a primer on scientific betting

[Meistro]

Given a series of even money wagers with an edge the fastest method of doubling your bankroll is to wager an amount of your bankroll that corresponds to your advantage. This is the so called Kelly Criterion. So if you have an advantage of 1% you should wager 1% of your bankroll. Employing this strategy gives you a 12.5% chance of busting and an 87.5% chance of doubling your bankroll. Wagering more than kelly is counter productive for the purposes of bankroll growth as your swings are too likely to cripple you. Given that blackjack is not a series of even money wagers as you can split, double down or receive a 150% payout it is advised to wager at most 75% of your advantage. Thus with an advantage of 1% (perhaps at TC +3 with okay but not great rules) and a bankroll of $10,000 your maximum wager would be $75.

Of course to many seasoned gamblers even a 12.5% risk of going broke before doubling is too high. You can offset your risk in two ways, either by wagering some fraction of kelly or by resizing your bets should you start to lose (or both). It is important to understand that the kelly criterion is only an upper bound on how much you should bet. For some gamblers it is important to bet near kelly. If you have a modest bankroll you risk being crippled by expenses should you not win at a certain rate. For others, if you have a very large bankroll, then you may wish to ameliorate the swings entailed with counting cards by betting a much smaller fraction. Still even if you choose to wager at 1/2 kelly or 1/4 kelly it is rational to make your wagers correspond in some fashion to the advantages you find yourself in. As each individual has a subjective tolerance for risk and demand for reward there is no perfect one size fits all betting scheme and it is advised to play around with a blackjack simulator to get an idea of what sort of hourly rates you can achieve and what sorts of standard deviation these betting schemes will entail.

Another reason to reduce your bets is for cover. A gambler may feel that wagers over a certain amount may attract undue attention. With counting cards beating the game is only half the battle; the other half is being allowed to play. For this reason some choose to avoid increasing their bets after they lose or decreasing after they win or simply restricting the maximum bet size even though their betting formula indicates they should be betting more. If you feel that a casino will back you off after a given aggregate win it may make more sense to grind out that aggregate win at a smaller max bet. How much you desire continued longevity at a given store can also play a factor. For example if a casino is located near your home then it may make more sense to use a gentler betting spread and also employ shorter sessions whereas if a casino is located half way around the world and you are only in that country for a few weeks a more aggressive 'slash and burn' style may be more optimal.

 

[sagefr0g]

sorry this isn’t so much a blackjack game issue, but at least its to do with betting or not betting on options, decision making, sort of thing.

@ Meistro, or anyone who wants to weigh in.

consider a ‘spectrum’ of positive expectation bets (as three options listed below), that only present perhaps four times a year during a years’ worth of trips. edit: (circa four times/hundred trips) end edit.

the average bet extended for the options listed below would be circa $1,375.00.

assume risk of ruin issues are under control.

bet option 1:

advantage 8.4% thru 10.63%

best case $392.90 thru $393.40

worst case expectation -$131.25 thru -$88.75

expected value $131.25 thru $152.75

bet option 2

advantage 10.67% thru 13.57%

best case $393.41 thru $393.95

worst case expectation -$87.90 thru -$42.00

expected value $153.18 thru $176.40

bet option 3

advantage 13.63% thru 16.77%

best case $393.96 thru $394.44

worst case expectation -$41.15 thru -$0.35

expected value $176.83 thru $197.47



it’s realized that option 3 is the most desirable option, option 2 is the second most desirable option and that option 1 is the least desirable option.

the question being, with respect to the scarcity with which the options present how would one quantify the relative value of the options?

and is option 1 even worth taking a chance on, or is it wisest to make the option 1 bet when it presents, because of opportunity risk?

is the problem presented, just a subjective qualitative certainty equivalent question or is there a way to properly, scientifically evaluate the decision?

i suspect the problem is just a matter of subjective qualitative certainty equivalence of a given individual.

edit: maybe to clarify the question a bit would be to put it this way.
how would one use best case, worst case expectation, expected value and advantage values to weigh the decision as to whether to make a bet or not for a given option given scarcity of the option?
it would seem there would be some calculable value that could be obtained from the above mentioned values that could influence one's decision.
end edit

 

[DSchles]

You state that ROR is not a problem; i.e., you are adequately bankrolled. All of the opportunities are clearly large positive expectation. So what is there to question? You have no reason to "rank" the plays. You obviously should play them all. Your question doesn't make much sense.

Don

 

[sagefr0g]

You state that ROR is not a problem; i.e., you are adequately bankrolled. All of the opportunities are clearly large positive expectation. So what is there to question? You have no reason to "rank" the plays. You obviously should play them all. Your question doesn't make much sense.

