Even taking 1x you reduce the edge from 1.41% to 0.85%, which beats every other game in the casino except 3:2 blackjack with proper basic strategyQuote:ChumpChangeI'll try to progress from 1X odds up to 3X odds. That HA looks harsh at 1X odds.

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how about this variation of the three point Molly - so that on your Come bets if a 7 is rolled they don't just reduce the loss but will get you a profit

example__________bet $25 pass line - the point is 6 - don't take odds - bet $50 on Come - the point is 4 - don't take odds - Bet $100 on Come - the point is 5

now take your odds - if you roll a 7 on the 2 come bets you still have a profit

of course, I'm not trying to say that this is a winning system

just an interesting - to me anyway - strategy

.

Quote:lilredrooster_____________

how about this variation of the three point Molly - so that on your Come bets if a 7 is rolled they don't just reduce the loss but will get you a profit

example__________bet $25 pass line - the point is 6 - don't take odds - bet $50 on Come - the point is 4 - don't take odds - Bet $100 on Come - the point is 5

now take your odds - if you roll a 7 on the 2 come bets you still have a profit

of course, I'm not trying to say that this is a winning system

just an interesting - to me anyway - strategy

.

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I have some questions.

Are you rolling the 7 after the three come bets are made? If so, you are losing $175 plus the odds.

If you are rolling the 7 on the next come out roll when your odds are "off" you are losing the flat bets of $175.

What are you betting when the 7 rolls that gives you a win? Is it the next step in a Martingale progression?

Quote:Ace2No such thing as a short handed shooter.

Quote:AlanMendelsonQuote:lilredrooster_____________

how about this variation of the three point Molly - so that on your Come bets if a 7 is rolled they don't just reduce the loss but will get you a profit

example__________bet $25 pass line - the point is 6 - don't take odds - bet $50 on Come - the point is 4 - don't take odds - Bet $100 on Come - the point is 5

now take your odds - if you roll a 7 on the 2 come bets you still have a profit

of course, I'm not trying to say that this is a winning system

just an interesting - to me anyway - strategy

.

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I have some questions.

Are you rolling the 7 after the three come bets are made? If so, you are losing $175 plus the odds.

If you are rolling the 7 on the next come out roll when your odds are "off" you are losing the flat bets of $175.

What are you betting when the 7 rolls that gives you a win? Is it the next step in a Martingale progression?

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okay, good questions

first - it's not a martingale - because you're betting $50 on Come after one point is established and $100 on Come after 2 points are established

in a martingale the player makes a bigger bet after a loss - there is no loss here

of course, you will sometimes lose $175 - nobody can design a system where you never lose - you also can win $175 if you make your 3 points - unlikely I guess

if the 7 gives you a win during the 2 Come bets you have a profit and go back to betting $25 on pass

so no, it's not a martingale, not at all - although the bets increase up to a point

also if you make your $100 point first you now have $75 on the table - so you bet $100 on Come again if you haven't taken odds - or you can take your odds down for the come out roll - if you want to - or you can just settle for what profit you already have and hope you get more - whatever

also, for some it might be a lot of money on the table - so they could decline to take odds - you trade that for losing a small % re the House Advantage

what's your opinion_____?????___________yay or nay

.

1. You're betting more into a negative expectation game.

2. You're betting more on a bet with a house edge rather than putting the money towards odds with no house edge.

OMG I'm talking about math.

Quote:tuttigymAnother words, hypotheses PROVE IT. PERFORM IT.

Quote:Ace2I don't think your math adds up since the expected loss on $1,000,000 would be $14,100, but I can tell you that if you made 1,000,000 passline bets there is a 95% chance your result will be within -1.21% and -1.61%. Your chance of being up on the casino after a million PL bets is effectively zero since that would be about 14 standard deviations above expectations...roughly the same chance as your house being struck by a meteor every night this week.

Your assumption above is educational speculation and guessing. Another words, hypotheses PROVE IT. PERFORM IT. I know you will continue to rail on the hypothetical and outlandish parallels and show your highly advanced math acumen, but until it is PERFORMED, they remain unproven hypotheses.

Did Markov ever gamble, i.e., craps?

Sorry about the arithmetic. I wrongly placed the decimal in my calculation.

Quote:Ace2Simulations are taken into the billions to provide a very high level of precision and confidence. And usually only done when something is impossible or too difficult to calculate directly.

