Poll: Reality check
 

In this thread, someone asked,

[ QUOTE ]
I think I have found a system that could make anyone money, playing roulette. [Martingale betting progression.]
Why doesn't everyone do this?

[/ QUOTE ]
Someone responded, in part,

[ QUOTE ]
If your bankroll is bigger than the house's and they allow you to play with a sufficiently high limit at the table, you can beat the crap out of them, through a simple progression.

[/ QUOTE ]

pzhon Casino Files Chapter 11
 

pzhon casino sets up a coin toss game, heads the casino wins, tails the player wins. The coin used is absolutely fair. However, pzhon casino charges a $1 fee per toss and allows a $100 max bet, giving it at least a 1% house edge.

pzhon casino figures this 1% +EV coin toss game will allow it to win the world eventually, if people will toss the coin enough times.

Kerry Packer hears about the game, cleans up some spare change he finds underneath a seat cushion, and shows up at the casino with $15,000 ready to flip coins at $100 a pop.

pzhon casino figured it didn't need much money to become a winner with its locked in 1% edge, and only has a $200 bankroll. pzhon greedily eyes Kerry Packer's $15,000 bankroll and figures after 15,000 or so tosses of the coin, all that money will be his.

Somewhere within the first 100 tosses of the coin, Kerry Packer manages to put together a string of three tail tosses in a row (3 tails in a row isn't really hard in 100 tosses, is it?) and wipes out pzhon's bankroll and all the accumulated $1 per toss profits gained up to that point.

Cursing what he figures to be pure luck to overcome his 1% house edge, pzhon can't believe he is broke. He convinces some investors to put up another $200, and goes up against Kerry Packer's bankroll which is now $15,200.

Again, pzhon is charging $1 per $100 toss and thinks he has Packer by the shorts. Again, somewhere in the first 100 tosses, tails outnumber heads by 3, and again pzhon goes bust.

How many times will pzhon have to lose his $200 bankroll to realize his 1% edge is useless against a much larger bankroll, when the bet size is $100????

Is Chapter 13 close behind, or will someone else take over the coin toss game and adjust the maximum bet size?
[img]/images/graemlins/confused.gif[/img]

Re: pzhon Casino Files Chapter 11
 

at some point there will be a run of 100 and the 15000 guy will go stone broke.

Re: pzhon Casino Files Chapter 11
 

"at some point there will be a run of 100 and the 15000 guy will go stone broke."

It is far more likely that an advantage of 3 tails will always occur before a run of 100 heads does. The tiny bankroll will be wiped out before that "at some point" run has a chance to happen.

Hence, the whole point, you need a proper bankroll to weather the bad streaks in order for the long run expectation to occur.

PS >>>>> To keep risk to the casino at an acceptable level, with a $200 bankroll and a 1% edge, the max bet should be around $2 dollars, not $100.

Re: pzhon Casino Files Chapter 11
 

Just to be devil's advocate a bit.. People keep talking about 100 tosses, but remember, the better only needs 8 loses in a row before he no longer has the bankroll to continue his progression. This makes it much more reasonable that the better can go bust.

Re: pzhon Casino Files Chapter 11
 

[ QUOTE ]
pzhon casino sets up a coin toss game, heads the casino wins, tails the player wins. The coin used is absolutely fair. However, pzhon casino charges a $1 fee per toss and allows a $100 max bet, giving it at least a 1% house edge.

[/ QUOTE ]
For simplicity, assume the casino wins 50.5% of the time instead. That way, there is no need to deal with bets under $100.

[ QUOTE ]
[Out chipped 150:2] Cursing what he figures to be pure luck to overcome his 1% house edge, pzhon can't believe he is broke.

[/ QUOTE ]
I have dozens of posts here on bankroll management (and several of my comments were even added to the Beginners FAQ), and I stated on the earlier thread that there was a high risk of ruin for a casino with a small bankroll. How do you come up with the idea that I would be shocked to lose? You are grossly misrepresenting my position. You are attacking a straw man because that is all you can defeat.

[ QUOTE ]
How many times will pzhon have to lose his $200 bankroll to realize his 1% edge is useless against a much larger bankroll, when the bet size is $100????

[/ QUOTE ]
The 1% HA is not useless, despite your repeated statements that it doesn't matter in the face of the bankroll disparity. In fact, the average amount the casino would have at the end is $626, for a $426 profit. The average number of rounds is 426. The casino wins 1/24 of the time instead of 1/76. That looks like the 1% edge has a large effect to me.

