamic. While the spin-outcomes themselves remain subject to the law of independent trials, the predictable, irrational betting that was made following 'streaks' now becomes an 'interdependent' betting trial when using the new Fictional Parimutuel Roulette Rules. This is because irrational betting behavior in a parimutuel market greatly changes the odds for perceptive rational players.

Predicting these irrational wagers in fictional parimutuel roulette is similar to card counting in blackjack.

thaskalos
02-23-2015, 08:04 PM
So in this fictional construct we are playing roulette...
And instead of a 2.7% house advantage with standard rules, we are instead playing a Parimutuel version, where the house takes it's 2.7% off the top, and the winners split the remaining moneys.
And black has now come up 7 times in a row.

This now presents a new dynamic.

The old Roulette Rules in the real world featured fixed odds. Thus, the predictable, irrational betting that was made following 'streaks' while amusing, remained an 'independent' betting trial of the previous spin.

the new Fictional Parimutuel Roulette Rules present a different dynamic. While the spin-outcomes themselves remain subject to the law of independent trials, the predictable, irrational betting that was made following 'streaks' now becomes an 'interdependent' betting trial when using the new Fictional Parimutuel Roulette Rules. This is because irrational betting behavior in a parimutuel market greatly changes the odds for perceptive rational players.

Predicting these irrational wagers in fictional parimutuel roulette is similar to card counting in blackjack.

How is predicting the irrational roulette wagers similar to card counting in blackjack? Is card counting also irrational?

Robert Fischer
02-23-2015, 08:53 PM
How is predicting the irrational roulette wagers similar to card counting in blackjack?

Predicting the irrational roulette wagers, and card counting, are similar because you do both by watching the action, and then wagering, once the previous trials indicate favorable odds.

tucker6
02-23-2015, 09:16 PM
Predicting the irrational roulette wagers, and card counting, are similar because you do both by watching the action, and then wagering, once the previous trials indicate favorable odds.
... but seeing black come up 7 times in a row is not the same as seeing seven straight hands full of face cards. Not similar at all. In roulette, there is no change in odds on the eighth spin, but there is a change in odds based on what the cards have done previously. Roulette is still independent.

I once was playing roulette in AC many moons ago, and after winning some cash at the BJ table, wandered over to the roulette wheel. I stood there for like 30 minutes trying to understand the betting scheme for the game. In all that time, never once did the first dozen come up on the board. So I belly up, and got $100 in chips. Bet $20 on the first dozen five straight times thinking this would be easy money, and walked away a few minutes later with only the knowledge that I'd never play roulette again. And I haven't lol.

Robert Fischer
02-23-2015, 09:24 PM
... but seeing black come up 7 times in a row is not the same as seeing seven straight hands full of face cards. Not similar at all. In roulette, there is no change in odds on the eighth spin, but there is a change in odds based on what the cards have done previously. Roulette is still independent.

Exactly.
This is why I had to create a construct for the example.
Once the parimutuel system is used, the value becomes tied into the behavior of the crowd rather than the percentage of a red or black spin.

Robert Fischer
02-23-2015, 09:44 PM
For example, let's say our study had shown that once 3 or more consecutive like-color spins occurred, that the Public would overbet the other color (e.g. 3 'red' in a row, and the public will now bet 'black' because the feel black is 'due'...)

"counting rules" for parimutuel roulette
---------------------------------------------
Consecutive spins of the same color form a 'count' equal to the number of consecutive spins in that set.

Bet when the count is 3 or greater.


red, black, black, red, red, black, black, black, black

0,.....0,.....+2,......0,...+2,...0,....+2,...+3(B ET), +4(BET)