This post among the thousands of math posts on this forum is the most accurate and revealing fact that shows the speculation associated with the hypotheses often produced to validate all forms of HA/HE as well as the expectation of results surrounding all forms of wagers.

tuttigym

Quote:AlanMendelsonAnything I'll say you'll disagree with. But here goes:

1. You're betting more into a negative expectation game.

2. You're betting more on a bet with a house edge rather than putting the money towards odds with no house edge.

OMG I'm talking about math.

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no, I don't disagree - your points are valid

my thing is - no matter what you do it's a negative expectation game - you can't get around that - also the thing is - when you take free odds - yes, there is no HA - but you didn't gain anything - your long term expectation on the free odds bet is zero - you increased your risk

but still, your point is valid - overall the HA is less when you take free odds

so, maybe some wouldn't mind sacrificing a tiny % if they enjoy playing this way

also, in the original 3 point Molly, if you look at it that way, why make any Come bets at all where the HA is greater than the free odds bet____________?

why not just take 5 time odds or 10 times odds on the first point if they let you and make no Come bets______________?????

in other words, if you look at it strictly from a % point of view it's better not to do a 3 point Molly at all

I don't actually know what times odds the different casinos will let you take now

.

If you're using a progression on the come bets in anticipation of a 7 wiping out previous come bets why not be a DP/DC player?

Classic. Did Gauss and Euler ever hit the casinos? If not, their mathematical contributions don’t applyQuote:tuttigym

Did Markov ever gamble, i.e., craps?

Quote:unJonSpeaking for myself, I make coke bets

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what is the greatest no. of kilos of cocaine you have ever won_____?????

sorry, I couldn't resist_____________________________________(~:\

.

Borderline trolling of Alan. Pointing at that saga seems geared to embarrass Alan, or to have him embarrass himself.Quote:WizardPosts illustrating Alan's stubborn misunderstanding of probability in the two dice problem have been moved to Two Dice Puzzle -- Part Trois.

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Wizard is currently suspended for three days for personal insult, so I propose we leave it at that.

hahaha. NiceQuote:lilredroosterQuote:unJonSpeaking for myself, I make coke bets

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what is the greatest no. of kilos of cocaine you have ever won_____?????

sorry, I couldn't resist_____________________________________(~:\

.

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Quote:Ace2Classic. Did Gauss and Euler ever hit the casinos? If not, their mathematical contributions don’t applyQuote:tuttigym

Did Markov ever gamble, i.e., craps?

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Yes, but they were tourists and could not figure anything out nor could they produce consecutive winning hands.

8-9 rolls doesn't seem to be a "per session" stat. But I can't find where you say the size of a session eitherQuote:WizardI ran a simulation of over 32 billion session using the Three-Point Molly. I assume 3-4-5x odds and the player turns off the odds on come bets on a come out roll. Here are some results:

Average rolls per session = 8.525470

I know what 'winning a point' means but I am confounded by not seeing any -4 or greater stats. Then again I don't know how you are defining a sessionQuote:WizardIn other news, here is the net number of points the player can expect to win. This only counts fully winning, including the odds. Winning a come bet with the odds turned off on a come-out roll does not count.

Net Points Won Probability -3 0.114039 -2 0.236719 -1 0.356293 0 0.113150 1 0.066998 2 0.041946 3 0.026353 4 0.016556 5 0.010399 6 0.006530 7 0.004101 8 0.002574 9 0.001616 10 0.001015 11 0.000637 12 0.000400 13 0.000251 14 0.000158 15 0.000099 16 0.000062 17 0.000039 18 0.000024 19 0.000015 20 0.000010 21 0.000006 22 0.000004 23 0.000002 24 0.000002 25+ 0.000003 Total 1.000000

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Quote:odiousgambit8-9 rolls doesn't seem to be a "per session" stat. But I can't find where you say the size of a session eitherQuote:WizardI ran a simulation of over 32 billion session using the Three-Point Molly. I assume 3-4-5x odds and the player turns off the odds on come bets on a come out roll. Here are some results:

Average rolls per session = 8.525470I know what 'winning a point' means but I am confounded by not seeing any -4 or greater stats. Then again I don't know how you are defining a sessionQuote:WizardIn other news, here is the net number of points the player can expect to win. This only counts fully winning, including the odds. Winning a come bet with the odds turned off on a come-out roll does not count.