Perhaps you wouldn't want to be the casino here, getting 75:1 on a 23:1 shot. However, the question was whether the situation is good for the player, who loses $426 on average. My position is that this gamble would not be a good one for the player, particularly if the player is risk-averse.

The size of your opponent's bankroll does not affect whether your wagers are +EV or not. That your opponent mighht be risk-averse, and might not be happy to accept a wager in his favor, does not make it a good one for you.

By the way, cardcounter0, the other 9 out of the first 10 people who voted disagreed with you. The consensus is that answer Cyrus gave was not appropriate. You were also alone in voting to say that his comment suggests progressions are a bad idea. You are trying to defend what Cyrus admitted was "intentionally provocative."

Re: pzhon Casino Files Chapter 11
 

[ QUOTE ]
You are attacking a straw man because that is all you can defeat.

[/ QUOTE ]

"Straw man" is one of the best-named fallacies, because it is memorable and vividly illustrates the nature of the fallacy. Imagine a fight in which one of the combatants sets up a man of straw, attacks it, then proclaims victory. All the while, the real opponent stands by untouched.

When your opponent sets up a straw man, set it on fire and kick the cinders around the stage. Don't worry about losing the Strawperson-American community vote.

Re: pzhon Casino Files Chapter 11
 

Why does the Bellagio have 10 million in it's cage?

Every bet you can make there has a house edge. Couldn't they just use the losers to pay off the winners? Why the need for a 10 million dollar reserve?

Except for a few select individuals, $10,000 is the most you can bet. Why? Why won't they allow a 10 million dollar bet.

You better contact the Bellagio with your "facts". They have a lot of money sitting around that could be better invested elsewhere.
[img]/images/graemlins/grin.gif[/img]

Re: pzhon Casino Files Chapter 11
 

[ QUOTE ]

You better contact the Bellagio with your "facts". They have a lot of money sitting around that could be better invested elsewhere.

[/ QUOTE ]
I'm a professional mathematician. Are you saying you disagree with what I am saying is a fact, as opposed to your distortions and hallucinations? Please clarify, and further damage your credibility.

If your opponent is underbankrolled, that does not convert a -EV game to a +EV game for you. That is a fact. If a casino were underbankrolled, it would not suddenly become a good idea to play roulette there.

Re: pzhon Casino Files Chapter 11
 

woooooooshhh!!!! over your head again.

Re: pzhon Casino Files Chapter 11
 

This is an interesting topic. I'd like to see it proved one way or the other.

Re: pzhon Casino Files Chapter 11
 

You don't have to be a professional mathematician to multiply EV by Amount Bet. But there is a thing called variance, usually expressed as standard deviation.

If you overbet your advantage, (or take bets that are larger than your advantage in relationship to your bankroll), you go broke.

Search the web for "Kelly Betting" and you should find an explanation of proper bankroll size and bet amounts based on variance.

There is more to bet sizing and bankroll than the question "Is it +EV or not".

And as pzhon refuses to admit, if you are overbetting your advantage, if you are underbankrolled you still stand a very good chance of going broke even making +EV bets.

Re: pzhon Casino Files Chapter 11
 

[ QUOTE ]

And as pzhon refuses to admit, if you are overbetting your advantage, if you are underbankrolled you still stand a very good chance of going broke even making +EV bets.

[/ QUOTE ]
It is a flat-out lie that I refuse to admit that being underbankrolled carries a high risk of ruin. I have stated it many times, in many different ways. This isn't something you could have overlooked. Saying otherwise shows a willful disregard for the truth.

In this thread, and in the previous, I have stated the following:

<ul type="square">"...there was a high risk of ruin for a casino with a small bankroll." "The casino wins 1/24 of the time instead of 1/76." That means I was acknowledging a 23/24 chance to bust out in that situation, out-chipped 75:1.

"You count it as a success if you lose on average, just because the house runs a risk of busting out?" [/list]
Here are some recent threads where I have discussed bankroll management, in addition to the active threads here in this forum:

<ul type="square">Long shots with odds

Advanced Risk Management

Variance in SNGs vs. cash games

Ever went broke?

When to fold AA, if ever?

EV implications when building your bankroll

Omaha bankroll requirement

Your chance is p - how much would you bet?

Bankroll adjustment for bonus whoring?

Typical statistics in limit vs. no limit.[/list]
Several of my comments on bankroll management were added to the Beginners' FAQ.

It appears you have no intellectual integrity. You can neither defend what you said nor refute my statements. Instead, you lie about what I have claimed, say I'm missing the obvious, and insult me. I will ignore you henceforth.

Re: pzhon Casino Files Chapter 11
 

pzhon &gt; cardcounter0

Check bounces
 

What a waste of a post.

