Martingale System in +EV game.
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My question is, how does Martingale compare to Kelly Criterion or just in general in +EV games? Is it viable to use then? Or pointless because you can just max bet whatever you're willing to risk?
Two specific examples I'd like to take a look at is:
1: While CCing in Blackjack and using Martingale during player advantage phases. Betting $5 min during negative expectation and during positive start with 5 units ($25) and double up on each loss so long as you still have player advantage. If the shoe or deck goes back to house advantage you drop back to minimum until you have the advantage again and continue your Martingale until you win once again.
ASSUMPTION: I'd wager this will just shoot variance through the roof as you still lose more times than you win even with the advantage in your favor because the +EV in CCing comes from naturals, doubling, and splitting.
2: While HCing in Blackjack, start with $50 and use Martingale the whole time. For simplicity sake say you can HC with 100% accuracy.
ASSUMPTION:How does this compare to flat betting just $50 or even $100? Faster gains with increased variance is my guess.
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Are my assumptions correct or is there info I am missing?
IMO it depends. In negative expectation, basically, you have to be willing to lose big once to balance off a lot of small wins. Is that really fun? When the Marty works, all it does is get you back to where you were.
If you had player advantage, the Kelly carefully maximizes your bet, so, no, it's no good there.
What casinos offer +EV games?Quote: Rorryin +EV games?
Quote: FleaStiffWhat casinos offer +EV games?
Do you read before you post??
So flat betting on quarters @1000 betting decisions per hour with 1% cashback produced about $25 per hour cashback. But by doubling up after a win you increased your wager per hour, hence increased your cashback per hour. But you also increased the variance. Myself and many others took advantage of it.
The question was how many times do you double. I would usually double up only twice then revert back to the 10 coin bet. So the progession during winning hands was 10 coins, 20 coins, 40 coins, unless a blackjack, double down, or double after the split was involved, in which case, the betting progession could be much higher.
Like I said, I only doubled twice then reverted back to the 10 coin bet. But some guys took it to extremes. One case in point. Shortly after Harrah's took over Binion's they had a big promotion with cashback and drawings. I found quarter triple play 10/7 double bonus and that's what I pounded on. But unknown to me was there were 3 machines in the rear bar on the Horseshoe side that had the full pay IGT video blackjack. There was a crew back there pounding on them. One of them went nuts on the double up. He went nuts to the point that he got a W-2G--from playing quarter video blackjack!
I would have loved to seen the look on the floor attendent's face. How in the hell do you get a W-2G from playing quarter video blackjack?!! It can only mean that the guy's progression had gotten him up to a $600 bet or more....and he won the hand. When you win in that spot the machines pays you back the $600 bet then pays you the $600 or more win. Hence, W-2G. Or he may have been betting a little less and caught a blackjack. Or he could have been in a double down situation. The other two players berated him for drawing attention by taking a W-2G. But he wouldn't let up. The 3rd W-2G got the play squashed.
While all of this was going on Anthony Curtis walked in the door. He knew the player who was doing all the doubling up and walked up and asked him what he was doing. Anthony didn't know anything about the IGT video blackjack. The guy was smart enough not to tell Anthony. If you tell Anthony about a play it's going to be in the next issue of Las Vegas Adviser, and the play will be immediately squashed. So he told Anthony he was bored and was just gambling. But he wasn't smart enough to avoid the W-2G's.
The other problem with the Martingale, depending on your bankroll, is a much higher Risk of Ruin than with using the Kelly Criterion. This is especially true the lesser the advantage and/or the lesser the probability of winning on any individual trial. For example, let's consider a theoretical game in which the player advantage is 2%, we're going with a 51% probability of winning against a 49% probability of losing:
(.51 * 1) - (.49 * 1) = .02 or 2% Player Advantage
Let's give the player a starting bet of $5 and a bankroll of $1,275.
That's good for an 8-step Marty: $5-$10-$20-$40-$80-$160-$320-$640 to start.
Without going into too many details, the probability of failure is:
(.49)^8 = 0.0033232930569600995
Thus, the probability of success for an individual trial:
1 - 0.0033232930569600995 = 0.9966767069430399
Okay, now 1,275/5 = 255+ which is the number of successful attempts it would take to double your bankroll, then be able to sustain a Martingale failure and still be ahead or even.
