There's a commonly accepted practice--the more you lose the less you bet; it's flip side is, the more you win, the more you should wager per "instance".
As a rough example, start out with a $300 buy-in. $5 PL and 25 odds. If this bet loses, theory says the next bet should be less... 5PL w/20 odds (approximating 10% of $270). Had the first bet won, the bet should be 5PL w/30 odds (10% of $330).
I can't search/Google for it because I don't know a short way to describe the mathematic principles involved. What's this regimen called?
Thank you.
How do I calculate my "advantage" for Kelly Criterion?
Moderators: 220Inside, DarthNater
How do I calculate my "advantage" for Kelly Criterion?
Last edited by dork on Mon Mar 31, 2014 8:44 am, edited 1 time in total.
-
SHOOTITALL
- Posts: 1016
- Joined: Mon Jul 25, 2011 6:42 pm
Re: What's the name of this "rule"?
You may be thinking of the Kelly Criteria. I think this discussion was done in Expert Speaks a couple of years ago. sia
Yep, hit the search but use only Kelly in Expert Speak.
Yep, hit the search but use only Kelly in Expert Speak.
Your craps plan? The dice gods laughed.
Re: What's the name of this "rule"?
Yes, that's it!! Thank you, SHOOTITALL. That was drivin' me nuts.
Re: How do I calculate my "advantage" for Kelly Criterion?
Edited to change title and add:
I've read Heavy's article on the Kelly Criterion... what's the method for determining my "advantage"? As you can imagine, a search for "advantage" yielded 'way too much.
Thank you.
I've read Heavy's article on the Kelly Criterion... what's the method for determining my "advantage"? As you can imagine, a search for "advantage" yielded 'way too much.
Thank you.
Re: How do I calculate my "advantage" for Kelly Criterion?
You're going to have to brush up on your math skills for one. The calculation for any single bet is fairly simple and the formula readily available. When you add multiple bets it gets very complicated. You're going to have to define your exact "edge" over your particular bets. Then you're probably going to want to come up with some sort of "blended" advantage based on those numbers. Last of all, you cannot vary from your betting strategy and effectively know what your edge is, so the entire effort becomes pretty frustrating. Of course, if you just want to bet pass line and odds it becomes a lot easier. You can even calculate your edge based on your SRR and come up with a pretty close approximation to what you're looking for. But when you add in Place bets on the six and eight, buy bets on the four and ten, continuous come bets, or whatever the heck your play is - and as I said before, it gets complicated. I used to refer people to Jim Hammon's Practical Casino Math, but it appears the book price is somewhat inflated these days. http://www.amazon.com/Practical-Casino- ... 0942828534
Barnes and Nobles thinks less of the book: http://www.barnesandnoble.com/w/practic ... 0942828467
Barnes and Nobles thinks less of the book: http://www.barnesandnoble.com/w/practic ... 0942828467
"Get in, get up, and get gone."
- Heavy
- Heavy
-
Mad Professor
- Posts: 1830
- Joined: Fri Jul 29, 2011 12:15 pm
Re: How do I calculate my "advantage" for Kelly Criterion?
Hi Dork,
If you don't mind, I'll just do a simple cut-and-paste out of my book, The Mad Professor's Crapshooting Bible:
Optimal Bet Size
Figuring out how much money to put in action when you have an edge has gotten the attention of a large number of bright people over the years.
There’s no reason to reinvent the wheel, and crapshooters don’t have to waste their time or money trying to figure it out anew. They can do what card counters have done, which is to apply the work that has already been done by bright people for other forms of investment.
Proper advice on how to bet your money at craps does not differ from proper advice on how best to invest your money in the stock market or real estate, or in building a new factory.
Proper advice for craps or any other investment requires three things:
~Realistic estimates of your bankroll
~Accurate estimates of the edge the investment is likely to provide
~Evaluation of the inherent risk the investment carries.
Crapshooters are lucky; it’s possible to quantify your expected edge and risk on any bet you may look at making.
While it’s possible to quantify your expected edge and risk to calculate optimal bets and bet sizes, the calculations are not easy enough to do in your head while you are standing at a crap table.
Therefore you need some easy-to-follow rules of thumb to determine the proper bets to make and their associated bet sizes. That is, you want some general rules that will give recommendations close to what is optimal.
The Kelly Criterion
The mathematics of calculating the optimal bet size is called the “Kelly Criterion” in honor of John L. Kelly, who wrote the first paper describing the methodology.
Most professional gamblers report satisfaction with betting an amount equal to 25% to 50% of the Kelly amounts; doing so is referred to as betting “quarter-Kelly” or “half-Kelly.”
This section explains how to capitalize on your precision-shooting skills by
betting quarter-Kelly to half-Kelly.
Optimal Bet Size and Wager Meet Joe Average
It’s okay to bet less than the optimal amount. Think of the optimal bet size as being what a computer would tell a machine to bet if the machine was betting your bankroll and could throw the dice exactly the way you do.
There are all kinds of reasons you might bet less than is optimal, including nerves or a casino that won’t comfortably take bets as big as you should be making.