Don

thank you for your response.

here’s a short story, that illustrates the problem. the other night, i wasn’t doing particularly well, only made $94.74, the night was almost over, far as i was concerned. but then i came upon a play that was a similar option to the ones i previously listed. this case was as follows:

advantage 1.94%
best case $390.79
worst case expectation -$310.60
expected value $40.52

i walked away from it, preferring to pocket my $94.74 for the night, rather than possibly being down $215.86 or less (worst case considered) for the night. of course, i was kicking myself over possibly not making another $40.52 or even up to another $390.79 should lady fortuna have smiled upon me. i have AP friends who would probably kick my a$$ for having not made the play or at least laugh me out of the casino. they’d be like, “what you’re afraid to lose $215, what a wuss, think long run, dummy.” you replied in a similar but kinder fashion, “You obviously should play them all.” part of what went through my mind when i walked away was, imagine that i was given $1,375.00 by my grandmother to put forth into a good quick result, but rarely occurring investment. it seemed to me that this wouldn’t be the investment i’d want to make for her, as it was only likely to bring forth $40.52 while possibly costing her $310.79 should the worst happen. on the other hand, should the factors have been such as option 3 (mentioned in the previous post) then i likely would have made the investment for her, expecting to have made circa $187.15 maybe even $394.20 if lucky and not likely to have lost more than $20.75.

yes, the options are clearly large positive expectation. that said, it’s surprising to me that there would be no reason to rank the plays, unless the rarity of the plays (again circa 4 opportunities a year for these cases) is a factor regarding a decision not to rank them. therein, may be the reason, i even felt compelled to put forth the question. scarcity of resources and opportunity cost is something i struggle to fully understand.

that said, it’s still surprising far as there being no reason to rank those options. blackjack bet sizing’s are ranked with respect to true counts and concurrent ev. such ranking can be a factor regarding when and if to wong a blackjack game. i don’t even know specifically how the bet levels are determined for such ranking, far as blackjack goes. far as i know it’s determined by simulation wherein the factors of tc level and frequency and win rate probability drive the propensity of blackjacks, successful double downs and successful splits, sorta thing. i haven’t a clue if factors such as best case, worst case expectation are taken into consideration with respect to blackjack bets. but they are parameters that can be easily determined for the type of bets i’ve been describing. plus the scarcity of plus ev bets for the bets i’ve been describing are far, far, far greater than plus ev bets in blackjack. point being, with blackjack play one finds a multitude of opportunities to realize rectification of a bet gone awry during a night, the types of bets i was describing, one may have to wait in the neighborhood of three months for the opportunity of such rectification.

hence my interest in the plausibility of using the known parameters of advantage, expected value, worst case expectation and best case to help decide if one wants to make the bet or not.

 

[London Colin]

hence my interest in the plausibility of using the known parameters of advantage, expected value, worst case expectation and best case to help decide if one wants to make the bet or not.

The relevant parameters are those of the Kelly Criterion, and the only reason not to make a bet would be if the min bet is greater than your Kelly bet.

E.g.,
If your bankroll is $1000 and you have a +1% EV opportunity that pays 2:1 then your Kelly bet is 1% * 1000 / 2 = $5.
If your bankroll is $1000 and you have a +10% EV opportunity that pays 200:1 then your Kelly bet is 10% * 1000 / 200 = $0.50.

Depending on the min bet, it may be that you can make the +1% EV bet, but should sit out the +10% EV bet.

One potential area for doubt, it seems to me, is what to do if your preferred bet size is some fraction of Kelly, and this is less than the min bet, but the min bet still does not exceed your full Kelly bet. It's tempting to follow a policy of making such bets, whenever this situation arises. I suppose the impact of that on the volatility of your bankroll will depend on just how often you can expect to face this dilemma.

 

[ZeeBabar]

I dont quite get all of this. I moved up from $10 to $25 min. bet after my BR crossed $25k, use a max bet of $150 (DD games) or 2 x $150. I now mostly play 2 hands of $25 each and move up to 2 hands of $150 at TC5 or greater.

Now my BR is about $48k and I am mulling if I am ready to try a $50 min bet. game using only one hand of $50 to one hand of $250 (1-5) spread in DD games. Its because I am more likely to get heads up games or with one person at the HL rooms.

Any comments are appreciated.

 

[Meistro]

Game speed / playing heads up is extremely important. You may also have more luck getting a heads up game at $25 min tables if you try playing at off-peak times. You could also consider simply increasing your max bet and spread.

 

[ZeeBabar]

Maestro, where I play, the $25 game is in the open area and the $50 minimum game is in the HL area. There is one table in open area with a DD game (double 9-11, no DAS) and another table in the HL room with the same rules. However, the penn is deeper in the HL room and you can play heads up for longer periods.