But, is this likely to happen?
Looking at the probability of system success, and needing that to happen 255 consecutive times:
(0.9966767069430399)^255 = 0.42790631292667347
As you can see, your Martingale has something in the neighborhood of a 57.2% chance of failure before you have had enough success to sustain a Martingale loss and still be profitable.
With this kind of advantage, and a $1,275 bankroll, I believe you'd be better off flat betting in terms of risk of ruin.
Doubling your bet repeatedly would increase the variance, however so would increasing the amount of the flat bet, either way you should design your wager so you have a low chance of breaking your bank.
Quote: chrisr
Doubling your bet repeatedly would increase the variance,
It increases the volatility, not the variance.
Quote: EvenBobIt increases the volatility, not the variance.
...what do you think happens to the variance if the volatility increases?
Quote: chrisr...what do you think happens to the variance if the volatility increases?
Doubling your bet has no effect on variance, how could it.
Variance has no idea what you're betting. Doubling your
bet has a volatile effect on your BR, which you want to
avoid. Nothing happens to the variance if you increase
the volatility, variance isn't effected by how much you bet
or don't bet.
Quote: EvenBobDoubling your bet has no effect on variance, how could it.
Variance has no idea what you're betting. Doubling your
bet has a volatile effect on your BR, which you want to
avoid. Nothing happens to the variance if you increase
the volatility, variance isn't effected by how much you bet
or don't bet.
unless you have a different definition of variance it certainly does.
variance is the average square difference from the mean. the more you bet the bigger that gets. an example, if i bet $1 on a coin flip that has a variance of 1, if i bet $10 on a coin flip that has a variance of 100
Quote: chrisr
variance is the average square difference from the mean.
Which has nothing to do with how much you
bet. The variance is the same if you bet $1
or $100. If you choose to double and triple
bets during unfavorable variance, you
increase the volatility. If you choose to make
small flat bets, you manage the volatility much
better. The variance for a particular bet is
there if you bet or not.
Quote: EvenBobWhich has nothing to do with how much you
bet. The variance is the same if you bet $1
or $100. If you choose to double and triple
bets during unfavorable variance, you
increase the volatility. If you choose to make
small flat bets, you manage the volatility much
better. The variance for a particular bet is
there if you bet or not.
i don't think you understand what variance is..
VAR(bet $1 then bet $1) < VAR(bet $1 then bet $2)
for a coin flip.. 2 < 5
Look at the Q&A of this appendix for examples:
https://wizardofodds.com/games/video-poker/appendix/3/
Quote: chrisri don't think you understand what variance is..
Variance applies to the outcome of your bets,
not how much you bet. For instance, betting
red only in roulette will have very little variance,
you'll be right around even all the time. It's
a break even bet. You lose at the house edge
because of the zeros. How much you bet or
don't bet has no influence on the variance of
this bet.
Whereas, counting cards in BJ will have big
swings in variance because the cards are
frequently not in your favor. How much you
bet doesn't effect the wild swings, how could
it. It only effects your BR.
Quote: EvenBobVariance applies to the outcome of your bets,
not how much you bet. For instance, betting
red only in roulette will have very little variance,
you'll be right around even all the time. It's
a break even bet. You lose at the house edge
because of the zeros. How much you bet or
don't bet has no influence on the variance of
this bet.
This just isn't true. Variance isn't a unitless measurement. Variance is measure in the same unit as what you are working with. So the variance of a bet is in square dollars since the bet was made in dollars. I couldn't see a single case where you would want to use variance as a unitless measure and not take into account bet size.
Quote: TwirdmanThis just isn't true. Variance isn't a unitless measurement.
Of course it is. It's the swings the bet makes, it has
nothing to do with the wager. Variance is there
whether you bet or not.
'The technical definition of variance is 'the average of the squared differences from the mean'.
Do you see any mention of money here?
Quote: EvenBobIt increases the volatility, not the variance.
