January 31st, 2010 at 10:31:21 PM
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So far, I've been looking into all this discussions on betting strategies, and I agree that in the long run, the only surefire way to profit in a casino, is to be the casino owner. ^_^

As far as I can see, discussions on betting strategies are for bets with about fairly even returns for its probable odds of occurring, such as 1 for 1 even bets or the 35 (36?) for 1 roulette bets, etc.

However, how do you factor in the bets which have a chance of getting more than the normal expected value for the bet? For example, in craps, the field bet gives a chance of getting 2 for 1 if you roll a 2 or 12, while other winning numbers only net you 1 for 1. Assuming one uses a martingale system, for the increased risk of getting fewer wins, say that every once in a while, after a small string of losses and the bet has been increased to a sizeable pot, then suddenly hitting a 2 or 12 and doubling that large pot to reset the martingale to 1 while winning a large pot. The longer streak of losing runs, the larger the potential winnings when a win also happens to be the 2 or 12.

Of course, this still falls under the martingale fallacy, even worse so, because the odds of winning are lower still due to the larger house edge in this bet, but what are your thoughts about such bets?

Alternatively, the player getting dealt a blackjack results in a 3 to 2 win payout, so a martingale player picks up an additional 50 percent of the pot size in addition to getting reset back to his initial starting unit, plus a win of that said unit.

As far as I can see, discussions on betting strategies are for bets with about fairly even returns for its probable odds of occurring, such as 1 for 1 even bets or the 35 (36?) for 1 roulette bets, etc.

However, how do you factor in the bets which have a chance of getting more than the normal expected value for the bet? For example, in craps, the field bet gives a chance of getting 2 for 1 if you roll a 2 or 12, while other winning numbers only net you 1 for 1. Assuming one uses a martingale system, for the increased risk of getting fewer wins, say that every once in a while, after a small string of losses and the bet has been increased to a sizeable pot, then suddenly hitting a 2 or 12 and doubling that large pot to reset the martingale to 1 while winning a large pot. The longer streak of losing runs, the larger the potential winnings when a win also happens to be the 2 or 12.

Of course, this still falls under the martingale fallacy, even worse so, because the odds of winning are lower still due to the larger house edge in this bet, but what are your thoughts about such bets?

Alternatively, the player getting dealt a blackjack results in a 3 to 2 win payout, so a martingale player picks up an additional 50 percent of the pot size in addition to getting reset back to his initial starting unit, plus a win of that said unit.

Last edited by: Elyt007 on Feb 1, 2010

February 1st, 2010 at 9:40:42 AM
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There is a qualitative answer to your question. Martingale and other betting strategies have no effect on house edge because they depend on the results of events in the past. People have memories, and we are geared by evolution to react to things that happened in the past. But little balls and cards have no memory and they don't care about the past. Payback schedule is irrelevant

People often don't like the field bet because there is high probability of losing the bet. The expected value is evened out by large bonus payouts on 2 and 12 which come every 1 out of 18 throws. Blackjack is similar, but the bonus payouts are much less (50% or 20%) and come 1 out of 21 hands. House edge is reduced by hitting, standing, doubling and splitting at appropriate times.

There is a quantitative answer to your question. In a game without any house edge like tossing a coin, you have to play 89 times until there is a 50/50 probability of getting 6 tails in a row. In a field bet in craps there is 20/36=55.556%

probability of losing and 16/36=44.444% of winning. The bonus payouts reduce the house edge to 2.778% (if triple a 12) which is much better than roulette. But because the odds of losing are so high, it only takes 53 rolls of the dice before there is more than a 50% probability of losing 6 field bets in a row. If you are playing martingale and you lose 6 in a row, you have lost 63*your initial bet.

People often don't like the field bet because there is high probability of losing the bet. The expected value is evened out by large bonus payouts on 2 and 12 which come every 1 out of 18 throws. Blackjack is similar, but the bonus payouts are much less (50% or 20%) and come 1 out of 21 hands. House edge is reduced by hitting, standing, doubling and splitting at appropriate times.

