Kelly Conundrum

bj bob

Well-Known Member
#1
I have recently arrived at a mathematically interesting milestone in my dedicated BJ bankroll and, after considering several possible solutions, I am throwing this one out to you guys for your sage input. Here's the scenario:
I am currently playing $5 units on SD and have started with a $2700 BR for these purposes only. I assume that this amount represents full (BJ) Kelly for a $5-20 spread. The problem has occured now that I have increased the BR by 50% and now stands at $4000. If I want to keep all the ratios the same, i.e. RoR, bet spreads, EV etc., then what can I do at this point? The options seem flawed for one reason or another:
1) Increasing min/max. bet would put me over Kelly.
2) There are no $7.50 chips.
3) Stretching spread would invite certain pit attention.
4) Compressing the spread (i.e. $10-30) would, I believe lower my EV.
So thus is the dilemma. Any mathematically acceptable suggestions out there that I haven't thought of?
 

mdlbj

Well-Known Member
#2
I think the obvious answer is to wait until you reach 5500 to change your bankroll unit. This will give you a 10 dollar Bankroll Unit and a 5 dollar betting unit @ .5 kelly. What are you looking for exactly?
 

EasyRhino

Well-Known Member
#3
bj bob said:
3) Stretching spread would invite certain pit attention.
I think you already know my vote. :)

Maybe adopt a "big off the top" strategy on SD, where you bet at least $10, have a max bet of $30, but drop to as low as $5 in negative counts? I dunno, doesn't sound like a great compromise.

At this awkward stage of bankroll, one idea would be just enjoying the lower risk of ruin with your current bankroll, and if it grows larger, increase your unit when it's more convenient.

Betting a red and two silver every min bet hand would probably drive the dealers (and you) too nuts to deal with for long.
 

bj bob

Well-Known Member
#4
mdlbj said:
I think the obvious answer is to wait until you reach 5500 to change your bankroll unit. This will give you a 10 dollar Bankroll Unit and a 5 dollar betting unit @ .5 kelly. What are you looking for exactly?
Yeah, That was my conclusion also, but I was trying to avoid that and the other obvious one, add another $1500 to the pot and voila! go to the $10 table. I guess my original premise was correct-there's no way to do it internally.
 
#5
1).

Kelly as an absolute indicator of RoR only applies to an unreal situation- a fixed, non-replenishable bankroll with no additional income. And still it gives you a 13% risk of ruin, assuming no resize. How much better is that than playing to a 20-25% RoR?

A better approach for a part-timer is to set your game for a win rate, that rate being the dollars per hour you are willing to play for, and see what your RoR is for that. Being also for a part-timer your biggest problem is running out of money in the middle of a trip, you have to be able to adjust your spread in case you start out bad, if you don't want the trip to end abruptly. Better to finish the trip playing for an abbreviated EV than spend it not playing for zero EV. So my approach would be to start out bold, then readjust depending on which way the wind blows.
 

bj bob

Well-Known Member
#6
Automatic Monkey said:
1).

Kelly as an absolute indicator of RoR only applies to an unreal situation- a fixed, non-replenishable bankroll with no additional income. And still it gives you a 13% risk of ruin, assuming no resize. How much better is that than playing to a 20-25% RoR?

A better approach for a part-timer is to set your game for a win rate, that rate being the dollars per hour you are willing to play for, and see what your RoR is for that. Being also for a part-timer your biggest problem is running out of money in the middle of a trip, you have to be able to adjust your spread in case you start out bad, if you don't want the trip to end abruptly. Better to finish the trip playing for an abbreviated EV than spend it not playing for zero EV. So my approach would be to start out bold, then readjust depending on which way the wind blows.
So you're saying that I should go right to the $10-40 spread and don't worry about anything else at this point, since I can always add to my BR?
You're also saying that Kelly pertains ONLY to non-replenishable funds, which I already have assumed. I was just trying to "play by the book" here and testing the validity of all the academia and not "cheat" so to speak.
BTW, I also have a separate BR for DD dalliances. Same thing applies?
 