The point is that you can bet less than the optimal amounts that we are talking about here; it’s just that your winnings will be significantly lower than your talents deserve.
Find Your Best Edge on Four, Five or Six
Finding your edge and then betting it appropriately is not all that complicated.
Whatever edge you have betting on the four you will also generally have betting on the ten when a large enough sampling is taken.
Whatever edge you have betting on the five you will also generally have betting on the nine when a large enough sampling is taken.
Whatever edge you have betting on the six you will also have generally betting on the eight when a large enough sampling is taken.
In other words, when you have an advantage over the Buy-4; then your approximate edge over the Buy-10 will generally be somewhat close to your edge over the B-4 when a large enough sampling of in-casino roll-stats are accumulated.
You will find that 'smoothing' effect affects each pair of twinned-numbers equally (5 with the 9 for example) as you gather more in-casino roll-stats. Sometimes one will lead the other...and at other times, the former leader will lag. Over time, each set of twinned numbers (like the 6 with the 8) will generally match each other in advantage).
When you decide which dice set gives you the best edge-per roll betting on the four, five or six, then you have an equally good set to use on the ten, nine, or eight, respectively. So for example, your best-set for the '6' will generally be the best set for the '8' as well.
Hardway and field bets are less desirable than bets on those box numbers, due to the extra risk.
You need extra return (a bigger edge) to balance that extra risk, and the hardway and field bets generally don’t promise enough edge to justify taking the extra risk. We’ll take a closer look at those later in this chapter.
So, when you are deciding what set to use for the biggest edge, consider only your edge betting on box numbers. A large portion of your advantage-play profit will flow from them.
How Much to Bet on Your Single Best Number
The math, by coincidence, works out in such a way as to give this rule of thumb for somebody who wants to bet on just one number:
Your optimal bet size is the proportion of your bankroll equal to your edge per roll.
For example, if you have an edge of 2% per roll place-betting the six, then your optimal choice for making only one bet is to place-bet the six with 2% of your bankroll. That 2% will give you between quarter-Kelly and half-Kelly. Note that with each loss, your total bankroll size drops.
Note also that you are basing this on your edge per roll, rather than your edge per decision. It takes an average of three to four rolls to reach a decision on a bet on a number, so your edge per bet is three or four times as large as your edge per decision. An edge of 2% per roll on a certain bet might mean an edge of 7% per decision.
We don’t have to adjust for variance as a separate step; using edge per roll instead of edge per decision automatically allows for variance.
Spreading Your Money Over Two Numbers
You can reduce the risk by spreading your money over two numbers. You can get more return on investment for the same amount of risk if you slightly increase the amount you are willing to bet, and then divide it into bets on two different numbers.
It works out that the amount you can justify betting increases by 50% if you can spread that money over two profitable numbers.
For example, if you have a 2% edge per roll place-betting the six, then you can justify betting 1.5% of your bankroll on the six and 1.5% of your bankroll on the eight, for a total of 3% of your bankroll in action. That 3% will give you between quarter-Kelly and half-Kelly.
The important thing to look at here is that you are putting your money where your precision-shooting edge is, and doing it in proportion to your edge over the house.
Spreading Your Money Over More Than Two Numbers
The first number you bet gives you most of your EV. Spreading money over two numbers gives you most of the possible risk reduction. There is not much additional benefit to spreading to a third number. As you spread out to more and more wagers, your overall edge diminishes faster than your risk diminishes.
If you spread your money over more than two numbers, the optimal amount of money to have out there for total bets does not increase much from what is recommended for two bets.
For example, if you have an edge of 2% per roll and can therefore justify
spreading 3% of your bankroll over two numbers, the amount of your bankroll that you should spread over three or more numbers is only slightly more than 3%.
By restricting the total amount of money that you expose to a seven-out at any particular point, regardless of the total number of wagers that you’ve spread that money on, you safeguard your bankroll.
Thus a good rule of thumb is to set your “seven exposure” (the amount of money you will lose if your next roll is a seven) at 150% of your edge times your bankroll, no matter how many numbers you spread bets over.
For example, if 150% of your edge times your bankroll is $300, then you can justify betting two numbers at $150 each, three at $100 each, four at $75 each, etc. Your seven exposure shouldn’t change when the number of bets that you spread that money across does.
Viewed another way, if you want to spread your money across as many validated-edge bets as you can, then you still have to restrict the total amount of your wagers to maintaining a proper bet size based on your bankroll.
If six and eight are your most profitable numbers and your point is something else, you might as well go ahead and take odds on your pass-line bet as well as place-betting the six and eight, but that’s it.
If your edge on four and six is approximately the same (for example if you have an edge of 2.0% per roll on six and 2.1% per roll on four), then go ahead and bet four, six, eight and ten if you want. Or bet any two of those numbers, or any three.
The more numbers you bet, the less you bet on each, because you want to hold your total seven-exposure down to about 3.2% of your bankroll. (The 3.2% is 150% of your 2.1% edge.)
The important thing to keep in mind is that spreading your money over each additional number means taking some money off of your other bets to put on the new number. That’s because all of your bets lose to a seven.