There is a quantitative answer to your question. In a game without any house edge like tossing a coin, you have to play 89 times until there is a 50/50 probability of getting 6 tails in a row. In a field bet in craps there is 20/36=55.556%

probability of losing and 16/36=44.444% of winning. The bonus payouts reduce the house edge to 2.778% (if triple a 12) which is much better than roulette. But because the odds of losing are so high, it only takes 53 rolls of the dice before there is more than a 50% probability of losing 6 field bets in a row. If you are playing martingale and you lose 6 in a row, you have lost 63*your initial bet.

February 1st, 2010 at 9:55:37 AM
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Quote:pacomartinIn a game without any house edge like tossing a dice,

tossing a coin, I think you mean

the Martingale can trade several sessions with small gains for one session where you get clobbered. That could actually be what some would like.

Even if so, I hate the bankroll needed. And the loss of control over how much I want to wager. And the fact that you are going nuts just trying to get back to even.

the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell! She is, after all, stone deaf. ... Arnold Snyder

February 1st, 2010 at 10:09:42 AM
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Personally, I feel that the field bet is a better candidate for a Martingale system than BlackJack, because in BJ, you not only have to factor in a BJ, but double downs and splits too.

So the field is easier to calculate. But it may not be a better bet.

And has been pointed out, here and counless other places, that betting systems are worthless.

A few months back, I posted a thread about a Craps Hardways System. Obviously, hardways are far from the 50/50 that a typical Martingale system relys upon.

The big downfall of this is that it depends upon the emotional dependence of not believing that you can lose twice as many times in a row as is the statistical norm.

And here's a thread about a Roulette System. It is a system for betting on a number - not betting red/black/etc as a typical Martingale System would assume.

So the field is easier to calculate. But it may not be a better bet.

And has been pointed out, here and counless other places, that betting systems are worthless.

You weren't looking hard enough.Quote:Elyt007As far as I can see, discussions on betting strategies are for bets with about fairly even returns for its probable odds of occurring, such as 1 for 1 even bets or the 35 (36?) for 1 roulette bets, etc.

A few months back, I posted a thread about a Craps Hardways System. Obviously, hardways are far from the 50/50 that a typical Martingale system relys upon.

The big downfall of this is that it depends upon the emotional dependence of not believing that you can lose twice as many times in a row as is the statistical norm.

And here's a thread about a Roulette System. It is a system for betting on a number - not betting red/black/etc as a typical Martingale System would assume.

I invented a few casino games. Info:
http://www.DaveMillerGaming.com/
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁

February 1st, 2010 at 10:46:51 AM
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Statistics uses the term independent events to describe two events whose outcome are unrelated to each other. But human evolution is entirely related to learned behavior influencing future events. Once the berry makes you sick, you don't eat the berry again. If the wolves in the ravine eat your cavemate in a ravine, you don't go in that ravine.

The character in the movie Benjamin Button gets hit by lightning seven times. Everyone knows this unlikely to the point of essentially being impossible. But unless you are engaged in dangerous behavior like standing under trees or in open fields in lightning storms, being hit by lightning once doesn't make it any less likely that you will be hit a second time over anyone else being hit.

This innate distaste about random events occurring outside of human control forces people to invent patterns. If you see a craps player hit their point over and over there is a natural tendency to want to bet on that person making their point again. I have a friend who draws to inside straights because she thinks it is more challenging to drawing to an outside straight.

I know the Wizard talks about con men that exploit this innate human drive to sell artificial systems, but casinos are the biggest exploiter. They hand out papers and pencils at baccarat tables so that people can discover patterns. A casino knows that if you put up an electronic board that keeps track of the last dozen roulette wheels will make people run over and bet the opposite color if it becomes heavily shaded in one direction or the other.

Try putting a list of 1's and 0's in a long line in an Excel spreadsheet. Do it once with using the random number generator [formula is =int(2*rand()) ]. If you make it 350 columns long there is better than a 50% chance that you will have a streak of at least 8 (either ones or zeros).

Try getting a friend to make a random list of ones and zeros in an Excel spreadsheet. Stress that you want them to make it as random as possible. The probability is very low that they will put streaks as long as 8, and in fact they often don't make them longer than five in a row. You can quickly tell which data is artificial and which is real. You can use techniques like this to determine when people are stuffing ballot boxes or are faking data for forms.