[ QUOTE ]
In this thread, someone asked,

[ QUOTE ]
I think I have found a system that could make anyone money, playing roulette. [Martingale betting progression.]
Why doesn't everyone do this?

[/ QUOTE ]
Someone responded, in part,

[ QUOTE ]
If your bankroll is bigger than the house's and they allow you to play with a sufficiently high limit at the table, you can beat the crap out of them, through a simple progression.

[/ QUOTE ]

[/ QUOTE ]

If you think that my (intentionally provocative) comment did not have anything to do with the question whether progressions are good or bad, please try to infer from my comment the following : What happens when your bankroll is NOT bigger than the house's and they WILL NOT allow you to play with a sufficiently high limit at the table?

Hint: Your only hopes of crushing the bank were those two conditions. So, without 'em, i.e. under conditions prevalent everywhere in casinos, you are busted, for sure, because progressions are no good in "reversing edge sign".

[ QUOTE ]
I'm a professional mathematician.

[/ QUOTE ] Thanks for the information. I'm truly sorry to see that you are also a professionally stubborn mule. To wit: You have tried to ridicule the endeavors in Blackjack of poster cardcounter0, by asking him about his bankroll strategy, etc.

What you have missed though (instead of seeing the connection that is necessary to make with finite BRs and finite lifetimes - we are NOT talking St. Petersburg here) is this very simple premise:

Cardcounter0 is playing with an edge over the house! (Just like the house plays with an edge in Roulette over the player that asked the original question.) Since cardcounter0 has an edge over the house, why is he playing with all that risk aversity and Kelly nonsense ?? Shouldn't his edge just carry him to positive-EV-land ?

That's what my comment was (pretty casually) trying to lead the discussion into. An area where a lot of things remain misunderstood, despite the efforts of many posters here (eg BZ) and elsewhere. I am bored by discussions about progressions (answer: they don't work - next question) which have nothing fresh or interesting to bring to the room.

Take care.

--Cyrus

Re: pzhon Casino Files Chapter 11
 

[ QUOTE ]
Why does the Bellagio have 10 million in it's cage?

Every bet you can make there has a house edge. Couldn't they just use the losers to pay off the winners? Why the need for a 10 million dollar reserve?

Except for a few select individuals, $10,000 is the most you can bet. Why? Why won't they allow a 10 million dollar bet.


[/ QUOTE ]
The reason is that:
1. Gaming regulators require it, and
2. Bellagio investors politely request that the Risk of Ruin for their casino is 0%, not 1% or 5%.

Let's say that I have $300 in my coin-flipping bankroll. If some fool with $15,000 wanted to take me on in a coin-flipping contest where I got a 1% commission on each flip, I'd probably take the bet (assuming I was convinced that everything was legit and I was guaranteed to collect if I won). It is true that my risk of ruin would be very high (over 90%). But if I have sufficiently over a 2% chance of increasing by bankroll by 50x it is still a good bet. (In reality, I'm risk-averse enough that I would want to negotiate a greater house advantage and be sure that even if I lost my coin-flipping bankroll, that it wouldn't be a major blow to my overall bankroll).

Bad Investment.
 

a 90% chance of getting wiped out completely means don't play.

Re: Bad Investment.
 

[ QUOTE ]
a 90% chance of getting wiped out completely means don't play.

[/ QUOTE ]

No it doesn't.

Note that Toonces didn't say that he was risking all his resources. He said that he was risking his "coin-flipping bankroll".

If there are no odds at which you are willing to accept a 90% chance of losing, then you are leaving a lot of money on the table.

Re: Bad Investment.
 

not throwing all my money away 90% of the time allows me to have money to make more money on much more lower variance props.

It's hard to pay the rent when you are completely broke with a "I had a 10% chance to make a lot of money" story.

Re: Bad Investment.
 

[ QUOTE ]
not throwing all my money away 90% of the time allows me to have money to make more money on much more lower variance props.

It's hard to pay the rent when you are completely broke with a "I had a 10% chance to make a lot of money" story.

[/ QUOTE ]

I understand.
The only way you can win an argument is to respond to an entirely different argument.

Re: Bad Investment.
 

"If your opponent is underbankrolled, that does not convert a -EV game to a +EV game for you. That is a fact. If a casino were underbankrolled, it would not suddenly become a good idea to play roulette there. "

Nope, but it makes it probably not the best idea for the casino to stay in operation, unless they have large reserves of cash that aren't in this "bankroll." The entire discussion is now complete.