If you feel compelled to bet on multiple wagers, then you have to understand and accept that you are taking some of the money off of your best bets (the ones where you have the highest player advantage) and redeploying it on other wagers where you don’t have as high of an edge.
Between Too Much and Too Little
Of course, you can bet at less than optimal if your or the casino’s comfort level isn’t high enough to permit optimal bet sizing. The flip side of that is betting beyond what is ideal.
If you consistently bet more than the optimal amount, you are putting yourself in a position where future losses are going to harm your bankroll more than future wins will help it.
Don’t try to outsmart your bankroll or overplay your edge over the house. Advantage playing means using your edge in a way that
will grow your bankroll but minimize your risk. If you put too much emphasis on advantage or risk, then your income will suffer.
Field Bets
Using the appropriate dice set, of course, you may find that your highest percentage edge comes from field bets.
The problem with field bets is risk: two or twelve pays triple (or double), and the other results win or lose even money. On a per-decision basis, that makes field bets riskier than bets on individual numbers.
When it comes to wagering money on the field, there are no no-decision rolls. Every roll results in a bet decision. In contrast, a bet on an individual number, say a place bet on the six, will have a large proportion of no-decision rolls.
However, the math does yield an optimal bet size for field bets, in case you want to make field bets with the appropriate set.
A good rule of thumb for an optimal bet size on the field is 10% of your edge per roll.
For example, if you have a 6% edge on field bets, you can justify betting 0.6% of your bankroll in the field. That is assuming you make only the field bet, and do not simultaneously have large bets riding on any other numbers.
If you want to make field bets along with bets on the box numbers, then a good rule of thumb is to include your field bet in your seven-exposure total. If, for example, you have calculated that you can afford $300 of seven exposure, and your edge on field bets is high enough that you want to bet the field, then it’s okay to put some of that total seven-exposure money in the field.
Hardway Bets
The advice for hardway bets is similar to the advice for field bets. The rule of thumb, if all you make is a hardway bet, is a proportion of your bankroll equal to 10% of your edge per roll on that specific hardway bet.
There really is no room for hardway bets in an optimal-betting strategy, and there definitely isn’t any room in it if you’ve got an edge on only two of the hardways, yet insist on wagering on all four of them.
If you enjoy betting hardways, and your skill gives you an edge for the set you are using, then go ahead and have fun; bet your hardways, but accept that you are doing it to enhance your enjoyment of the game, and not because the mathematics of optimal betting recommend it, nor because it will enhance your profit.
If you don’t have a substantial edge over the hardway bets that you wager, then you are giving back some of the player advantage that you’ve worked so hard to obtain.
Putting It All Together
Precision shooting is a thinking-person’s game, yet the decisions you have to make are not that difficult:
Determine the size of your bankroll.
Decide on a dice set.
Find your best bet for that set.
Know your edge per roll for that best bet.
Spread 150% of your edge per roll times your bankroll
over at least two numbers.
Throw the dice and hope the seven does not show.
Optimal Bet Size if Your Edge Is Negative
If your edge is negative, which is another way of saying the casino has an edge over you, then your optimal bet size is zero. Zip. Nada.
That is also the optimal amount to bet on a random roller, and the optimal amount to bet on your own rolls if your dice are not behaving the way you want them to.
Accurately Predicting Your Future Success
Your dice set and your foundation frequencies give the best predictions of what you are going to roll an excess of in the near future. That is, given your in-casino foundation frequencies, you know what each different dice set will offer in terms of betting opportunities.
When you are making your betting decisions, simply look at which set is strongest for a given set of bets, and make your decisions based on that. As your skills improve, your foundation frequencies change, and your betting opportunities progress along with them.
Keeping current with your most exploitable betting opportunities means keeping tabs on developments and changes in your foundation frequencies. As your foundation frequencies change, so too will your optimal bet size, the set you choose, and the numbers you bet.
Optimal Bets Are Not for Everyone, or Every Casino
Now that I have explained optimal bet size, let me add that I do not always bet that way myself. Instead, there are many occasions when I grossly underbet my edge.
My own foundation frequencies and bankroll suggest betting hugely every time that I pick up the dice, but instead of making maximum bets in every casino I enter, I try to identify each casino’s comfort level, and identify a target win for each casino.
I bet big enough to give myself the expectation of achieving that target win
in an hour or less, and often just in one hand (one complete turn with the dice); then I leave as soon as I achieve it.
By winning just enough to stay within a given casino’s comfort level, I can play at the same house on a continuing basis. I generally move around quite a bit instead of hitting the same casino multiple days in a row, and especially on the same shift day after day.
If you are getting heat, it might be because of something that you are doing. If you are winning table-maximum bets (or anything beyond what the casino is currently comfortable with losing, and that amount is often far below the posted maximum-bet limit), then you deserve to be banned, barred, tarred, feathered, and drawn and quartered, and have each one of your bodily organs liquefied
and fed to Satan himself.