Net Points Won Probability -3 0.114039 -2 0.236719 -1 0.356293 0 0.113150 1 0.066998 2 0.041946 3 0.026353 4 0.016556 5 0.010399 6 0.006530 7 0.004101 8 0.002574 9 0.001616 10 0.001015 11 0.000637 12 0.000400 13 0.000251 14 0.000158 15 0.000099 16 0.000062 17 0.000039 18 0.000024 19 0.000015 20 0.000010 21 0.000006 22 0.000004 23 0.000002 24 0.000002 25+ 0.000003 Total 1.000000

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Looks like a “session” is one shooter. Until a seven out.

That can be called a "hand" ... if that is what it is, a hand can only have one failed attempt on a point, or what am I missing? oh, wait, a 7-out can cause 3 simultaneous losses ... but not 4 in a 3 pt mollyQuote:unJon

Looks like a “session” is one shooter. Until a seven out.

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if a casino offers 10 times odds and a player wants to bet $110 when a pass line bet is available___________

the best he can do in percentage terms is to bet $10 pass and $100 free odds on the point

no other combination of bets - assuming the same dollar amount is bet - can match that in the long run

players don't do that because it's not a fun way to play

so obviously, although making good percentage bets are a consideration for many, a major consideration for almost all players is to play in a way that is enjoyable for them

.

That's a great way to play. Only problem is no casino on the strip offers 10x odds. Cromwell use to but not sure if they still do...I would not stay there thoughQuote:lilredrooster_____________

if a casino offers 10 times odds and a player wants to bet $110 when a pass line bet is available___________

the best he can do in percentage terms is to bet $10 pass and $100 free odds on the point

no other combination of bets - assuming the same dollar amount is bet - can match that in the long run

players don't do that because it's not a fun way to play

so obviously, although making good percentage bets are a consideration for many, a major consideration for almost all players is to play in a way that is enjoyable for them

.

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To stay out of the ghettoQuote:AlanMendelsonStation and Boyd all offer 10x. Why limit this to Strip Odds?

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Quote:Ace2To stay out of the ghettoQuote:AlanMendelsonStation and Boyd all offer 10x. Why limit this to Strip Odds?

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Red Rock is certainly a ghetto.

You'll never see more than 3/4/5 in a desirable strip casino.

If it's anything like other remote casinos I've visited, it's essentially a nursing home with gamblingQuote:AlanMendelsonQuote:Ace2To stay out of the ghettoQuote:AlanMendelsonStation and Boyd all offer 10x. Why limit this to Strip Odds?

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Red Rock is certainly a ghetto.

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I'm also making PB's based on a split of the winning Come + odds bet ($6 Come + $6 odds wins then I bet $6 on each of two PB's, total of 4 PB's from two Come + odds wins). Then I run a progression on each PB. A super Hot Shooter could come close to maxing out a few PB bets for me on my progression (9 in a row). I'm also running a 9 in a row progression on the PL, but not the odds.

I'll raise the PL/Come + odds bets when I pass certain win goals.

I'll probably call it a won session when I'm up 105 line + odds bets.

I see structuring TITOs in my future.

This all above my level of comprehensionQuote:ChumpChangeI'm trying to limit my 2+ hours sessions to losing 15 line + odds bets, or winning 15 line + odds bets. But if Hot Shooters make their way to the bubble machine, I could see a 45 line + odds win.

I'm also making PB's based on a split of the winning Come + odds bet ($6 Come + $6 odds wins then I bet $6 on each of two PB's, total of 4 PB's from two Come + odds wins). Then I run a progression on each PB. A super Hot Shooter could come close to maxing out a few PB bets for me on my progression (9 in a row). I'm also running a 9 in a row progression on the PL, but not the odds.

I'll raise the PL/Come + odds bets when I pass certain win goals.

I'll probably call it a won session when I'm up 105 line + odds bets.

I see structuring TITOs in my future.

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Quote:Ace2The only casinos that pay more than 3/4/5 odds are the ones that must do so in order to attract customers.

You'll never see more than 3/4/5 in a desirable strip casino.

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There's a history behind 3, 4, 5 odds. Jimmy Wike who was once the casino manager of Caesars Palace, created the 3, 4, 5 odds system so that his dealers would be able to make the same payout regardless of the point. It was an efficiency move to speed the game and cut down on dealer errors.

It was quickly adopted by other casinos.