#7
bj bob said:
So you're saying that I should go right to the $10-40 spread and don't worry about anything else at this point, since I can always add to my BR?
You're also saying that Kelly pertains ONLY to non-replenishable funds, which I already have assumed. I was just trying to "play by the book" here and testing the validity of all the academia and not "cheat" so to speak.
BTW, I also have a separate BR for DD dalliances. Same thing applies?
DD I assume refers to double deck, not Hooters girls right? Yes all the same. The RoR calculated by the Kelly criterion assumes not only no replenishment but no resizing of bets, and at full-Kelly 13% of the players' BR's will go to zero, while 87% will go to infinity. Being we can resize any time we want, as well as quit playing until we get more funds, and will never make it to infinity, in the real world we have a lot of flexibility around this guideline.

One thing it's good to not stray from is Kelly-proportional betting when defining the slope of your spread, meaning, the bet at each count should be proportional to the advantage at that count. Because you get the maximum total advantage for a constant risk when you do that, and if you deviate then you don't get paid fairly for the additional risk you are assuming.
 

EasyRhino

Well-Known Member
#8
Wait, you have a separate stash of funds that you use for double deck? I'd recommend combining those funds, treating it as one bankroll, and using it for whichever game you're playing.

Of course, the DD game is going to require a bigger spread to be profitable, and if you want to keep risk the same as SD, that means you'll have to move the spread downward as well as upward. (smaller min bet for DD than SD)
 

bj bob

Well-Known Member
#9
On paper only

EasyRhino said:
Wait, you have a separate stash of funds that you use for double deck? I'd recommend combining those funds, treating it as one bankroll, and using it for whichever game you're playing.

Of course, the DD game is going to require a bigger spread to be profitable, and if you want to keep risk the same as SD, that means you'll have to move the spread downward as well as upward. (smaller min bet for DD than SD)
My single deck BR and double deck are documented as separate entities for accounting purposes only. I'm sure you can appreciate that, being an accountant yourself. The reason is just for tracking purposes, as I can keep up with $/hr. averages and bankroll fluctuation differences between the two, again solely for academics and making sense of the more theorhetical aspects such as N0 etc.
 

Sonny

Well-Known Member
#10
bj bob said:
I am currently playing $5 units on SD and have started with a $2700 BR for these purposes only. I assume that this amount represents full (BJ) Kelly for a $5-20 spread.
Your max bet is .7% of your bankroll? That sounds pretty small for full Kelly. I would expect a max bet of around $40 at a 2% advantage, which is probably close to where your max bet should be. That’s just my guess.

bj bob said:
The problem has occured now that I have increased the BR by 50%
I wish we all had problems like that. :laugh:

bj bob said:
The options seem flawed for one reason or another:
1) Increasing min/max. bet would put me over Kelly.
Why? Now that your BR is bigger you should be able to resize your bets in order to preserve your full Kelly stats. As long as your bets are the same percentage of your total BR you should be fine.

bj bob said:
2) There are no $7.50 chips.
Ah, that’s a problem. You could use $7 units but that would look clumsy and piss off the dealers. Since you’re not ready to move up to $10 units I would stick with $5 units until you're ready to double up.

bj bob said:
3) Stretching spread would invite certain pit attention.
Another problem. This is where the plan “on paper” gets squashed by real life. To use a bigger max bet will bring more attention so you need to find some new techniques. Either get some new cover tricks, AP tricks or look at other games to play. If they won’t handle your action at the SD tables then think about how you would beat the other tables. Maybe you’re ready to graduate to the DD tables or shoe games. Maybe you’re ready to graduate to some clever “tricks” to beat the SD game instead of straight counting.

As you start to “outgrow” your BR you have to either accept the same EV or find a way to make your bigger bets work. Most books don’t talk about that at all.

bj bob said:
4) Compressing the spread (i.e. $10-30) would, I believe lower my EV.
Right. You don’t want to compress your spread too much, but if your min bet was a 50/50 mix of $5/$10 bets (maybe a random progression in neutral/neg counts?) then you would be laying down nice cover and your min bet is now $7.50. Who needs $7.50 chips? Sometimes a mixed strategy will work better than a pure strategy.

-Sonny-
 

EasyRhino

Well-Known Member
#11
bj bob said:
My single deck BR and double deck are documented as separate entities for accounting purposes only.
Okay, that's a good point, but are you saying that besides the $4000, you have MORE money also dedicated to gambling?