Casinos don’t like to lose. Winning table-maximum bets is a stupid way to play. Playing above a casino’s loss-tolerance comfort level just because optimal betting calls for it might mean being banned from further dice tossing at that casino if you win. Common sense says don’t do that.
Don’t Underestimate Your Skill
You may have kept track of your results from day one of your journey on the road to dice setting success. While that is a good way to see how far you have come since you started, the overall numbers pertaining to SRR (sevens:rolls ratio) or any other statistics can be deceiving when you look at rolls that you have accumulated over an extended period of time.
Ask yourself if your precision shooting is better or worse now than it was three or four months ago. If it is better, but you are still using ancient rolls to calculate your edge and determine your best betting opportunities, then you may be shortchanging yourself.
If you derive those figures from the entirety of all of the hands you have thrown over all of the months or years since you began, then you are unfairly diluting and underestimating your current skill level.
By considering your shooting numbers within too big of a historical range or too large of an improving-skills picture, you may not be able to see the forest for all of the trees. Or alternatively, the forest may be impairing your ability to find the one species of tree that you are presently interested in harvesting.
If indeed you have improved, then you may find it more profitable to use a sort of sliding-scale snapshot to measure where you are now compared to where you were last year.
Your roll statistics from the last three or four weeks, if you have enough rolls, are more indicative of your current skill than the average over all the throws that you have made since you first started down this precision-shooting trail.
Your recent roll performance is more relevant to present-day betting opportunities, and is also more pertinent when it comes to repairing current shooting flaws and shortcomings.
Giving more weight and relevance to the most recent statistics allows your current betting to be more in tune with your current abilities.
Your snapshots or time frames of progress measurement should be of a sufficient size to ensure that you aren’t having a few lucky or aberrant sessions, but recent enough to fairly and reasonably measure your ongoing progress.
You can keep all of the roll statistics that you have compiled since day one, but you should definitely view them only in their proper perspective with a forward-moving average, where you consider only the last maybe 360, 720, 1080 or 2160 rolls to indicate your current competence. By using a sliding average, you’ll still be able to chart your overall progress, but your right-here right-now wagering possibilities won’t be hidden.
The more accurately you are able evaluate the merits of your current precision-shooting efforts, the better you’ll be able to determine where your best betting opportunities are.
Edited to add color.
MP
If you don't mind, I'll just do a simple cut-and-paste out of my book, The Mad Professor's Crapshooting Bible:
Optimal Bet Size
Figuring out how much money to put in action when you have an edge has gotten the attention of a large number of bright people over the years.
There’s no reason to reinvent the wheel, and crapshooters don’t have to waste their time or money trying to figure it out anew. They can do what card counters have done, which is to apply the work that has already been done by bright people for other forms of investment.
Proper advice on how to bet your money at craps does not differ from proper advice on how best to invest your money in the stock market or real estate, or in building a new factory.
Proper advice for craps or any other investment requires three things:
~Realistic estimates of your bankroll
~Accurate estimates of the edge the investment is likely to provide
~Evaluation of the inherent risk the investment carries.
Crapshooters are lucky; it’s possible to quantify your expected edge and risk on any bet you may look at making.
While it’s possible to quantify your expected edge and risk to calculate optimal bets and bet sizes, the calculations are not easy enough to do in your head while you are standing at a crap table.
Therefore you need some easy-to-follow rules of thumb to determine the proper bets to make and their associated bet sizes. That is, you want some general rules that will give recommendations close to what is optimal.
The Kelly Criterion
The mathematics of calculating the optimal bet size is called the “Kelly Criterion” in honor of John L. Kelly, who wrote the first paper describing the methodology.
Most professional gamblers report satisfaction with betting an amount equal to 25% to 50% of the Kelly amounts; doing so is referred to as betting “quarter-Kelly” or “half-Kelly.”
This section explains how to capitalize on your precision-shooting skills by
betting quarter-Kelly to half-Kelly.
Optimal Bet Size and Wager Meet Joe Average
It’s okay to bet less than the optimal amount. Think of the optimal bet size as being what a computer would tell a machine to bet if the machine was betting your bankroll and could throw the dice exactly the way you do.
There are all kinds of reasons you might bet less than is optimal, including nerves or a casino that won’t comfortably take bets as big as you should be making.
The point is that you can bet less than the optimal amounts that we are talking about here; it’s just that your winnings will be significantly lower than your talents deserve.
Find Your Best Edge on Four, Five or Six
Finding your edge and then betting it appropriately is not all that complicated.
Whatever edge you have betting on the four you will also generally have betting on the ten when a large enough sampling is taken.
Whatever edge you have betting on the five you will also generally have betting on the nine when a large enough sampling is taken.
Whatever edge you have betting on the six you will also have generally betting on the eight when a large enough sampling is taken.
In other words, when you have an advantage over the Buy-4; then your approximate edge over the Buy-10 will generally be somewhat close to your edge over the B-4 when a large enough sampling of in-casino roll-stats are accumulated.
You will find that 'smoothing' effect affects each pair of twinned-numbers equally (5 with the 9 for example) as you gather more in-casino roll-stats. Sometimes one will lead the other...and at other times, the former leader will lag. Over time, each set of twinned numbers (like the 6 with the 8) will generally match each other in advantage).