As you probably know the typical craps player bets only 2X odds which was why WYNN felt justified in reducing odds to 2X.

As an aside, Riviera for a short while before its closing offered 1000X (correct, one thousand times) odds with a $10 flat bet.

I know of one member of this forum who played there with 1000X odds. He didn't do well, he told me.

Maybe, but WYNN financial reports state that they weren't making enough profit on 3/4/5 so they dropped to 2/2/2.5Quote:AlanMendelson

As you probably know the typical craps player bets only 2X odds which was why WYNN felt justified in reducing odds to 2X.

Quote:Ace2Maybe, but WYNN financial reports state that they weren't making enough profit on 3/4/5 so they dropped to 2/2/2.5Quote:AlanMendelson

As you probably know the typical craps player bets only 2X odds which was why WYNN felt justified in reducing odds to 2X.

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Would that statement in the Wynn report indicate to you that more players were winning at craps?

Quote:AlanMendelsonWould that statement in the Wynn report indicate to you that more players were winning at craps?

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There is a difference between players winning at craps and players not losing enough at craps to make a table with a crew of 4 profitable.

Quote:DieterQuote:AlanMendelsonWould that statement in the Wynn report indicate to you that more players were winning at craps?

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There is a difference between players winning at craps and players not losing enough at craps to make a table with a crew of 4 profitable.

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You'll have to explain that to me.

If a casino is not making money with 3, 4, 5 odds but is making money with 2x odds, they must have been paying out more money with 3, 4. 5 odds.

Quote:AlanMendelsonQuote:DieterQuote:AlanMendelsonWould that statement in the Wynn report indicate to you that more players were winning at craps?

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There is a difference between players winning at craps and players not losing enough at craps to make a table with a crew of 4 profitable.

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You'll have to explain that to me.

If a casino is not making money with 3, 4, 5 odds but is making money with 2x odds, they must have been paying out more money with 3, 4. 5 odds.

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Odds don't make the casino money.

The casino only makes money on the base passline bet.

If a player wants (about) $100 in action, they can get it by:

- putting $100 on the line

- putting $35 on the line and taking 2x odds

- putting $25 on the line and taking 3x odds

My plucking numbers from thin air guess is that it was costing the casino around $125 an hour to keep the table open when they made the change, but they felt that raising table minimums would not be a helpful competitive market adjustment. Taking smaller odds would make people increase their base bet - the one where the house enjoys an edge - to get their desired amount of action down.

But the casino is more likely to win every odds bet on the right way bets because the casino has an edge on the flat bets.

And dont call me a math denier.

Quote:AlanMendelsonOdds are paid with no house edge... and with no player edge.

But the casino is more likely to win every odds bet on the right way bets because the casino has an edge on the flat bets.

And dont call me a math denier.

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I think you said it yourself - odds are paid with no house edge.

The house will win the player's odds bets more frequently.

The house will pay off the player's winning odds bets at a multiple.

As far as I know, "denier" is a way of discussing the thickness of cloth.

Quote:Dieter

The house will win the player's odds bets more frequently.

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Are you sure casinos dont make a profit from the odds?

Quote:AlanMendelsonQuote:Dieter

The house will win the player's odds bets more frequently.

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Are you sure casinos dont make a profit from the odds?

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Nope!

... but if they do, it's not from EV.

You're a math denier ... OK, is 'logically challenged' better? you can't say there is no edge and then say the casino is 'more likely to win' all in the same statement and not be committing an obvious fallacyQuote:AlanMendelsonOdds are paid with no house edge... and with no player edge.

But the casino is more likely to win every odds bet on the right way bets because the casino has an edge on the flat bets.

And dont call me a math denier.

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Quote:odiousgambitYou're a math denier ... OK, is 'logically challenged' better? you can't say there is no edge and then say the casino is 'more likely to win' all in the same statement and not be committing an obvious fallacyQuote:AlanMendelsonOdds are paid with no house edge... and with no player edge.

But the casino is more likely to win every odds bet on the right way bets because the casino has an edge on the flat bets.

And dont call me a math denier.

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Let's try this again:

Odds are paid at true odds. (Its unfortunate that the same word has two meanings in the same sentence but that's what it is.) And the House is more likely to win each Odds bet.

Let's look at an example of the MATH:

consider the point of 4.

There are 3 ways to roll the dice to win, and 6 ways to roll the dice to lose. On every roll the House is more likely to win.

