Optimal bet on true count?

[eds27]

Hi.
I wonder how do I know what my optimal bet would be according to true-count?. I guess it depends on the spread. Most casinos I play at offer at least 1-5 spreds ($5 min - $25 max).

I have seen people use spreads like:
TC -1 Bet 5 (base)
TC 0 Bet 5
TC 1 Bet 10
TC 2 Bet 15
TC 3 Bet 20
... (basically multipling by 2, 3, 4 depending on the count)

and other people using something like:
TC -1 Bet 5 (base)
TC 0 Bet 10
TC 1 Bet 20
TC 2 Bet 35
TC 3 Bet 50
(increasing way more than the other player...)

How do I calculate my optimal bet? does it depend on the number of decks? penetration?
Is there any online calculator or table l could use?

 

[MadMax]

Easy Reading

Some of it depends on number of decks. Using different counts can change betting. Another factor is your bankroll. Just about every modern book on blackjack has a very good explanation of optimal betting.

Max

 

[E-town-guy]

You should post the rules including the pen. and also post your BR. With a $5-25 table it would be really hard to make much of anything at it. You'd have better luck, profit wise, working at McDonalds

I think to make any money you'd have to be really aggressive so bet big as soon as you had the advantage. Since the table max is low you wouldn't have to have a huge BR so here's one idea:

Avoid playing when the count drops below -1

TC = -1,0 $5
TC = 1, $10
TC = 2, $10, 10
TC = 3, $25, 25
TC >= 4, $25, 25, 25 or as many squares as you feel comfortable betting

Some will say this is too aggressive but if you're really daring and trying to make a buck you can max bet as soon as the TC favors you. So at TC=2 you could bet $25 on as many squares as you can get your hands on.

 

[The GameMaster]

Calculating the Optimal Bet

If, by "optimal bet" you mean how much to bet at a particular True Count, it's primarily a function of your advantage and your total bankroll.

For example, if the rules of the game give the casino a 0.50% edge before the shuffle and you're using the Hi/Lo Count or some other count where your advantage increases by 0.50% for each increase of 1 in the True Count (TC), then at a TC of 3, your advantage is about 1%. An optimum betting system calls for you to bet an amount of your bankroll that's equivalent to your advantage; this is known as the "Kelly Criterion", but it wasn't really designed for use in Blackjack, so it has to be modified. Instead of betting 1% of your bank roll at TC 3, you should reduce it somewhat, which takes splitting and doubling into effect. For most games, betting 75% of "Kelly" will work just fine.

To summarize, if your advantage at TC 1 is zero, the optimum (but not the realistic) bet is zero.

If your advantage at TC 2 is 0.50%, your optimum bet is 0.50%*.75*total bankroll. Thus, if you have a $5000 bankroll, your optimum bet is 0.50% times .75, times $5000 or $18.75, which you may have to round up to $20 in real-life play.

If your advantage at TC 5 is 2.0%, your optimum bet is 2.0% times .75, times $5000 or $75. And so forth.

By calculating the optimal bet for each True Count, you will also create a bet "ramp" or schedule - how much to bet when. While a ramp like that is optimal - it gets the most $$$ in the long run - it might reduce your overall advantage somewhat. Generally, a ramp where your top bet is put out at TC 4 will give you a bigger overall advantage, but it comes at higher risk.

A nice byproduct of the optimum bet calculation is that it can give you a good idea as to what size bankroll you'll need. For example, if you want to bet, say, $100 at TC 4, your bankroll should be 1.5% (your advantage) times .75 = .01125 divided into $100, which equals $8888.

I should also note that "Kelly" betting has a risk-of-ruin of 13.5%, which is way too high for anyone but recreational Blackjack players. Those of us who pay our bills from our winnings are more inclined to use a 1 or 2% risk-of-ruin, which means we don't necessarily bet optimally, but in time our bankrolls get so big (some words of encouragement for you) that our top bet is several times that of the typical table limit anyway. At that point, you just blast the casino with huge bets for an hour or so and walk away, win or lose. The alternative is team play, but that's another topic for another time.