Volatility and variance refer to the same thing. Variance is a well-defined mathematical concept while volatility is slot-marketing speak for "how bumpy will the ride of this slot game be?" But they're both referring to the same thing. When slot floor managers talk about volatility, they're talking about variance. The reason we use "volatility" is because saying "the game has a variance of 38.6" is far less meaningful to the typical casino operator than "the game has medium-low volatility".
But if you mean something else by "volatility" I'm not sure what it is.
Quote: MathExtremist
But if you mean something else by "volatility" I'm not sure what it is.
You can change the volatility without changing the
variance, they have nothing to do with each other.
If I'm flat betting $5 on red every time, the bet
has a low variance and a low volatility. Low variance
because you will always be around even. Low
volatility because you're flat betting. Start using
a Marty on the bet and now you have a lot of
volatility. You can lose a lot of money very quickly.
The variance didn't change at all when the bet
size changed. Volatility in this case refers to the amount of
uncertainty and risk involved when you increase
the size of the bets using a progression.
Quote: EvenBobOf course it is. It's the swings the bet makes, it has
nothing to do with the wager. Variance is there
whether you bet or not.
'The technical definition of variance is 'the average of the squared differences from the mean'.
Do you see any mention of money here?
The mean is based on the bet. I mean what do you think the mean of a bet is. Again mean isn't a unit less measure. Say I have 4 guys running 1 guy runs 2 miles, 2nd 3, 3rd 5, 4th 6. The mean of that is 4 miles not just 4. So yes if you read the definition properly money is mentioned when you are talking about betting.
Quote: EvenBob'The technical definition of variance is 'the average of the squared differences from the mean'.
Do you see any mention of money here?
I've been away from this forum for a while, and been lurking for a while since I've started reading again, but this line has brought me out of retirement. Hilarious. Well-done, Bob.
Come on, this HAS to be an elaborate troll. Dare I say it -- post of the year?
Quote: TwirdmanThe mean is based on the bet. I mean what do you think the mean of a bet is. .
The problem here is, I'm using volatility in a different way.
But it doesn't alter the fact that changing bet size
doesn't change variance. Card counting in BJ has a
high variance not because of the bet sizes, but because
you only have a 1% advantage over the house. The
variance will be the same no matter what you bet.
.Quote: EvenBobThe problem here is, I'm using volatility in a different way.
But it doesn't alter the fact that changing bet size
doesn't change variance. Card counting in BJ has a
high variance not because of the bet sizes, but because
you only have a 1% advantage over the house. The
variance will be the same no matter what you bet.
Again why do you persist in saying this. It is only true if variance was a unitless measurement its not. Variance most definitely does change when you increase a bet. And variance and volatility are synonyms. It is meaningless to suggest volatility goes up but variance doesn't make sense. It would be like suggesting I moved farther away from something but didn't increase my distant from it.
Quote: AxiomOfChoiceI've been away from this forum for a while, and been lurking for a while since I've started reading again, but this line has brought me out of retirement. Hilarious. Well-done, Bob.
?
If your bet of choice is 3 SD's from the mean consistently, it's
3 SD's from the mean no matter what size the bet is. The amount
bet has nothing to do with anything.
Quote: EvenBobIf your bet of choice is 3 SD's from the mean consistently, it's
3 SD's from the mean no matter what size the bet is. The amount
bet has nothing to do with anything.
That is the z-score of something and you're right that doesn't change with bet size. 3 SD away is 3 SD away regardless of bet size. Difference is a larger bet increase what that SD is since SD is a measurement that has unit in this case dollars.
Oh another way to look at it variance is defined as E[X^2]-E[X]^2 are you suggesting the expected value of a bet doesn't change with bet size because that is ludicrous.
Quote: Twirdman.
Variance most definitely does change when you increase a bet. .
Variance has nothing to do with bet size. You
can't alter variance by raising and lowering
your bet.
Quote: Twirdmanare you suggesting the expected value of a bet doesn't change with bet size because that is ludicrous.
Who said anything about EV.
Quote: EvenBobWho said anything about EV.
Variance is intrinsically linked with EV. EV is used in the calculation. So if you are saying variance doesn't change with bet size then neither can EV.