If the 4 wins, it is paid two to one which is equal to the true odds.

That's the MATH.

Quote:AlanMendelsonQuote:odiousgambitYou're a math denier ... OK, is 'logically challenged' better? you can't say there is no edge and then say the casino is 'more likely to win' all in the same statement and not be committing an obvious fallacyQuote:AlanMendelson

But the casino is more likely to win every odds bet on the right way bets because the casino has an edge on the flat bets.

And dont call me a math denier.

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Let's try this again:

Odds are paid at true odds. (Its unfortunate that the same word has two meanings in the same sentence but that's what it is.) And the House is more likely to win each Odds bet.

Let's look at an example of the MATH:

consider the point of 4.

There are 3 ways to roll the dice to win, and 6 ways to roll the dice to lose. On every roll the House is more likely to win.

If the 4 wins, it is paid two to one which is equal to the true odds.

That's the MATH.

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What does that have to do with making money? House wins $10 twice when point of four isn’t hit. House loses $20 once when point of four is made. House breaks even.

Quote:unJonQuote:AlanMendelsonQuote:odiousgambitQuote:AlanMendelson

But the casino is more likely to win every odds bet on the right way bets because the casino has an edge on the flat bets.

And dont call me a math denier.

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Let's try this again:

Odds are paid at true odds. (Its unfortunate that the same word has two meanings in the same sentence but that's what it is.) And the House is more likely to win each Odds bet.

Let's look at an example of the MATH:

consider the point of 4.

There are 3 ways to roll the dice to win, and 6 ways to roll the dice to lose. On every roll the House is more likely to win.

If the 4 wins, it is paid two to one which is equal to the true odds.

That's the MATH.

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What does that have to do with making money? House wins $10 twice when point of four isn’t hit. House loses $20 once when point of four is made. House breaks even.

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I originally asked if the House breaks even? I don't know. I don't see the books.

Does the House break even???

Quote:AlanMendelsonQuote:unJonQuote:AlanMendelsonQuote:odiousgambitQuote:AlanMendelson

But the casino is more likely to win every odds bet on the right way bets because the casino has an edge on the flat bets.

And dont call me a math denier.

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Let's try this again:

Odds are paid at true odds. (Its unfortunate that the same word has two meanings in the same sentence but that's what it is.) And the House is more likely to win each Odds bet.

Let's look at an example of the MATH:

consider the point of 4.

There are 3 ways to roll the dice to win, and 6 ways to roll the dice to lose. On every roll the House is more likely to win.

If the 4 wins, it is paid two to one which is equal to the true odds.

That's the MATH.

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What does that have to do with making money? House wins $10 twice when point of four isn’t hit. House loses $20 once when point of four is made. House breaks even.

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I originally asked if the House breaks even? I don't know. I don't see the books.

Does the House break even???

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Only the house knows what actually happened. The expectation of the house would be that it will break even on odds bets.

What he said.^Quote:DieterQuote:AlanMendelson

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There is a difference between players winning at craps and players not losing enough at craps to make a table with a crew of 4 profitable.

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If everyone played PL with 3/4/5 odds the casino would lose money. If everyone played basic strategy in blackjack the casino would lose money. Edges of under half a percent..

In both cases the squares (poor BJ players, place/hardway bettors) subsidize the sharps (3/4/5 bettors) and allow such low edge games to exist

Some players might want to seek out even higher odds than 3/4/5 like 10x or even 100x. I don't because the higher odds are always at remote and/or low-end casinos, and also because it's not that much of an absolute difference. With 3/4/5 the edge is only 0.37%, and IMO once you're under half a percent you're effectively at zero. It's a miniscule edge

okay, here's the thing_____________most would say free odds is a really good deal________________but is it really___________?????

when you take free odds you reduce the overall HA on your entire bet__________________but

you didn't gain anything____________you increased your risk

if you make one thousand $1.00 bets on the pass line - your expectation is to lose on average $14.10

on average his pass line bet will end up as a point about 667 times

if on those 667 times he bets ten times free odds he has increased the total size of all of his bets from $1,000 to $7,670

but his long run expectation is to lose exactly the same amount___________$14.10

on the up side - just as he has greatly increased his risk of losing much more - he has also greatly increased his chance of winning much more

but basically it's a wash - the only thing that has really increased are the thrills and chills

.