GM

 

[zengrifter]

I should also note that "Kelly" betting has a risk-of-ruin of 13.5%, which is way too high for anyone but recreational Blackjack players. Those of us who pay our bills from our winnings are more inclined to use a 1 or 2% risk-of-ruin, which means we don't necessarily bet optimally, but in time our bankrolls get so big (some words of encouragement for you) that our top bet is several times that of the typical table limit anyway. At that point, you just blast the casino with huge bets for an hour or so and walk away, win or lose. The alternative is team play, but that's another topic for another time. GM

If you bet 1/2 your full advantage, and are prepared to cut your unit size in half if the BR tanks by 50% you should have less than a 2% RoR. zg

 

[The GameMaster]

Hello, zg.

Good point, thanks. While "full" Kelly betting implies you can never go broke because you'd be constantly lowering your bets as your bankroll declined in a losing streak, the reality is that you might have to bet $1.12 at some point, which is probably impossible. Because of all the rounding and the requirement to make non-optimum minimum bets, etc., the math involved gives us the 13.5% ROR. However, as Zengrifter stated, if one is willing to cut the bet size after a 50% loss, the ROR can be reduced. The only problem with it - from a personal point of view - is that you lost 50% at "x" bet sizes and are now trying to make it back at one-half "x" bet sizes, so it's now a long grind. But, it sure beats going broke!

GM

 

[Splittingten's]

Hi, I know this question is a little off topic but would appreciate it if someone took the time to help me. I want to know if I am playing a winning game of Blackjack so first let me give you the rules of the game.
6D shoe, 80% penetration, DAS, Surrender allowed, Re-split Aces, Can't hit split Aces, BJ pays 3 to 2, 5$ Min, $1,000 max. Re-split up to four times. Mid-entry shoe available, Can double on any two cards. Dealer hits soft 17. The house edge should come out to about 0.48%.
I have two strategy's, here they are:
Strategy 1: Wong in at a true count of + 1 and flat bet $60 on one spot until the true count falls below +1.
Strategy 2: Start with $1,000 for the session, min bet $5 then once the true count goes to +1 I bet one spot of $60.
Don't feel the need to take in to account bankroll management because I know I am sufficiently rolled but feel free to throw around some numbers. I also know that this type of play will get me a lot of heat.( I'm not worried about getting heat right now, I am just worried about weather or not I can beat the game.)
I shouldn't forget to add that I play most basic strategy deviation's.
One more question, would I have an advantage at a true count of +1 if the house edge was over 0.50%? If I was playing a slightly different game with a house edge of lets say 0.56% then would raising my bet at a true count of +1 be a mistake because the house still have a very slight edge over me still?
THANK YOU so much for reading my post and taking the time to answer it if you do. I really appreciate all the help you provide and I have learnt a great deal from just reading what some of you have to say in your posts. Sorry for not opening up a new thread about this. I'm new to the site.

 

[Taff]

I would say raising your bet at +1 is usually a mistake let alone putting out what appears to be your Max bet. I play ENHC so all my games are around the .50 area HE and I only start raising at +2. I have S.17 which makes our games similar. You're going to lose money.

 

[Meistro]

Optimal bet = advantage * bankroll * .7

So with a 1% advantage and a $10,000 bankroll your optimal wager would be $70.

This is the upper bound of optimal wagering. But you may choose to experience milder fluctuations, and also suffer from a lower hourly win rate, by multiplying by .35 instead of .7. So the formula would then become :

advantage * bankroll * .35

So with a 1% advantage and a $10,000 bankroll your optimal wager would be $35

It is important to look at advantage, and not true count, because with different rule sets you will have different advantages at the same true count. For example under the extremely liberal Colombian rule set of ENHC, S17, DAS, DA2, ES, RSA the average advantage over the TC 1 bin is %+0.7 whereas with the hideous S17, ENHC, NDAS, No resplit, DA2 ruleset of evolution gaming (online live dealer blackjack) there is no player advantage on average over the TC 1 (TC 1.01-1.99) set.

Advantage per true count is determined through simulation. Purchase CVCX from the qfit website, or beg someone here to do a sim for you.