The character in the movie Benjamin Button gets hit by lightning seven times. Everyone knows this unlikely to the point of essentially being impossible. But unless you are engaged in dangerous behavior like standing under trees or in open fields in lightning storms, being hit by lightning once doesn't make it any less likely that you will be hit a second time over anyone else being hit.

This innate distaste about random events occurring outside of human control forces people to invent patterns. If you see a craps player hit their point over and over there is a natural tendency to want to bet on that person making their point again. I have a friend who draws to inside straights because she thinks it is more challenging to drawing to an outside straight.

I know the Wizard talks about con men that exploit this innate human drive to sell artificial systems, but casinos are the biggest exploiter. They hand out papers and pencils at baccarat tables so that people can discover patterns. A casino knows that if you put up an electronic board that keeps track of the last dozen roulette wheels will make people run over and bet the opposite color if it becomes heavily shaded in one direction or the other.

Try putting a list of 1's and 0's in a long line in an Excel spreadsheet. Do it once with using the random number generator [formula is =int(2*rand()) ]. If you make it 350 columns long there is better than a 50% chance that you will have a streak of at least 8 (either ones or zeros).

Try getting a friend to make a random list of ones and zeros in an Excel spreadsheet. Stress that you want them to make it as random as possible. The probability is very low that they will put streaks as long as 8, and in fact they often don't make them longer than five in a row. You can quickly tell which data is artificial and which is real. You can use techniques like this to determine when people are stuffing ballot boxes or are faking data for forms.

February 1st, 2010 at 7:02:43 PM
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Thanks for all your answers! I was actually going to use Sic Bo as my example, until I realised I got my math wrong. :P

I was actually talking more about how it would affect strategy, since in an even bet, Martingalers increase their bet until a win happens, resetting back to their starting unit and making a win of that starting unit.

If someone martingales in a bet which has a bonus win, should he incorporate the bonus winnings as part of his expected winnings?

Alternatively, if he decides to set aside all the bonus winnings (effectively slowly withdrawing from the game), what would be the likelihood that a player breaks even or even makes a surplus before he busts out of the game with an empty bankroll?

I was actually talking more about how it would affect strategy, since in an even bet, Martingalers increase their bet until a win happens, resetting back to their starting unit and making a win of that starting unit.

If someone martingales in a bet which has a bonus win, should he incorporate the bonus winnings as part of his expected winnings?

Alternatively, if he decides to set aside all the bonus winnings (effectively slowly withdrawing from the game), what would be the likelihood that a player breaks even or even makes a surplus before he busts out of the game with an empty bankroll?

February 2nd, 2010 at 11:38:05 AM
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In craps, a bonus winning would be on a field bet on the 2 or 12 which pays double and triple. But then you are talking about a HA of 11.11% with keeping the bonuses, which makes it a bad martingale. Better off to play roulette.

In blackjack, a bonus winning would be a "blackjack". But with Martingaling in Blackjack, you might be forced to double down, split, and possibly lose an already leveraged hand.

In blackjack, a bonus winning would be a "blackjack". But with Martingaling in Blackjack, you might be forced to double down, split, and possibly lose an already leveraged hand.

-----
You want the truth! You can't handle the truth!

February 2nd, 2010 at 4:06:03 PM
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Quote:Elyt007Alternatively, if he decides to set aside all the bonus winnings (effectively slowly withdrawing from the game), what would be the likelihood that a player breaks even or even makes a surplus before he busts out of the game with an empty bankroll?

Roughly 2:1 against you accomplishing that with no house edge. Even higher depending on the game. With no HA and a minimum bankroll of 63*initial bet (which would hold you for up to 6 losses in a row), you have to bet 89 times before your probability of losing 6 in a row is over 50%. But on average you must bet 126 times before doubling your bankroll.

If you reverse the Martingale so that every time you win you double your bet, then each run will end with a -1*unit, instead of +1*unit. You are gambling that you will hit a streak of 6 wins and cash out, before you whittle away your bankroll one unit by one unit. This Let it Ride strategy is less onerous, because you will walk away with less than double your bankroll. If your initial bankroll is 63 units, then the first 20-40 streaks will end up at -1 each time. When you hit the winnning streak you won't have double your bankroll, but if you must walk away satisfied.