Quote: EvenBobIf your bet of choice is 3 SD's from the mean consistently, it's
3 SD's from the mean no matter what size th bet is. The amount
bet has nothing to do with anything.
Ok Bob...
As you said, variance is the average of the squared distances from the mean.
Let's say that you are playing a fair coin-flipping game. You win 50% of the time, and you lose 50% of the time.
Say that Player A bets $5 per flip. Half the results are +$5; half the results are -$5. The mean is $0. All the results have a distance of $5 from the mean (either +$5 or -$5) so the squared distances from the mean are all 25 square dollars (because $5 x $5 = 25 square dollars). So, each bet has an expected value of $0 and a variance of 25 "square dollars".
Now say that Player B bets $100 per flip. The mean is still $0, but now the square distance from the mean is 10,000 dollars squared. So, player B has an EV of $0 per bet, and a variance of 10,000 square dollars per bet.
Note that a square dollar is not a particularly useful real-world measure (since square dollars don't exist in the real world), which is why people usually talk about standard deviation, which is the square root of variance. Variance is only useful in that it's additive (the variance of two bets is the sum of the variances of the individual bets). So, if you make a $5 bet and a $100 bet on those coin flips, your variance is 10,025 square dollars, and your standard deviation is the square root of that number (which is $100.125).
These are how the terms "variance" and "standard deviation" are defined. They are well-defined mathematical terms that you can find in any beginner textbook on statistics. If you mean anything else, it would be best if you used different terms, to avoid confusion.
Micky The term for the double up is called a Let It Ride feature. It was the only way you could get more action in because of the 10 coin max. The Williams BJ machines were very fun and exiting. They had quarters all over Laughlin and a few in LV, Gold Spike had one of the last ones in Vegas.Quote: mickeycrimmThere was one situation I know of where a "reverse martingale" was profitable. Someone will have to correct me on whether this is called a reverse martingale or not. I'm not that hip to the terminology. It was with the IGT full pay video blackjack, and before that on the Williams early surrender video blackjack (100.42%). These games were mostly in quarters and the most you could bet was 10 coins. But some of the machines had a double up feature where you could double your bet after a win. The IGT game, for instance, was breakeven, so the earn came from cashback or freeplay on your action.
So flat betting on quarters @1000 betting decisions per hour with 1% cashback produced about $25 per hour cashback. But by doubling up after a win you increased your wager per hour, hence increased your cashback per hour. But you also increased the variance. Myself and many others took advantage of it.
The question was how many times do you double. I would usually double up only twice then revert back to the 10 coin bet. So the progession during winning hands was 10 coins, 20 coins, 40 coins, unless a blackjack, double down, or double after the split was involved, in which case, the betting progession could be much higher.
Like I said, I only doubled twice then reverted back to the 10 coin bet. But some guys took it to extremes. One case in point. Shortly after Harrah's took over Binion's they had a big promotion with cashback and drawings. I found quarter triple play 10/7 double bonus and that's what I pounded on. But unknown to me was there were 3 machines in the rear bar on the Horseshoe side that had the full pay IGT video blackjack. There was a crew back there pounding on them. One of them went nuts on the double up. He went nuts to the point that he got a W-2G--from playing quarter video blackjack!
I would have loved to seen the look on the floor attendent's face. How in the hell do you get a W-2G from playing quarter video blackjack?!! It can only mean that the guy's progression had gotten him up to a $600 bet or more....and he won the hand. When you win in that spot the machines pays you back the $600 bet then pays you the $600 or more win. Hence, W-2G. Or he may have been betting a little less and caught a blackjack. Or he could have been in a double down situation. The other two players berated him for drawing attention by taking a W-2G. But he wouldn't let up. The 3rd W-2G got the play squashed.
While all of this was going on Anthony Curtis walked in the door. He knew the player who was doing all the doubling up and walked up and asked him what he was doing. Anthony didn't know anything about the IGT video blackjack. The guy was smart enough not to tell Anthony. If you tell Anthony about a play it's going to be in the next issue of Las Vegas Adviser, and the play will be immediately squashed. So he told Anthony he was bored and was just gambling. But he wasn't smart enough to avoid the W-2G's.
