[The Baron]

Im new here and I wanted to know what is considered a "unit". I see people saying they bet 2 units on this game, 3 units on that game. How do you figure out what a unit is?

[punchmaster]

Originally Posted by rad0324

Im new here and I wanted to know what is considered a "unit". I see people saying they bet 2 units on this game, 3 units on that game. How do you figure out what a unit is?

I see that term also, and the only unit I'm really concerned about it the one below my belt that has given countless climaxes to the ladies.

What they're talking about has to do with money management in relation to your bankroll. Hopefully your fortunate to start off with say a 5K bankroll. You really should be wagering a percentage of your bankroll per event. I use percentages, generally 1% to 5% of my bankroll ($50 to $250 on 5K) whereas these other fellas may say 1 to 5 units, whereas the only unit I'm concerned with is ...... see above.

[curious]

Originally Posted by rad0324

Im new here and I wanted to know what is considered a "unit". I see people saying they bet 2 units on this game, 3 units on that game. How do you figure out what a unit is?

I can't speak for anyone else, but if you are talking about my post, a unit is that amount as a percentage times your bank. So, 5 units is your bankroll x 5%, 3 units is your bankroll x 3%. I use the kelly criterion and a risk of ruin % of 1%, which makes the unit size basically equal the expected value. Kelly says you should always multiply your bankroll x expected value x the risk of ruin you are willing to accept, since I use 1% as risk of ruin, the risk of ruin falls away and you are left with expected value. I am oversimplifying the formula to make is easy to explain so please any nitpickers who want to flame me for not having the formula "exactly" right please put your flame in the private zone.

In my humble opinion, your standard bet size should be 1% of your bankroll. More than that and you are overbetting your bank. If the expected value is more than slightly more than 50-50 then you can bet the expected value x your bankroll.

[punchmaster]

Originally Posted by curious

In my humble opinion, your standard bet size should be 1% of your bankroll. More than that and you are overbetting your bank. If the expected value is more than slightly more than 50-50 then you can bet the expected value x your bankroll.

That's fine for starters but if you get to a point where you really know what your doing in a particular sport- you've got to get it up to 5% if you want to start winning some money.

[curious]

Originally Posted by punchmaster

That's fine for starters but if you get to a point where you really know what your doing in a particular sport- you've got to get it up to 5% if you want to start winning some money.

Yes, on a game where you KNOW you have an expected value of 105% then you would bet 5% of your bankroll on that game. I agree.

[Ganchrow]

Originally Posted by curious

I I use the kelly criterion and a risk of ruin % of 1%, which makes the unit size basically equal the expected value. Kelly says you should always multiply your bankroll x expected value x the risk of ruin you are willing to accept, since I use 1% as risk of ruin, the risk of ruin falls away and you are left with expected value. I am oversimplifying the formula to make is easy to explain ...

A more accurate way to simply state Kelly would be that a bettor should set his "to-win" amount to equal his edge.

For example, if you had an edge of 5% (what you're referring to as an expected value of 105%) you'd bet the following:

• odds of +100: bet 5% of bankroll
• odds of -110: bet 5.5% of bankroll
• odds of -200: bet 10% of bankroll
• odds of +200: bet 2.5% of bankroll

You'll note that in each one of these cases a win would net you the same 5% of bankroll.

As to what you refer to as "risk-of-ruin", I'm actually not sure how this makes sense in the context of Kelly. One frequently speaks of a Kelly multiplier, such that a Kelly multiplier of 1/2 would imply a bets of (approximately) half of the full-Kelly stake, and in general a kelly multiplier of κ would imply bets of (approximately) κ × the full-Kelly stake. But of course this has nothing to do with risk-of-ruin in any traditional sense.

Actually, even from an arithmetical perspective, I'm a bit perplexed by your risk-of-ruin coefficient. You state, "Kelly says you should always multiply your bankroll x expected value x the risk of ruin you are willing to accept," and then curiously continue with "since I use 1% as risk of ruin, the risk of ruin falls away and you are left with expected value", which if I hadn't seen you write elsewhere I'd assume to be a typo.

Using Kelly or (much more typically) some fraction thereof, can frequently be a valuable risk management tool for the advantage player. However, what you've described, while perhaps (depending on how you explain your risk-of-ruin coefficient) close to Kelly for bets at odds near even, will drastically diverge as odds lengthen or shorten away from that point.