Let me re-emphasize that no betting system changes the fundamental expectation of the game. The Let it Ride strategy is more likely to work, because the goal is less than doubling your bankroll. All betting systems use past results as a fundamental variable, and past results only means something to people, not to inanimate objects which are not altered in some physical way by the past.

February 19th, 2010 at 12:40:31 AM
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Thanks for all the replies!

Currently, I'm trying a martingale strategy on the dozens bet (pays 3 for every 1).

What I'm doing :

Playing it like a regular martingale, capping myself at a loss streak of 6. Taking 2/3 of wins to continue the martingale as usual, and reserving the remaining 1/3 as pure winnings to be taken home.

Goal : to break even or make a profit before the initial bankroll goes belly up, in which I'll walk away with whatever I set aside.

Reasoning :

Using simple math (and not counting the green 0 and 00), its about 1/2 to win and 1/2 to lose on an even bet, right? But by exposing myself to an additional 1/6 of risk, I can increase my potential winnings per bet from +1 unit at end of losing streak, to (1+entire amount of last bet that won)units. Of course, the green 0's throw off the exact percentages, but the winning amount reasoning still stands.

Progress so far :

Don't really have a computer simulator program written up to test a billion simulations, so I'm just testing it against the free play roulette programs thats found everywhere. Unfortunately, I'm only breaking even so far, will let you know how it turns out. :D

Currently, I'm trying a martingale strategy on the dozens bet (pays 3 for every 1).

What I'm doing :

Playing it like a regular martingale, capping myself at a loss streak of 6. Taking 2/3 of wins to continue the martingale as usual, and reserving the remaining 1/3 as pure winnings to be taken home.

Goal : to break even or make a profit before the initial bankroll goes belly up, in which I'll walk away with whatever I set aside.

Reasoning :

Using simple math (and not counting the green 0 and 00), its about 1/2 to win and 1/2 to lose on an even bet, right? But by exposing myself to an additional 1/6 of risk, I can increase my potential winnings per bet from +1 unit at end of losing streak, to (1+entire amount of last bet that won)units. Of course, the green 0's throw off the exact percentages, but the winning amount reasoning still stands.

Progress so far :

Don't really have a computer simulator program written up to test a billion simulations, so I'm just testing it against the free play roulette programs thats found everywhere. Unfortunately, I'm only breaking even so far, will let you know how it turns out. :D

February 19th, 2010 at 6:38:51 AM
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ElyT007: I am kind of amazed that with all the math "expertise" exhibited on this site that there seems to be no one thinking a little bit outside the box.

First, I am not a real fan of any Martingale systems wagering. Most all believe that unless there is an unlimited bankroll and no table limits, losses will bankrupt most any player.

However, for fun, try this at the craps table.

After the point is established ($5 table), Place the 9 for $5 (4 ways to win and 6 ways to lose). A 7 out you lose then double the bet on the 9, again after the point is established.

What is neat is that the odds paid on a win along with doubling the bet provides a net win for all previous losses. The last wager (the 6th) will be $160. The odds during the six points (or $175 in 5 previous wagers) say that the 9 will show (not a certainty). The payout on the last bet of $160 will be $224. Your net win will be $49.00. The bad news is that if the sixth wager loses, the total loss would $315. Not a great return, but it can be fun. I have tried it three times during '09 - won all three times at the fouth bet or lower. If you want better odds of winning, the 6 or 8 are available starting at the $6 bet level.

Think about it.

tuttigym

First, I am not a real fan of any Martingale systems wagering. Most all believe that unless there is an unlimited bankroll and no table limits, losses will bankrupt most any player.

However, for fun, try this at the craps table.

After the point is established ($5 table), Place the 9 for $5 (4 ways to win and 6 ways to lose). A 7 out you lose then double the bet on the 9, again after the point is established.

What is neat is that the odds paid on a win along with doubling the bet provides a net win for all previous losses. The last wager (the 6th) will be $160. The odds during the six points (or $175 in 5 previous wagers) say that the 9 will show (not a certainty). The payout on the last bet of $160 will be $224. Your net win will be $49.00. The bad news is that if the sixth wager loses, the total loss would $315. Not a great return, but it can be fun. I have tried it three times during '09 - won all three times at the fouth bet or lower. If you want better odds of winning, the 6 or 8 are available starting at the $6 bet level.

Think about it.

tuttigym