The penn is what makes the $50 attractive. There are two better games at two better casinos in my town but they have started taking counter measures and pen is under one deck.

 

[LV Bear]

Maestro, where I play, the $25 game is in the open area and the $50 minimum game is in the HL area. There is one table in open area with a DD game (double 9-11, no DAS) and another table in the HL room with the same rules. However, the penn is deeper in the HL room and you can play heads up for longer periods.

The penn is what makes the $50 attractive. There are two better games at two better casinos in my town but they have started taking counter measures and pen is under one deck.

Be aware that you will face much more scrutiny in the high limit room, especially if you are the only player there.

 

[LV Bear]

here’s a short story, that illustrates the problem. the other night, i wasn’t doing particularly well, only made $94.74...

How do you make 74 cents? At first, I thought it was a typo, but it was repeated later in the long post.

 

[sagefr0g]

The relevant parameters are those of the Kelly Criterion, and the only reason not to make a bet would be if the min bet is greater than your Kelly bet.

E.g.,
If your bankroll is $1000 and you have a +1% EV opportunity that pays 2:1 then your Kelly bet is 1% * 1000 / 2 = $5.
If your bankroll is $1000 and you have a +10% EV opportunity that pays 200:1 then your Kelly bet is 10% * 1000 / 200 = $0.50.

Depending on the min bet, it may be that you can make the +1% EV bet, but should sit out the +10% EV bet.

One potential area for doubt, it seems to me, is what to do if your preferred bet size is some fraction of Kelly, and this is less than the min bet, but the min bet still does not exceed your full Kelly bet. It's tempting to follow a policy of making such bets, whenever this situation arises. I suppose the impact of that on the volatility of your bankroll will depend on just how often you can expect to face this dilemma.

thank you for the response. i'm a bit unable to keep up with your statements, but i'm sure it's just my lack of expertise with respect to kelly bets. i'll try and mull over your response to see if i can better understand. it'll probably take some time though.
i did however find an answer with respect to my question originally posed.
i should have qualified my question with a description of my quirky erratic demeanor and position taking when it comes to advantage play. in essence i'm goal driven with respect to a given trip. the goal is based on what has been my average trip win over a fairly long time period. for a given trip, i like to achieve at least close to that average or (of course) above that average. if that happens, i'm happy. hence my question regarding some bet that may have a nice high advantage and (seemingly paradoxically) the question of whether i wanna make it or not. so it's just a quirk, a preference (and perhaps a dumb one), but it is what it is, or it is how i am. so yep, i may or may not pass up a plus ev bet depending on my quirky goal driven position. my problem was, how do i decide if i want to make some bet, or pass it by. essentially, for me, it's a 'qualitative' certainty equivalence problem. definitively i wouldn't pass up a for 100% sure winner, but if i know the bet isn't a 100% winner even though it has a nice high positive ev i might in fact pass it up (reason being, the bet could make me not realize my trip goal). again, my problem was how to decide if i want to forgo the bet or make the bet.
the solution for my quandary didn't turn out to be definitive, but it did turn out to be more informative than just being scared or afraid to make the bet, lol .
the solution turned out to be something, i read about in the past, but hadn't realized how i might use it.
it's the ratio of expected value to worst case expectation, one gamble at a time:
expected value/worst case expectation
if the above ratio is a positive number, there is no way in hell that i'd pass it up
if the above ratio is a negative number, then i'd be mulling over whether or not i'd want to make the bet. but one thing that would help my decision making in such negative number cases would be the size of the negative number.
if the ratio is >= -1 <0 , i'd likely not make the bet
if the ratio is < -1,-2, -3,... i'd be deciding, on the fence, sorta thing. might do it, might not. edit: the more negative the more likely i'd make the bet end edit.
again that's just for the rare, scarce sort of bets that i might run into when i'm close and near to my trip average. (quirky, i know, but a fact of life for me)
if anyone thinks that's strange, the even funnier thing is, at the beginning of a trip, or on a trip where i haven't made any money or am unable to find any other advantageous plays, i very likely would make just about any positive expectation bet (including the rare scarce ones described), with out a real lot of regard for the expected value to worst case ratio. i say funny, but i guess most ap's would say that's the thing to do all the time.

edited (correction for negative ratio s above) & (stated not make bet for ratio > -1 <0 )

 

[sagefr0g]

How do you make 74 cents? At first, I thought it was a typo, but it was repeated later in the long post.

no disrespect sir, but i'd prefer not to go into that. but here's a hint, the bet isn't necessarily on blackjack.
your inquiry reminds me of a question that i've wondered about.
is there any game, any game what so ever in a casino that one could play and be absolutely guaranteed to make at least 1 cent?
if anyone knows, please lemme know