[curious]

Originally Posted by Ganchrow

A more accurate way to simply state Kelly would be that a bettor should set his "to-win" amount to equal his edge.

For example, if you had an edge of 5% (what you're referring to as an expected value of 105%) you'd bet the following:

• odds of +100: bet 5% of bankroll
• odds of -110: bet 5.5% of bankroll
• odds of -200: bet 10% of bankroll
• odds of +200: bet 2.5% of bankroll

You'll note that in each one of these cases a win would net you the same 5% of bankroll.

As to what you refer to as "risk-of-ruin", I'm actually not sure how this makes sense in the context of Kelly. One frequently speaks of a Kelly multiplier, such that a Kelly multiplier of 1/2 would imply a bets of (approximately) half of the full-Kelly stake, and in general a kelly multiplier of κ would imply bets of (approximately) κ × the full-Kelly stake. But of course this has nothing to do with risk-of-ruin in any traditional sense.

Actually, even from an arithmetical perspective, I'm a bit perplexed by your risk-of-ruin coefficient. You state, "Kelly says you should always multiply your bankroll x expected value x the risk of ruin you are willing to accept," and then curiously continue with "since I use 1% as risk of ruin, the risk of ruin falls away and you are left with expected value", which if I hadn't seen you write elsewhere I'd assume to be a typo.

Using Kelly or (much more typically) some fraction thereof, can frequently be a valuable risk management tool for the advantage player. However, what you've described, while perhaps (depending on how you explain your risk-of-ruin coefficient) close to Kelly for bets at odds near even, will drastically diverge as odds lengthen or shorten away from that point.

I see what the problem is. First, expected value and odds are not the same thing. Just because the book is offering +$400 does not mean that you will receive $400 for every $100 bet. Suppose Dallas vs New England has Dallas at +$400 moneyline. Just because you bet $100 on Dallas does not mean you will receive $400. Even if you could make this bet over enough number of trials to enter into the law of large numbers it does not mean you can expect $400 for every $100 bet. The odds the book gives do not reflect the true expected value. If this event occurred over enough trials to be in the law of large numbers the outcome as a percentage would not equal the odds given by the bookmaker. I know you know this. So perhaps I am using the term expected value differently than you are.

The true expected value is the winnings or losses you would have if you bet at these odds over a large number of trials. Let's say that you calculated that if this game was played 1 million times, Dallas would win the game 23% of the time. To make it simple we will use 100 games for the calculations. So, for 100 games Dallas would go 23-77. If you bet on each of these games you would end up winning $9200 on the 23 games @ +$400 and losing $7700 on the 77 games @$100. So, the profit would be $1500. Betting $100 on 100 games is $10,000 at risk, netting $1,500 means you got back $11,500. The expected value is then $11,500 for $10,000 bet or 15%. So, if your "guess" that Dallas would win this matchup 23% of the time is correct and a book is offering the matchup at +$400 then the expected value is 1.15, not 4. Of course I would NEVER bet 15% of my bank on any one bet, I don't care what Kellly says, which brings me to my second point.

Second, determining the raw kelly number is only the first step. Now we have to look at variance, and use variance to calculate risk of ruin. I am only willing to tolerate a risk of ruin near zero, so I am going to lower the kelly number quite a bit. Kelly does not care about variance, Kelly would let you take your bankroll down to 1% of its original size right before you doubled it. I would have a heart attack.

So, I want to use a bet size small enough that risk of ruin is 1%.

So, the unit sizes I give are the true expected value plugged into kelly but then using a risk of ruin of 1% to get a bet size that will keep variance very low.

This is standard practice in blackjack because the variance in blackjack is so ridiculous.

[Ganchrow]

Originally Posted by curious

I always want risk of ruin to be 1%, I don't know how else to explain it. Some people have a larger tolerance for risk of ruin, I don't. To be clear what I mean when I use the term risk of ruin,the risk that the bankroll will become zero.

Expected value takes into account the odds, so I really don't know what you are talking about. Expected value is simply "If I bet X, the expectation is that I will win Y". The odds have to be a part of the equation, otherwise how will you know what you expect the win to be? Kelly tells me how much of my bankroll to bet given an expected value and a risk of ruin that I am willing to tolerate. It really isn't that difficult.

While what you're describing may well be a staking strategy with which you're entirely comfortable, it is most decidedly not Kelly.

The risk-of-ruin with Kelly is zero. This is true of any percentage staking strategy.