 

[Splittingten's]

First off and foremost, I would like to thank both of you for taking the time out of your day to help me. I really appreciate it!. Secondly, I have an OK understanding of how the Kelly Criterion works but I was just wondering if I was playing a positive E.V game with the rules I posted earlier (6D shoe, 80% penetration, DAS, Surrender allowed, Re-split Aces, Can't hit split Aces, BJ pays 3 to 2, 5$ Min, $1,000 max. Re-split up to four times. Mid-entry shoe available, Can double on any two cards. Dealer hits soft 17. The house edge should come out to about 0.48%) disregarding bank roll. Oh and also, what does ENHC mean? I'm going to google it right now but in case I can't find it on google it would be nice if you can explain that to me too.
Thanks again for taking the time to help me out!
Also, I forgot to mention, I am using Hi-Lo.

 

[sagefr0g]

ENHC means european no hole card.

far as the $5 bet when tc <= 0 and $60 bet when tc >= 1 , it appears that tactic would be plus ev for the game in question.
i used a spreadsheet for a very similar game and data from BJA pg 248 table 10.67, rule H17 DAS LS 4.5/6 pen (note: i'm not sure what the re-split aces or can't hit split aces rule was for table 10.67)
HE = 0.451%
given a 10 grand bank
your:
wl% = 0.725%
ROR = 10.09%
circa 689 hr's to double bank
ev/hr = $14.52
sd/hr = $355.84
avg bet/hand = $20.02
risk of halving bank = 31.77%
chance of doubling roll (no time limit) 90.83%
chance of busting 9.17%

take all that with a grain of salt, in case i made a typo in the spread sheet or totally messed something up.

 

[Meistro]

ENHC is an acronym which stands for 'European No Hole Card'. This is a method of dealing blackjack where the dealer does not take a hole card and in the event of a double down or split against a dealer ten or ace where the dealer ends up with blackjack after taking their hole card (after the players' hands are resolved) the dealer takes all bets. For example

You have 8, 8 on a $50 bet dealer has T.

You split and get 9 on the first hand and stay and get 9 on the second hand and stay. The dealer then pulls an ace for blackjack. You bet lose both $50 bets for $100 in total. This is in contrast with the other most common way of dealing blackjack without a hole card, OBO, which is functionally the same as holecard blackjack. Here the dealer does not take a hole card until the players' hands are resolved, as in ENHC, but in the event of dealer blackjack the player loses the original bet only (OBO) not any doubles, splits or busted hands.

ENHC is more common in Europe (duh) and South America. OBO is common in Western Canada.

This is an unfavourable rule that increases the house edge for a basic strategist by around 0.1% and as a matter of strategy you never split or double against ace or ten, with the exception of splitting AA vs T.

Either betting schedule listed in the OP will generate some long term expected value in the game you have described. But how much you should be betting depends on your bankroll and your advantage.

 

[Splittingten's]

Thank you both so much for your help. I appreciate it very much! @ Sagefrog, when you ran your simulation did you include all basic strategy deviaton's? Also, can you please run the same simulation for me if only the Illustrious 18 was used?
Sorry for asking so many questions. I just thought it would be best to get all the answers now or it would take me more time to get them later.
Thanks again!

 

[sagefr0g]

@ Splittingtens
i didn't run a simulation, i used a spreadsheet that is set up to use the parameters of advantage, frequency and standard deviation with respect to true count (hi/lo). those parameters work in conjunction with a load of formulas (also from mostly BJA) in excel to yield the results i mentioned, plus other results unmentioned. the parameters i obtained from the book Blackjack Attack pg 248 table 10.67.
the simulations used to create table 10.67 did use I18 & fab4 deviations. table 10.67 is one of a large number of tables created from what's named in BJA the "World's Greatest Blackjack Simulation". CVCX was used to create the tables, twenty billion rounds dealt to produce each table.

edit: i assume the reason my spread sheet gave a HE = 0.451% instead of a HE = 0.4835% is because the simulation that created table 10.67 used I18 & fab4 deviations.