Double Down For Less
My logic being that you view the double down bet as a completely independent bet...
e.g, You have $100 bet on a hand and you have 6.5 v dealer 6. By taking only one more card (i.e. doubling down) you have a 63.8% chance of winning. Therefore plugging this into a Kelly Calculator (63.8% probability of a win versus a payoff of 50%) says you should bet 27.60% of your bank. Assuming your bank is equal to the original $100 bet on the hand, then you should double down for less and bet $27.60
As a side thought, it would be interesting to run a computer simulation that, when doubling down, uses the Kelly bet as above. Then after a few million trials, you can compare payoffs for just the doubled down bets for kelly stakes versus tradition 100% stakes.
You shouldn't be playing if you can't afford to double down 11 v 6.Quote: jedijonShould you not follow the Kelly Criterion for doubling down at Blackjack if the casino offers 'Double Down for Less'?
My logic being that you view the double down bet as a completely independent bet...
e.g, You have $100 bet on a hand and you have 6.5 v dealer 6. By taking only one more card (i.e. doubling down) you have a 63.8% chance of winning. Therefore plugging this into a Kelly Calculator (63.8% probability of a win versus a payoff of 50%) says you should bet 27.60% of your bank. Assuming your bank is equal to the original $100 bet on the hand, then you should double down for less and bet $27.60
As a side thought, it would be interesting to run a computer simulation that, when doubling down, uses the Kelly bet as above. Then after a few million trials, you can compare payoffs for just the doubled down bets for kelly stakes versus tradition 100% stakes.
If for some reason you found yourself in a situation like that. Perhaps you bet $100 thinking you had $100 in your wallet but you had less I'm sure someone would buy the rest of your double action. Please be a good sport and offer it to your neighbor.
Quote: jedijonIt's not a question of not being able to afford to double down Axel, I'm just raising the question that given the choice to double down for less, is using a Kelly stake a more efficient/accurate mathematical staking strategy to use based on your advantage?
Kelly Criterion > Maximize EV.
If one were to maximize his EV, he would wait until the card (deck, shoe, whatever) composition was +EV, then bet his entire net worth, to maximize his EV. (Or rather, perhaps bet 1/3 or 1/4 of his net worth, so that you can split & double.)
In your example, you said you should bet 27.6% of your bankroll, according to Kelly. Is your bankroll really $100? Because 27.6% of $100 is $27.60, which is the amount you claimed to be the BR. Bankroll is not how much you've wagered, how much is in your pocket, but the total amount of money you've put forward into your gambling bankroll.
I guess what I'm really asking is, taking the bankroll issue aside for now, if you are allowed to double down for less then is betting your initial stake again the mathematically correct play, given Kelly theory?
Another way to look at is if you bet $100, then double down for another $100, by Kelly this infers your bank is $362.32? (362.32 * 27.6% = 100).
This is a very small bank if you're betting $100 per hand!
I'm sure my logic is flawed somewhere, but just putting it out there for discussion, i think it's interesting.
So deriving the bank from Kelly infers a ridiculously small bankroll (ie when betting 100 and doubling for another 100) but at the same time you are increasing the house edge if you double for less.
Hmmm, bit of a paradox...
Quote: jedijonThanks RS, nice to have a constructive comment. I take take your point on the bankroll.
I guess what I'm really asking is, taking the bankroll issue aside for now, if you are allowed to double down for less then is betting your initial stake again the mathematically correct play, given Kelly theory?
Mathematically correct play is different than Kelly.
As far as blackjack is concerned, I'm not sure about any basic-strategy changes when maximizing Kelly criterion (whereas regular basic strategy maximizes EV). But there are risk-averse index plays (if you're a card counter). And it basically deals with this kelly-criterion, risk vs EV, idea. If the count is high enough to gain an advantage on doubling a Ten vs T (for example), do you do it? Maybe doubling down will get you an extra $1 in EV, but also putting up an extra $100 at risk. I don't know what the answer is to your question -- what changes there are, if any, to doubling down (or doubling down for less), if you're looking at a kelly-criterion type strategy as opposed to maximizing EV.
A little while back, someone posted on a VP forum (think it was NOTI who posted it)....but basically came up with a few situations in video poker where you can go for the lower-risk play and lose a tiny percent in value, while lowering your risk a good amount but increasing the HE a little bit.
I think what you're trying to do is possible and isn't "crazy talk" (as I'm sure some people will say)....but other than that, I don't think I can be of much help. =(
PS: The strategy would be dependent on the size of the player's bankroll relative to the initial bet. For someone with a $5K bankroll betting $10 (betting 0.2% of their BR) is going to have differences when compared to a $10K bankrolled player betting $1K, compared to a $100K BR betting $100.
