Calculating Max Bet/ROR with Renewable Bank Roll?

[weballinoutacontro]

edit: more appropriate title would've been Replenishable Bank roll

Trying to figure out what my appropriate max bet should be.

I recently got CVCX, but haven't had too much time to play with it yet, since I can't install it on my work computer, which is where I at least feel like I am what 99% of the time.

I tend to keep around $2k in cash to roll up to my local casinos for poker and blackjack, plus my ATM withdrawal limit comes to around $1500.

However, I don't really keep a dedicated playing bankroll, all that I really need to figure out is a TRIP bankroll, and then a maximum bet to be reasonably confident I won't bust out on that in a short couple of days or whatever. Does CVCX have any kind of capability like this? ROR for a very short trip is obviously much, much tinier than it would be for an overall non-replenishable bank roll.

I usually play in CO, where max bet is $100. I have a solid amount of hours logged here, and the most I've ever gone down in one playing session losing a lot of max $100 bets is something like $800, and never come close to even emptying my wallet of the $2k ish I usually have on me, running a maximum possible spread of either $5 or $10 up to $100.



But, say I'm making a trip to Vegas soon - the most I wouldn't really mind losing is somewhere around $5k or so, but could probably stomach between $5-10k. Question is then, how much should my max bet be, given that this is only a TRIP bankroll. I do log my sessions and keep a separate accounting for my poker, BJ, and day job, but fact of the matter is, (and without wanting to disclose my actual earnings here,) it is very unlikely that my casino winnings would approach what I make in my day job

I would say, I'd be looking find a standard % chance of ROR (what do most people go for. <5%?), but only after maybe 20 or max 30 hours of play, and likely less than even 20.

Given these parameters, can anyone help me guess at an appropriate spread? If it matters, I'm NOT a risk averse person, so definitely want to spread on the larger side. Would going 10:1 at something like $25-250 make sense? Is bigger reasonable? Too big?

Side question might be, I hear you get better rules and stuff in high roller rooms (I've been to Vegas, but not as an AP before). Is this true, and if so, what is the typical min to get that? Or, would it just be a terrible idea to spread in a high roller room?

Thanks

[Stealth]

I had this comment in my excel file for bet design but I don't recall the author.

Perhaps it will help in you search for an answer.

The question is, if you play part time and add to your bankroll regularly from non-gambling sources, what part of this future income can you include in your current bankroll when sizing
bets?

It turns out to be a somewhat tricky problem because in Kelly theory any fixed amount eventually gets swamped by an exponentially increasing bankroll.

It is solvable in closed form. I have derived a formula which I have cross-checked with simulation results to confirm that the desired risk of ruin is maintained. I also believe the
formula applies to pure Kelly betting (i.e., constant bet re-sizing) although I have not confirmed that through sims.

Suppose you have $9000 currently available for gambling and you can add $3000 a month to that amount. You only play around 12 hours a month, and desire a 5% RoR. What size bankroll
can you pretend you have when you size your bets?

MathProf responded that if you are really sure about your savings rate, you could add 12 months to your bankroll making it $45,000. I responded that it will depend critically on the
doubling time of the games you find. A high-quality game requires more of your bankroll to be available right away. I guessed that you could include non-gambling income proportional to the
doubling time, N 0 Someone else reported that you could simply use double your initial bankroll as your effective bankroll.

Here is my formula:

B = B 0 ( 1 + sqrt(1 + 4 I N 0/(k B 0)) ) / 2

B 0 is your actual present bankroll,
I is your non-gambling income per round (or the
non-gambling income per month divided by the number of
rounds you play per month),
N 0 is the doubling time in rounds,
k is your Kelly factor (use 0.7071 if you desire 5% RoR and no
unit resizing),
B is your effective bankroll that you are allowed to use to size
your bets,
and sqrt() is the "square root" function.

Deciding on effective bankroll: B 0 is $9000.

I is $3000/1200 = $2.50, assuming 100 hands per
hour and 12 hours play per month.
* Now we need to know the quality of the games that will be played. Spreading fairly aggressively on handhelds, let’s say his doubling time is N 0 = 10,000 rounds. To get a RoR of 5% you choose k = 0. This assumes no unit resizing.

Plug in all the numbers -- his $9000 bankroll is now $23,402. Note that this is considerably less than MathProf’s recommended $45,000, but I will try to redeem his intuition shortly. If we instead assume that his N 0 is 20,000 rounds then his effective bankroll is $30,849, and if we use N 0 =
40,000 then we get $41,491.

[weballinoutacontro]

Interesting. Thanks for the post.

I'd be interested to know where the OP of that post derived that formula from

[Meistro123]

Bankroll doesn't have to refer to the amount of cash you have on you. You can have $3000 cash and $7000 in a bank account specifically devoted to blackjack and consider this a $10,000 bankroll. From the information you have provided $250 seems pretty reasonable. You could also drop down to $150 if you lose $3k or so just to ensure that you stay in action throughout your whole trip.

[Monty]

Here is my formula:

B = B 0 ( 1 + sqrt(1 + 4 I N 0/(k B 0)) ) / 2

B 0 is your actual present bankroll,
I is your non-gambling income per round (or the
non-gambling income per month divided by the number of
rounds you play per month),
N 0 is the doubling time in rounds,
k is your Kelly factor (use 0.7071 if you desire 5% RoR and no
unit resizing),
B is your effective bankroll that you are allowed to use to size
your bets,
and sqrt() is the "square root" function.

From what I remember this was quite a controversial formula. They also use n0 different from the traditional Don S. creation.

[Stealth]

From what I remember this was quite a controversial formula. They also use n0 different from the traditional Don S. creation.

I wish I could recall the author but I assure you I recognized him at the time. If you think it was controversial, do you have a suggested improvement.

What do mean by using N0 different than Don?

I use this in my bet design software and it seems very rational. I am always happy to have one of the stat whiz's correct the formula by providing a better one. I have been unsuccessful locating such.