The Kelly stake is a function of odds offered and a function of expectations (which as you've correctly pointed out is itself a function of odds offered). The correct single-bet Kelly stake as a function of edge and decimal odds is:

full Kelly stake = edge / (odds - 1)

and as a function of win probability and odds is:

full Kelly stake = (prob * odds - 1) / (odds - 1)

If you haven't done so already you might want to check out:
Expected Value vs Expected Growth (Kelly criterion Part I) and Maximizing Expected Growth (Kelly criterion Part II)

[curious]

Originally Posted by Ganchrow

While what you're describing may well be a staking strategy with which you're entirely comfortable, it is most decidedly not Kelly.

The risk-of-ruin with Kelly is zero. This is true of any percentage staking strategy.

The Kelly stake is a function of odds offered and a function of expectations (which as you've correctly pointed out is itself a function of odds offered). The correct single-bet Kelly stake as a function of edge and decimal odds is:

full Kelly stake = edge / (odds - 1)

and as a function of win probability and odds is:

full Kelly stake = (prob * odds - 1) / (odds - 1)

If you haven't done so already you might want to check out:
Expected Value vs Expected Growth (Kelly criterion Part I) and Maximizing Expected Growth (Kelly criterion Part II)

Please do not try to educate me on Kelly. I have been playing blackjack at the pro level for over 15 years. We live, eat, drink, breathe, and sleep kelly.

Sorry, the risk of ruin in the kelly formula is not zero, it is infinity. Kelly does not care about variance. Kelly would let you run your 1 million dollar bank to one penny right before the bank doubled to 2 million.

No one in their right mind would use Kelly without adjusting it using a risk of ruin that made sense for the variance they can tolerate.

Personally, my temperment cannot tolerate much variance, which is why I always adjust kelly so that my risk of ruin is 1%.

[BatemanPatrickl]

Originally Posted by curious

Please do not try to educate me on Kelly. I have been playing blackjack at the pro level for over 15 years. We live, eat, drink, breathe, and sleep kelly.

Sorry, the risk of ruin in the kelly formula is not zero, it is infinity. Kelly does not care about variance. Kelly would let you run your 1 million dollar bank to one penny right before the bank doubled to 2 million.

No one in their right mind would use Kelly without adjusting it using a risk of ruin that made sense for the variance they can tolerate.

Personally, my temperment cannot tolerate much variance, which is why I always adjust kelly so that my risk of ruin is 1%.

[matekus]

curious,

With respect, is it possible that you are confusing Schlesinger's Risk of Ruin Formula used by BJ players to calculate session bankroll with the Kelly Criterion used to calculate optimal staking?

matekus

[curious]

Originally Posted by matekus

curious,

With respect, is it possible that you are confusing Schlesinger's Risk of Ruin Formula used by BJ players to calculate session bankroll with the Kelly Criterion used to calculate optimal staking?

matekus

No, I am not confujsing them. I am combining them. Kelly does not care about variance. Kellly would be perfectly happy for your $100,000 bankroll to go to one penny just before it doubled to $200,000. While this might be great in a computer simulation, a human being's psyche cannot handle swings like that. Using full Kelly will give you one hell of a wild ride. You have to smooth out the variance so that a human being can actually bet without having a nervous breakdown or a heart attack or jump out the window.

[matekus]

Originally Posted by curious

While this might be great in a computer simulation, a human being's psyche cannot handle swings like that. Using full Kelly will give you one hell of a wild ride...

Maslov & Zhang (1998) "Optimal Investment Strategy for Risky Assets" derive a formula that explicitly includes both expectation and standard deviation.

Stake = Bankroll * (Expectation / ((Expectation ^ 2) + Variance))

Any value?

matekus

[Ganchrow]

Originally Posted by curious

Sorry, the risk of ruin in the kelly formula is not zero, it is infinity.

The term "risk-of-ruin" refers to a probability. As such claiming that Kelly implies an "infinite risk-of-ruin" makes no more sense than claiming that a particular team has an infinite probability of winning a particular game.

Within the context of sports betting, the term "risk-of run" refers to the probability of a player losing all or substantially all of his bankroll, thus rendering him completely unable to continue his participation within the market. Now in theory, every staking strategy that specifies bet recommendations as a percentage less than 100% of a player's bankroll (e.g., Kelly, where the Kelly stake will always be specified as a percent and, except in the trivial case where win probability = 1, will only always be less than 100%) will ha