When you decide which dice set gives you the best edge-per roll betting on the four, five or six, then you have an equally good set to use on the ten, nine, or eight, respectively. So for example, your best-set for the '6' will generally be the best set for the '8' as well.
Hardway and field bets are less desirable than bets on those box numbers, due to the extra risk.
You need extra return (a bigger edge) to balance that extra risk, and the hardway and field bets generally don’t promise enough edge to justify taking the extra risk. We’ll take a closer look at those later in this chapter.
So, when you are deciding what set to use for the biggest edge, consider only your edge betting on box numbers. A large portion of your advantage-play profit will flow from them.
How Much to Bet on Your Single Best Number
The math, by coincidence, works out in such a way as to give this rule of thumb for somebody who wants to bet on just one number:
Your optimal bet size is the proportion of your bankroll equal to your edge per roll.
For example, if you have an edge of 2% per roll place-betting the six, then your optimal choice for making only one bet is to place-bet the six with 2% of your bankroll. That 2% will give you between quarter-Kelly and half-Kelly. Note that with each loss, your total bankroll size drops.
Note also that you are basing this on your edge per roll, rather than your edge per decision. It takes an average of three to four rolls to reach a decision on a bet on a number, so your edge per bet is three or four times as large as your edge per decision. An edge of 2% per roll on a certain bet might mean an edge of 7% per decision.
We don’t have to adjust for variance as a separate step; using edge per roll instead of edge per decision automatically allows for variance.
Spreading Your Money Over Two Numbers
You can reduce the risk by spreading your money over two numbers. You can get more return on investment for the same amount of risk if you slightly increase the amount you are willing to bet, and then divide it into bets on two different numbers.
It works out that the amount you can justify betting increases by 50% if you can spread that money over two profitable numbers.
For example, if you have a 2% edge per roll place-betting the six, then you can justify betting 1.5% of your bankroll on the six and 1.5% of your bankroll on the eight, for a total of 3% of your bankroll in action. That 3% will give you between quarter-Kelly and half-Kelly.
The important thing to look at here is that you are putting your money where your precision-shooting edge is, and doing it in proportion to your edge over the house.
Spreading Your Money Over More Than Two Numbers
The first number you bet gives you most of your EV. Spreading money over two numbers gives you most of the possible risk reduction. There is not much additional benefit to spreading to a third number. As you spread out to more and more wagers, your overall edge diminishes faster than your risk diminishes.
If you spread your money over more than two numbers, the optimal amount of money to have out there for total bets does not increase much from what is recommended for two bets.
For example, if you have an edge of 2% per roll and can therefore justify
spreading 3% of your bankroll over two numbers, the amount of your bankroll that you should spread over three or more numbers is only slightly more than 3%.
By restricting the total amount of money that you expose to a seven-out at any particular point, regardless of the total number of wagers that you’ve spread that money on, you safeguard your bankroll.
Thus a good rule of thumb is to set your “seven exposure” (the amount of money you will lose if your next roll is a seven) at 150% of your edge times your bankroll, no matter how many numbers you spread bets over.
For example, if 150% of your edge times your bankroll is $300, then you can justify betting two numbers at $150 each, three at $100 each, four at $75 each, etc. Your seven exposure shouldn’t change when the number of bets that you spread that money across does.
Viewed another way, if you want to spread your money across as many validated-edge bets as you can, then you still have to restrict the total amount of your wagers to maintaining a proper bet size based on your bankroll.
If six and eight are your most profitable numbers and your point is something else, you might as well go ahead and take odds on your pass-line bet as well as place-betting the six and eight, but that’s it.
If your edge on four and six is approximately the same (for example if you have an edge of 2.0% per roll on six and 2.1% per roll on four), then go ahead and bet four, six, eight and ten if you want. Or bet any two of those numbers, or any three.
The more numbers you bet, the less you bet on each, because you want to hold your total seven-exposure down to about 3.2% of your bankroll. (The 3.2% is 150% of your 2.1% edge.)
The important thing to keep in mind is that spreading your money over each additional number means taking some money off of your other bets to put on the new number. That’s because all of your bets lose to a seven.
If you feel compelled to bet on multiple wagers, then you have to understand and accept that you are taking some of the money off of your best bets (the ones where you have the highest player advantage) and redeploying it on other wagers where you don’t have as high of an edge.
Between Too Much and Too Little
Of course, you can bet at less than optimal if your or the casino’s comfort level isn’t high enough to permit optimal bet sizing. The flip side of that is betting beyond what is ideal.
If you consistently bet more than the optimal amount, you are putting yourself in a position where future losses are going to harm your bankroll more than future wins will help it.
Don’t try to outsmart your bankroll or overplay your edge over the house. Advantage playing means using your edge in a way that
will grow your bankroll but minimize your risk. If you put too much emphasis on advantage or risk, then your income will suffer.
Field Bets
Using the appropriate dice set, of course, you may find that your highest percentage edge comes from field bets.