Quote:lilredrooster______________

okay, here's the thing_____________most would say free odds is a really good deal________________but is it really___________?????

when you take free odds you reduce the overall HA on your entire bet__________________but

you didn't gain anything____________you increased your risk

if you make one thousand $1.00 bets on the pass line - your expectation is to lose on average $14.10

on average his pass line bet will end up as a point about 667 times

if on those 667 times he bets ten times free odds he has increased the total size of all of his bets from $1,000 to $7,670

but his long run expectation is to lose exactly the same amount___________$14.10

on the up side - just as he has greatly increased his risk of losing much more - he has also greatly increased his chance of winning much more

but basically it's a wash - the only thing that has really increased are the thrills and chills

.

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Agree with all this. But if people gamble for this thrills and chills, then the odds bets are unquestionably a positive by increasing the thrills and chills without increasing how much you are expected to lose.

Quote:lilredrooster______________

okay, here's the thing_____________most would say free odds is a really good deal________________but is it really___________?????

when you take free odds you reduce the overall HA on your entire bet__________________but

you didn't gain anything____________you increased your risk

if you make one thousand $1.00 bets on the pass line - your expectation is to lose on average $14.10

on average his pass line bet will end up as a point about 667 times

if on those 667 times he bets ten times free odds he has increased the total size of all of his bets from $1,000 to $7,670

but his long run expectation is to lose exactly the same amount___________$14.10

on the up side - just as he has greatly increased his risk of losing much more - he has also greatly increased his chance of winning much more

but basically it's a wash - the only thing that has really increased are the thrills and chills

.

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But what about the downside?

What if the House keeps winning because the House has an edge on every flat bet?

This is why I don't know if the casinos break even on the odds but actually turn a profit on the odds.

I cant imagine the bean counters allowing a true break even bet.

We've already had an extensive discussion on this. You are not increasing your bet, you are reallocating it. If you're a $100 PL bettor with no odds, you would not add 3/4/5 odds to that, increasing your avg bet to nearly $400. You would reduce your flat bet to $25, effectively reallocating most of your $100 to the free odds and keeping your total bet/variance at a similar level as a $100 PL bet with no odds, but reducing the edge by about 75%Quote:lilredrooster______________

okay, here's the thing_____________most would say free odds is a really good deal________________but is it really___________?????

when you take free odds you reduce the overall HA on your entire bet__________________but

you didn't gain anything____________you increased your risk

if you make one thousand $1.00 bets on the pass line - your expectation is to lose on average $14.10

on average his pass line bet will end up as a point about 667 times

if on those 667 times he bets ten times free odds he has increased the total size of all of his bets from $1,000 to $7,670

but his long run expectation is to lose exactly the same amount___________$14.10

on the up side - just as he has greatly increased his risk of losing much more - he has also greatly increased his chance of winning much more

but basically it's a wash - the only thing that has really increased are the thrills and chills

.

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If a $100 PL bettor plays for three hours (assume 100 bets resolved in that time) his total amount wagered is 100 * $100 = $10,000. The edge is that times 1.41% = $141 and the standard deviation is 100^.5 * $100 = $1000

If instead he plays $25 on the passline with 3/4/5 odds, his expected total amount wagered is ((6/18 * $25 + 3/18 * $100 + 4/18 * $125 + 5/18 * $150) * 100) = $9,444. The edge is 100 * $25 * 1.41% = $35 and the standard deviation is 100^.5 * 4.92 * $25 = $1230

So similar total amount wagered and variance. The edge, however, is 75% lower with 3/4/5 odds

Incidentally, playing with odds is more fun due to the varying bet size and payout ratio. Just flat betting the passline gets boring

Caveat: both math and statistics are used in this example so it will be irrelevant to some members. Last night you probably had a gambling session that didn't result in a loss exactly matching the expected loss, which completely voids the validity of math, statistics and house edge.

Quote:Ace2Some players might want to seek out even higher odds than 3/4/5 like 10x or even 100x. I don't because the higher odds are always at remote and/or low-end casinos, and also because it's not that much of an absolute difference.

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Some of the most enjoyable gambling I've done has been at remote low-end casinos. I understand some of them have raised table minimums to $5 in response to the recent public health concerns.

I understand if your personal aesthetic demands a more upscale experience, but watching someone sweat when they've got $20 on the felt after splits and doubles is good entertainment.