If so, I say, draw a big line in your spreadsheet, continue to track results separately if you wish, but feel free to up your unit.
 
#12
To bj bob

I would recommend doubling your bets once you increase your bankroll by 75%. If you lose down to 150% of your starting bank then go back to your original bets. If you think about it this is a betting ladder up and down that you can use with your bankroll.

Example:

If you have a starting bankroll of $10,000, once your bankroll increases to $17,500 then double your bet. If you lose down to $15,000 then go back to your original bets.

If you are willing to add outside funds to your bank if needed then double your bets now.

What everyone else has said is fine, it's mostly a risk vs. reward decision you have to make.

Good Luck
 

bj bob

Well-Known Member
#13
Sonny said:
Your max bet is .7% of your bankroll? That sounds pretty small for full Kelly. I would expect a max bet of around $40 at a 2% advantage, which is probably close to where your max bet should be. That’s just my guess.
-Sonny-
It's my understanding that the Kelly ratio when used for BJ is supposed to be .76% of true Kelly due to the less than 50/50 nature of the game as well as accounting for doubles and splits, correct?
 

bj bob

Well-Known Member
#14
Sonny said:
Right. You don’t want to compress your spread too much, but if your min bet was a 50/50 mix of $5/$10 bets (maybe a random progression in neutral/neg counts?) then you would be laying down nice cover and your min bet is now $7.50. Who needs $7.50 chips? Sometimes a mixed strategy will work better than a pure strategy.

-Sonny-
That is the same thought I had while thinking of a way around this. The whole idea of alternating unit bets in an apparently "random" fashion would drive a pit nuts (if most already aren't already:grin: ), and would be especially useful in the anal atmosphere of Reno. The only question I had was if it is still mathematically correct, which after this discuusion, apparently is yes.
 
#15
bj bob said:
That is the same thought I had while thinking of a way around this. The whole idea of alternating unit bets in an apparently "random" fashion would drive a pit nuts (if most already aren't already:grin: ), and would be especially useful in the anal atmosphere of Reno. The only question I had was if it is still mathematically correct, which after this discuusion, apparently is yes.
Yes. You have increased luxury of moving your bets around. zg
 

bj bob

Well-Known Member
#16
EasyRhino said:
Okay, that's a good point, but are you saying that besides the $4000, you have MORE money also dedicated to gambling?

If so, I say, draw a big line in your spreadsheet, continue to track results separately if you wish, but feel free to up your unit.
OK folks! You heard it here first. I just got officially certified to "mingle" funds by a professional Calif. accountant. I feel blessed! Easy, could you sign and stamp my spreadsheet to make it official?
I must, however, maintain my self imposed discipline until my SD bankroll has doubled while maintaining my own SD.:whip: :whip:
 

sagefr0g

Well-Known Member
#17
bj bob said:
OK folks! You heard it here first. I just got officially certified to "mingle" funds by a professional Calif. accountant. I feel blessed! Easy, could you sign and stamp my spreadsheet to make it official?
I must, however, maintain my self imposed discipline until my SD bankroll has doubled while maintaining my own SD.:whip: :whip:
EasyRhino is a professional Calif. accountant?! what the heck did he need with my simple lil excel spreadsheet that keeps track of money won/lost over time at what ever casino sans graph? scared of you Easy ..... lol.
 

bj bob

Well-Known Member
#18
Good to know

zengrifter said:
Yes. You have increased luxury of moving your bets around. zg
That will make my next trip to the High Sierra a little more interesting.
Hey Zg, BTW thanks for sending me that stash of toad powder for my induction to Exec. Member status. It reminds me of the good 'ol '60's. Sure been feelin' warm and fuzzy all evening. Does it also come in menthol?
 

sagefr0g

Well-Known Member
#19
bj bob said:
That will make my next trip to the High Sierra a little more interesting.
Hey Zg, BTW thanks for sending me that stash of toad powder for my induction to Exec. Member status. It reminds me of the good 'ol '60's. Sure been feelin' warm and fuzzy all evening. Does it also come in menthol?
next thing you know you guys will be lickin frogs.... lol
 
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