It's not rocket science. I'm a 20 year old who got a D in high school math, and this entire argument is silly. A game can have a high expectation, even if you will typically go broke. This doesn't make it a bad bet unless "going broke" is a very negative outcome.

To put an end to this
 

Ok, listen carefully.
Yes, being underbankrolled will make you a dog against a larger br even if you have a +EV situation. BUT guess what? pzhon got himself another 200 and then another, which means that his bankroll is NOT 200, but much more than that. A bankroll is defined by how much money you have to throw at a proposition before you will no longer have ANY money. So if someone came up to me with 200 and that offer, I'd take it if I knew that the game ended when one of us went broke. But if he can keep buying in for 200, eventually his +EV will rear its head and he will take back what we won from me and then some.

Re: To put an end to this
 

</font><blockquote><font class="small">Svar på:</font><hr />
So if someone came up to me with 200 and that offer, I'd take it if I knew that the game ended when one of us went broke.

[/ QUOTE ] Why?

You people are hopeless.

Re: To put an end to this
 

I'd like to give this a shot if no one minds. I'm new though, so be kind.

pzhon is right in that every single event of the flip is -EV for the player. The same way any single hand of blackjack is -EV for a player unless there is something like a bonus to offset the expected loss. The limited bankroll is that bonus.

If you think of each coin flip in the progression of coinflips as a decision tree and assume equal bankrolls in either direction, the player will bust in more then 50% of the eventual outcomes. However (!!!) because of the house limited roll, some of the tree will be artifically pruned out. How much depends on how small the casino bankroll is with respect to the bet size and not with respect to the player's bankroll. If the casino has enough BR to cover three losing flips before busting and the number of flips needed to approach EV is 100, it doesn't really matter if the player has BR of 15k or 150k.

Let's see if I can demonstrate my point.

$50 Flips

1st Flip(Casino = 100, Player = 1500)
a. Player won (Casino = 51, Player = 1549)
b. Player lost (Casino = 150, Player = 1450)
a.1 Player won(casino = 2(basically broke), Player = 1598)

Now if we could continue this tree indef. downwards, the number of leaves where the casino makes money would exceed the number of leaves when the player makes money. However, the limited casino bankroll means that the tree will be artifically pruned once the casino goes broke, therefore reducing its edge. By how much is a calculation I can't really undertake at 6am est, but offhand, I'd say it depends on casino BR v betsize. The higher the ratio, the less edge it gives up.

So yes, the any single event of the flip is -EV if EV is computed based on infinite number of tosses and infinite player/casino bankrolls. In the real world, casinos' rolls are basically an approximation of infinity. But if the roll is small, the approximation is bad. That skews results. Therefore situationally, this could be a +EV gamble for the player. I'm sure someone will step up and either back me up with some rigorous analysis or disprove me with the same. I suspect if you plot expectation vs finite bankrolls of various sizes(BR) approximating infinity (INF) in EV calculations, you will find that under certain values for BR (low v betsize), the EV will be positive for the player.

In other words, if we played out this situations infinite amt of times (casino BR $200, bet size $50, player BR $1500) the player will bust the casino more times then casino will make money off this deal. But the higher the BR, the more precise the approximation, the closer actual expectation will approach theoretical expectation.


--Polly

Re: To put an end to this
 

</font><blockquote><font class="small">Svar på:</font><hr />
In other words, if we played out this situations infinite amt of times (casino BR $200, bet size $50, player BR $1500) the player will bust the casino more times then casino will make money off this deal

[/ QUOTE ] This is correct.

</font><blockquote><font class="small">Svar på:</font><hr />
Therefore situationally, this could be a +EV gamble for the player. I'm sure someone will step up and either back me up with some rigorous analysis or disprove me with the same. I suspect if you plot expectation vs finite bankrolls of various sizes(BR) approximating infinity (INF) in EV calculations, you will find that under certain values for BR (low v betsize), the EV will be positive for the player.

[/ QUOTE ] But this is wrong.

I don't need rigorous analysis. There's no question about it: -EV is -EV.

Re: To put an end to this
 

[ QUOTE ]

pzhon is right in that every single event of the flip is -EV for the player...
this could be a +EV gamble for the player.

[/ QUOTE ]
No. It can never be +EV for player.

Suppose your task is to write down numbers that add up to 100 (or more). The catch is that you can only write down negative numbers. Your method can be very complicated: You can use the day of the week to decide on the next number, you can toss a coin to choose a number, you can use a progression of numbers, etc. Can you write down negative numbers that add up to 100? No.

No collection of negative numbers adds up to a positive number. This is true even if you have a method for choosing them that is so complicated you aren't quite sure what the sum is.