Quote: jedijonYes I agree Bleeding. I was replying to RS at the same time you posted and as you can see, I was thinking along the same lines.
So deriving the bank from Kelly infers a ridiculously small bankroll (ie when betting 100 and doubling for another 100) but at the same time you are increasing the house edge if you double for less.
Hmmm, bit of a paradox...
It doesn't infer a small bankroll....it means you'd have to have at least a BR of X (where X is a small number) in order to make that $100 double-down proper according to Kelly.
But try looking at something like doubling down 11 vs A (in H17 game), splitting 3's or 6's vs 7, splitting 8's vs T & A. That number (27.6%) is going to be much different for those hands.
As far as I'm aware there are no casinos where you can 'split for less' only 'double for less'. I used the below link (replace the two gaps with a . ) for my info. Anything Blue and greater that 50% I apply the kelly formula which simplifies to: Stake = Prob - (1-Prob) or (Prob - 50%) * 2 with an even money payoff.
The biggest advantage you will ever have is 6,5 v 6 = 63.8% chance of winning by taking one more card (doubling down), giving a 27.6% kelly bet. The lowest is 51.2% giving a 2.4% kelly bet.
www blackjackinfo com/double-down-probabilities/
Quote: jedijonThanks for your thoughts RS
As far as I'm aware there are no casinos where you can 'split for less' only 'double for less'.
Many casinos will allow you to split for less when you have a bet up for the dealer. I generally do not add another tip on a split or double down.
Quote: jedijonIt's not a question of not being able to afford to double down Axel...
It would appear from your opening post it is about not being able to afford by not having the proper bankroll, or "bank" as you refer to it. Any player that has a proper bankroll/RoR for the game has already considered kelly moving in to his spread/bankroll considerations. 11v6, as you stated, is a 63.8% favorite when doubling. These scenarios are already accounted for in the game itself, with the house edge/etc. If you're spread already considers kelly, and the edges of individual hands are concluded in an overall house edge, then picking this particular situation where you're not well funded is kind of a moot point. You should be funded, or you should play, as Axel stated.Quote: jedijon... Assuming your bank is equal to the original $100 bet on the hand, then you should double down for less and bet $27.60...
Quote: jedijonThanks for your thoughts RS
As far as I'm aware there are no casinos where you can 'split for less' only 'double for less'. I used the below link (replace the two gaps with a . ) for my info. Anything Blue and greater that 50% I apply the kelly formula which simplifies to: Stake = Prob - (1-Prob) or (Prob - 50%) * 2 with an even money payoff.
The biggest advantage you will ever have is 6,5 v 6 = 63.8% chance of winning by taking one more card (doubling down), giving a 27.6% kelly bet. The lowest is 51.2% giving a 2.4% kelly bet.
www blackjackinfo com/double-down-probabilities/
63.8% is not the correct figure to use in this case. You have to use the value of the hand (expected value), NOT the win %. The value would be WinRate - LossRate.
ie: 0.638 - 0.296 = 0.342
But, I'd recommend for a basic strategy only player, to just follow regular basic strategy, double for the full amount when called for a double, split when necessary, etc. Play at a level you're comfortable with. If you're counting or doing some other form of AP, then this type of thing may make sense to do (alto if it gets more complicated, since you'd have to do the math including deck composition).
Quote: jedijonKelly Calculator (63.8% probability of a win versus a payoff of 50%) says you should bet 27.60% of your bank.
Is "bank" your term or is "of your bank" exactly what the Kelly Calculator says? (I have no experience with it.) One thing that is clear in this thread is that it is unclear exactly what is being referred to by "bank". If it is referring to your bankroll, perhaps it is suggesting that you double for less if 27.6% of your bankroll is less than the bet amount.
Not sure I agree with 0.342 as the number to use. This is less than the implied payout probability 0.5 (even money prob) so a there is no kelly bet in this case (or reason to double as it's < 0.5).
Kelly, for me, is pretty black and white. If the true probability of you winning is greater than the probability implied from the odds offered, then you have a bet.
In this case, 0.638 is the probability of you winning the hand by taking one more card only.
Thought experiment..... If you approached a professional gambler who religiously used Kelly for his stakes and said, "I have a game to play with you in which you have a 63.8% chance of winning. If you win i will pay you even money". He would bet 27.6% of his bankroll.
Let's say he bets $1000. You then tell him, sorry the rules have changed, you've already got $1000 bet on the outcome of this game. Do you still want to bet this extra $1000?
What would he say and do?
It is not winrate*BR or WinRate/var*BR.
Probably because of Romes good old quit while I'm ahead post. People are now trying to find ways to double down for less...Yikes. Good job Romes glad to see you are doing your part in keeping casino's in business.
Where is the triple down blackjack variation? Did someone invent one of them yet?