The problem with field bets is risk: two or twelve pays triple (or double), and the other results win or lose even money. On a per-decision basis, that makes field bets riskier than bets on individual numbers.
When it comes to wagering money on the field, there are no no-decision rolls. Every roll results in a bet decision. In contrast, a bet on an individual number, say a place bet on the six, will have a large proportion of no-decision rolls.
However, the math does yield an optimal bet size for field bets, in case you want to make field bets with the appropriate set.
A good rule of thumb for an optimal bet size on the field is 10% of your edge per roll.
For example, if you have a 6% edge on field bets, you can justify betting 0.6% of your bankroll in the field. That is assuming you make only the field bet, and do not simultaneously have large bets riding on any other numbers.
If you want to make field bets along with bets on the box numbers, then a good rule of thumb is to include your field bet in your seven-exposure total. If, for example, you have calculated that you can afford $300 of seven exposure, and your edge on field bets is high enough that you want to bet the field, then it’s okay to put some of that total seven-exposure money in the field.
Hardway Bets
The advice for hardway bets is similar to the advice for field bets. The rule of thumb, if all you make is a hardway bet, is a proportion of your bankroll equal to 10% of your edge per roll on that specific hardway bet.
There really is no room for hardway bets in an optimal-betting strategy, and there definitely isn’t any room in it if you’ve got an edge on only two of the hardways, yet insist on wagering on all four of them.
If you enjoy betting hardways, and your skill gives you an edge for the set you are using, then go ahead and have fun; bet your hardways, but accept that you are doing it to enhance your enjoyment of the game, and not because the mathematics of optimal betting recommend it, nor because it will enhance your profit.
If you don’t have a substantial edge over the hardway bets that you wager, then you are giving back some of the player advantage that you’ve worked so hard to obtain.
Putting It All Together
Precision shooting is a thinking-person’s game, yet the decisions you have to make are not that difficult:
Determine the size of your bankroll.
Decide on a dice set.
Find your best bet for that set.
Know your edge per roll for that best bet.
Spread 150% of your edge per roll times your bankroll
over at least two numbers.
Throw the dice and hope the seven does not show.
Optimal Bet Size if Your Edge Is Negative
If your edge is negative, which is another way of saying the casino has an edge over you, then your optimal bet size is zero. Zip. Nada.
That is also the optimal amount to bet on a random roller, and the optimal amount to bet on your own rolls if your dice are not behaving the way you want them to.
Accurately Predicting Your Future Success
Your dice set and your foundation frequencies give the best predictions of what you are going to roll an excess of in the near future. That is, given your in-casino foundation frequencies, you know what each different dice set will offer in terms of betting opportunities.
When you are making your betting decisions, simply look at which set is strongest for a given set of bets, and make your decisions based on that. As your skills improve, your foundation frequencies change, and your betting opportunities progress along with them.
Keeping current with your most exploitable betting opportunities means keeping tabs on developments and changes in your foundation frequencies. As your foundation frequencies change, so too will your optimal bet size, the set you choose, and the numbers you bet.
Optimal Bets Are Not for Everyone, or Every Casino
Now that I have explained optimal bet size, let me add that I do not always bet that way myself. Instead, there are many occasions when I grossly underbet my edge.
My own foundation frequencies and bankroll suggest betting hugely every time that I pick up the dice, but instead of making maximum bets in every casino I enter, I try to identify each casino’s comfort level, and identify a target win for each casino.
I bet big enough to give myself the expectation of achieving that target win
in an hour or less, and often just in one hand (one complete turn with the dice); then I leave as soon as I achieve it.
By winning just enough to stay within a given casino’s comfort level, I can play at the same house on a continuing basis. I generally move around quite a bit instead of hitting the same casino multiple days in a row, and especially on the same shift day after day.
If you are getting heat, it might be because of something that you are doing. If you are winning table-maximum bets (or anything beyond what the casino is currently comfortable with losing, and that amount is often far below the posted maximum-bet limit), then you deserve to be banned, barred, tarred, feathered, and drawn and quartered, and have each one of your bodily organs liquefied
and fed to Satan himself.
Casinos don’t like to lose. Winning table-maximum bets is a stupid way to play. Playing above a casino’s loss-tolerance comfort level just because optimal betting calls for it might mean being banned from further dice tossing at that casino if you win. Common sense says don’t do that.
Don’t Underestimate Your Skill
You may have kept track of your results from day one of your journey on the road to dice setting success. While that is a good way to see how far you have come since you started, the overall numbers pertaining to SRR (sevens:rolls ratio) or any other statistics can be deceiving when you look at rolls that you have accumulated over an extended period of time.
Ask yourself if your precision shooting is better or worse now than it was three or four months ago. If it is better, but you are still using ancient rolls to calculate your edge and determine your best betting opportunities, then you may be shortchanging yourself.
If you derive those figures from the entirety of all of the hands you have thrown over all of the months or years since you began, then you are unfairly diluting and underestimating your current skill level.