I played $1 denominations at the Reno Hilton and Harrah's and lake Tahoe, cash back was good at some places and card pulling was a thing. You may make a few thousand, but they thought you lost 10's of thousands. I would often Let it ride just to over $1000. Hosts were offering RFB and over 20% losses back, some cash, but mostly gift shop, I would get gold chains, nice watches, collectibles, air fair, limos rides all over town or from the Reno airport up to the lake. The Hosts would even pay for mall shopping sprees, when you brought back your Receipt. I heard Donnie O crushed the Williams BJ in the Midwest on promotions. As you probably know Williams machines often malfunctioned if you favor.
The Colorado Bell had a bank of .25 with cash back and many good promotions, like the $100 jackpot contests. Bring a Girl/ friend and You almost guaranteed yourself 1st for $7,777 and 2nd place, can't remember what 2nd place was 4 or 5k I think. After the 3rd or 4th year winning this (not just on the Williams) I was uninvited.
At Binion's they also had a few $1 denomination IGT video blackjack at the bar along with the .25. The person (B.M.), that got the hand pays, was in fact, playing the $1. He is a, very nice, humble, smart guy. This was very out of character for him, so it's unclear why he did this. I din't ask, I walked in and right back out, when I seen the first hand pay, to avoid heat. I have a feeling something else was going on. It may have had something to do with needing a higher average bet, in order to get the $400 a week for 2 months in bounce back, probably something more interesting. I could have been just a run of bad luck and he had to double down and split few times in a row, One day I'll ask him, It will possibly be a no comment.
On a side note, I like Anthony C..... He won't usually kill a play in progress by writing about it. He has walked in on me many times, while I was playing something Juicy. I have kindly asked him to not expose the play, he has yet to do so. He didn't even take advantage of the play much.
(A) Are collispores rombalish?
(B) Are unicorns nice persons?
(C) Does being accused in precinct XXX mean you are innocent or guilty?
Explanation:
- Undefined concept: You can say anything about "Volatility" since it has no definition.
- Nonexisting concept: "Variance" of a game does not exist per se, don't argue about its properties.
- Undefined context: The only real thing is "variance OF A RANDOM VARIABLE". Contenders are talking about differrent r.v., no surprise they come with different answers.
Quote: EvenBobThe problem here is, I'm using volatility in a different way.
Yes it is. If you used it in the same way as everyone else, that problem goes away.
Quote: kubikulannThis silly discussion about variance and volatility makes me think of three analog debates.
(A) Are collispores rombalish?
(B) Are unicorns nice persons?
(C) Does being accused in precinct XXX mean you are innocent or guilty?
Explanation:
- Undefined concept: You can say anything about "Volatility" since it has no definition.
- Nonexisting concept: "Variance" of a game does not exist per se, don't argue about its properties.
- Undefined context: The only real thing is "variance OF A RANDOM VARIABLE". Contenders are talking about differrent r.v., no surprise they come with different answers.
Perhaps, but context matters. In common casino manufacturer parlance (which is where the operators learned it), "volatility" is a relative measurement of variance ("high", "low", etc.), and the "variance of a game" is calculated based on a specific wager for that game, usually denominated in "coins" or "units" rather than absolute currency values. In other words, variance (in this context) is usually computed in units rather than currency, so it doesn't actually matter how much a unit is worth.
Quote: AxelWolfI Don't know what the exact difference is. I just know, the only time we would use the word volatility, was when describing games like, Triple Double or Super Aces. no matter the denomination. We would never say 9/6 jacks was volatile, even when discussing playing a $100 machine. Risky would be the word used for that.
That's the whole point. Variance is a calculable number, but slot floor managers neither want to nor need to worry about quantitative statistics for the variance of a given machine. It is sufficient to understand that the qualitative "volatility" of 9/6 JoB is relatively far lower than the volatility of TDB, so that's what they get told, and they in turn tell their players the same thing.
Here's an example of an IGT-produced video poker newsletter, "The Inside Straight," from 2009. These are written for slot floor managers.
http://www.videopokerforcasinos.com/pdf/tis/TIS-August2009_REV_ONLINE.pdf
See the table on page 3.