By considering your shooting numbers within too big of a historical range or too large of an improving-skills picture, you may not be able to see the forest for all of the trees. Or alternatively, the forest may be impairing your ability to find the one species of tree that you are presently interested in harvesting.
If indeed you have improved, then you may find it more profitable to use a sort of sliding-scale snapshot to measure where you are now compared to where you were last year.
Your roll statistics from the last three or four weeks, if you have enough rolls, are more indicative of your current skill than the average over all the throws that you have made since you first started down this precision-shooting trail.
Your recent roll performance is more relevant to present-day betting opportunities, and is also more pertinent when it comes to repairing current shooting flaws and shortcomings.
Giving more weight and relevance to the most recent statistics allows your current betting to be more in tune with your current abilities.
Your snapshots or time frames of progress measurement should be of a sufficient size to ensure that you aren’t having a few lucky or aberrant sessions, but recent enough to fairly and reasonably measure your ongoing progress.
You can keep all of the roll statistics that you have compiled since day one, but you should definitely view them only in their proper perspective with a forward-moving average, where you consider only the last maybe 360, 720, 1080 or 2160 rolls to indicate your current competence. By using a sliding average, you’ll still be able to chart your overall progress, but your right-here right-now wagering possibilities won’t be hidden.
The more accurately you are able evaluate the merits of your current precision-shooting efforts, the better you’ll be able to determine where your best betting opportunities are.
Edited to add color.
MP
Last edited by Mad Professor on Mon Mar 31, 2014 10:14 am, edited 2 times in total.
Re: How do I calculate my "advantage" for Kelly Criterion?
Wow that is a lot of information, and yes I do have your book. This is my simple way. 8% of my bankroll, not my buy in. So to make it easy let say $1000, that would be $80. Look at my numbers per bone tracker. Spread it between and point. So 15% 6 & 8 I would put $ 30 on each . That leaves me $ 10 pass and $10 for odds. If my point is either 6 or 8 I change it up a little, mattering how may points I have made. after one Hit on the 6 or 8, if I throw a other number I drop to $12. If I am still throwing 6 & 8's I stay up till another number shows. I played this, this past weekend and it worked well. I am not a very good gambler, so take it as it is.
offaxis
Re: How do I calculate my "advantage" for Kelly Criterion?
Man, I've got a lot of (re)reading to do... and even more math work.
Thank you both, Heavy and MP, for your posts!
Thank you both, Heavy and MP, for your posts!
Re: How do I calculate my "advantage" for Kelly Criterion?
Note that bankroll is defined differently by most AP's than how you and I would define it. For them it's the total amount of money you'd have to win before you'd say "enough is enough" and give the game up. In other words, by their definition total bankroll includes money you may not even have yet. I'd stick with a percentage of my "trip" bankroll just to keep it simple - and sane.
"Get in, get up, and get gone."
- Heavy
- Heavy
-
shunkaha
Re: How do I calculate my "advantage" for Kelly Criterion?
One thing I'd like to add to what has been said, the main issue with any method of betting your edge, it is predicated on the idea that edge is proven and consistent. Usually neither of those things happen to be true, not that they couldn't be but usually they aren't. I should probably clarify what I mean by proven and consistent since in theory they could mean different things to different people. Some people have a nasty tendency to look at a very small sampling of data and attempt to extrapolate from it...
Full Definition of EXTRAPOLATE
transitive verb
1 : to infer (values of a variable in an unobserved interval) from values within an already observed interval
2 a : to project, extend, or expand (known data or experience) into an area not known or experienced so as to arrive at a usually conjectural knowledge of the unknown area <extrapolates present trends to construct an image of the future>
b : to predict by projecting past experience or known data <extrapolate public sentiment on one issue from known public reaction on others>
In other words they make a wild ass guess based on the tendency of the brain to try to seek patterns rather than look at statistics [for instance last trip a woman said 10 was her number, then tossed 5 hard 10s in one hand... the pattern seemed to bear out what she said, the remaining hands statistically said 10 was not her number even if it was kind to her that hand], another example from that trip, my shooting could be taken and examined and based upon which portion was observed the person looking to bet accordingly would think I could toss comeouts but no box numbers to speak of or they could think the converse was true... depending on which table and what part of the night... both are true. The problem comes in not having enough data to determine what is variance and what is the statistical norm for either the shooter in general or that shooter on that table. In my case, and I am by no means saying that I am a great shooter I am merely using myself because I am the only shooter I have complete knowledge of as opposed to anecdotal evidence of their shooting. I know that typically I can either do well on comeouts, numbers, or points, but not all of the above in one hand, I just have to determine what I am doing at that point and act accordingly, sometimes I have bad nights in which I cannot do well in any of those things.
The problem comes in when a player believes he knows what edge he has but does not, or does not at that moment. I say this because too many people go into a casino underfunded, for instance in baccarat if there was no vig on the banker bet you'd have an edge of something like 3%, yet I have personally seen nights that a player could lose $1,000s if not $10s of thousands betting something that they should have an edge in, because variance wiped out that edge and without enough money would wipe out their entire bankroll. The real question being, how may tosses do you track to know your edge, and based on the money you wish to bet how big should your total bankroll or trip bankroll be to survive variance, beyond that, at what point do you spot when variance ceases to be variance and becomes a new statistical norm for you on that table, etc.
Anyway, just food for thought.
Full Definition of EXTRAPOLATE
transitive verb
1 : to infer (values of a variable in an unobserved interval) from values within an already observed interval
2 a : to project, extend, or expand (known data or experience) into an area not known or experienced so as to arrive at a usually conjectural knowledge of the unknown area <extrapolates present trends to construct an image of the future>
b : to predict by projecting past experience or known data <extrapolate public sentiment on one issue from known public reaction on others>
In other words they make a wild ass guess based on the tendency of the brain to try to seek patterns rather than look at statistics [for instance last trip a woman said 10 was her number, then tossed 5 hard 10s in one hand... the pattern seemed to bear out what she said, the remaining hands statistically said 10 was not her number even if it was kind to her that hand], another example from that trip, my shooting could be taken and examined and based upon which portion was observed the person looking to bet accordingly would think I could toss comeouts but no box numbers to speak of or they could think the converse was true... depending on which table and what part of the night... both are true. The problem comes in not having enough data to determine what is variance and what is the statistical norm for either the shooter in general or that shooter on that table. In my case, and I am by no means saying that I am a great shooter I am merely using myself because I am the only shooter I have complete knowledge of as opposed to anecdotal evidence of their shooting. I know that typically I can either do well on comeouts, numbers, or points, but not all of the above in one hand, I just have to determine what I am doing at that point and act accordingly, sometimes I have bad nights in which I cannot do well in any of those things.
The problem comes in when a player believes he knows what edge he has but does not, or does not at that moment. I say this because too many people go into a casino underfunded, for instance in baccarat if there was no vig on the banker bet you'd have an edge of something like 3%, yet I have personally seen nights that a player could lose $1,000s if not $10s of thousands betting something that they should have an edge in, because variance wiped out that edge and without enough money would wipe out their entire bankroll. The real question being, how may tosses do you track to know your edge, and based on the money you wish to bet how big should your total bankroll or trip bankroll be to survive variance, beyond that, at what point do you spot when variance ceases to be variance and becomes a new statistical norm for you on that table, etc.
Anyway, just food for thought.
Re: How do I calculate my "advantage" for Kelly Criterion?
Thanks again, Guys!
I agree with you Heavy... I was never gonna run the calculations against my bankroll; I thought I'd be overwhelmed enough restricting it to my trip stake.
Shunkaha, there ain't no doubt my sampling is too small. I've only got a logbook of 8 or 9x720 rolls...and they date back 8-10 weeks. I've got a 'signature' number... I don't record my live casino throws, but it's either the 5, 6, 8, or 9.
I record the box numbers I roll with chips as indicators in the rack when I roll, and most often I seem to hit 8's and 9's, but I wouldn't swear the 5 or 6 doesn't populate the chip rack as often. In any case, there's certainly not a provable single signature number yet in my sampling. That's gonna make it a LOT tougher to come up with a figure for an EV.
I agree with you Heavy... I was never gonna run the calculations against my bankroll; I thought I'd be overwhelmed enough restricting it to my trip stake.
Shunkaha, there ain't no doubt my sampling is too small. I've only got a logbook of 8 or 9x720 rolls...and they date back 8-10 weeks. I've got a 'signature' number... I don't record my live casino throws, but it's either the 5, 6, 8, or 9.
I record the box numbers I roll with chips as indicators in the rack when I roll, and most often I seem to hit 8's and 9's, but I wouldn't swear the 5 or 6 doesn't populate the chip rack as often. In any case, there's certainly not a provable single signature number yet in my sampling. That's gonna make it a LOT tougher to come up with a figure for an EV.-
London Shooter
- Posts: 2590
- Joined: Sat Sep 21, 2013 3:15 am
Re: How do I calculate my "advantage" for Kelly Criterion?
Dork- if you are recording box numbers with chips then surely it will be worthwhile having a small notebook with you and just total things up and write them down after each hand? This is what I have just started doing myself - not recording each roll by roll as I think I would find that too disruptive, but just the total for each box number, all trash, come out winners and then add a 7 out to each hand.
Re: How do I calculate my "advantage" for Kelly Criterion?
DUH!! Right! Thanks, LS.
-
Bankerdude80
- Posts: 1895
- Joined: Sat Jul 13, 2013 6:05 pm
Re: How do I calculate my "advantage" for Kelly Criterion?
I thought I'd bump this thread which touches on right sizing your bets.heavy wrote:I suspect Wong WAS right. Properly size your bets from the beginning and go for it. If you have definite proof of your advantage then you should play a Kelly sized bet and just stick with it. Of course, none of us are going to stand at the table and not bet for the next ten shooters while waiting for the dice. It's betting on the random rollers that ultimately gives the casinos their advantage over us. Combine that with stupid betting practices when we DO have the dice and there's the drain on your bankroll.
BUMP.
"Take the Money and Run...."
- Steve Miller Band
- Steve Miller Band