top bet problem
- Thread starter beyondbj
- Start date
The ONLY reason for this is to avoid being "made" by the casino staff; which obviously IS a pretty good reason by itself. If casinos absolutely did NOT care about card counters, we would ALL be employing a humongous bet spread. :grin:
jnrwilliam
Active Member
1. most r designed or playing in USA, big spread is not advised there.
2. ur spread is 1-37 or 1-60 ?
full kelly is very risky if ur Br. = all ur money n no other income to refill.
most pros i know take 1/4 Kelly or even bigger fraction.
do u realise ROR is big.
but always using 1 kelly to adjust the bet size
will never ruin and can make the bankroll expanding in quickest way ,
right ?
jnrwilliam
Active Member
when u encounter a big -ve swing,
lose N units n then win N units at the following day.
u may have a new idea.
in theory, u never ruin.
blackjack avenger
Well-Known Member
Kelly Theory & the Real World
With Kelly resizing:
50% chance of losing 50% of bank
10% chance of losing 90% of bank
25% chance of losing 75% of bank
80% chance of losing 20% of bank
If you lose a large % of your bank can you keep playing when considering table minimums?
If you don't resize down constantly you risk of losing a certian % of bank is higher then you think.
If the OP has been playing full kelly for a while perhaps now or at the next ATH or even comfortable betting limits don't continue raising bets on wins but let the bank grow to a more conservative kelly fraction. However, keep lowering bets on losses if bank preservation is important.
With Kelly resizing:
50% chance of losing 50% of bank
10% chance of losing 90% of bank
25% chance of losing 75% of bank
80% chance of losing 20% of bank
If you lose a large % of your bank can you keep playing when considering table minimums?
If you don't resize down constantly you risk of losing a certian % of bank is higher then you think.
If the OP has been playing full kelly for a while perhaps now or at the next ATH or even comfortable betting limits don't continue raising bets on wins but let the bank grow to a more conservative kelly fraction. However, keep lowering bets on losses if bank preservation is important.
thats true , u may lost half your bankroll or even more
but who gurantee you can play longer time before being blacklisted , according to 1/3 or 1/4 kelly . do u feel u can still winning the same profit in each casino?
the casino in this world is limited , our time is limited , may be u can win 10000-30000 US in each casnio , the game is over
jnrwilliam
Active Member
as i know, cc play with full or half kelly is unusual.
barred in 1 casino, still many casinos u can go.
barred by ur own BANKROLL, nowhere 2 go.
for me, better game over than i am over[if i lose 90% of my br.]
only one i know play half kelly is to play sponsor's money n he didn't know
who n what is Kelly.
He has nothing now.
play half kelly got ruin ??
i think only if u have a very large bankroll , otherwise playing 1/3 kelly , can u get break even for the air ticket or hotel charge for each trip ?
jnrwilliam
Active Member
my Eng. is not good enough to express my sense of humour.
barred by ur own bankroll= u can't play anymore cos u lose all $$$
Full Kelly betting is ONLY efficient for games that offer only even-money bets.
Because of the fact that the rules of blackjack allow splits and double downs, a player who plays full Kelly theoretically has a 100% chance of tapping out at some time in the future. And this DOES take into account constant resizing of bets, of course. The optimal bet for blackjack is approximately 0.6 Kelly.
Because of the fact that the rules of blackjack allow splits and double downs, a player who plays full Kelly theoretically has a 100% chance of tapping out at some time in the future. And this DOES take into account constant resizing of bets, of course. The optimal bet for blackjack is approximately 0.6 Kelly.
Kelly is not restricted to even-money bets, it is restricted to 2-outcome bets.
However, the basic principle leading to Kelly betting for 2-outcome bets are most simply expanded to bets with any payout structure.
I can offer up a simple example which clearly demonstrates why full Kelly is not optimal for an other than even-money bet:
Suppose someone were stupid enough to offer you a proposition, where for a fee of whatever size you wish, he'll flip a coin - and if it comes up tails, you lose; but if it comes up heads, he'll pay you QUADRUPLE. Although you have a 100% advantage over him, if you were follow full Kelly and bet 100% of your BR, you would tap out exactly 50% of the time. With a certainty of virtually 100%, he would soon have ALL of your money; whereas someone who were to bet something like half - Kelly would soon have all of the money in the entire world.
(This IS a 2-outcome bet; perhaps I'm misunderstanding what Mango's trying to say?
)
Suppose someone were stupid enough to offer you a proposition, where for a fee of whatever size you wish, he'll flip a coin - and if it comes up tails, you lose; but if it comes up heads, he'll pay you QUADRUPLE. Although you have a 100% advantage over him, if you were follow full Kelly and bet 100% of your BR, you would tap out exactly 50% of the time. With a certainty of virtually 100%, he would soon have ALL of your money; whereas someone who were to bet something like half - Kelly would soon have all of the money in the entire world.
(This IS a 2-outcome bet; perhaps I'm misunderstanding what Mango's trying to say?
)London Colin
Well-Known Member
The Kelly criterion does NOT say that you would bet 100% of your BR. The Kelly fraction is EV/Payoff. (So EV/4 if the payoff odds are 4:1)
In situations where there isn't a single, fixed payoff (i.e. more than 2 simple win/lose outcomes), an approximation to Kelly is required. The one used for blackjack is EV/Var.
I can offer up a simple example which clearly demonstrates why full Kelly is not optimal for an other than even-money bet:
Suppose someone were stupid enough to offer you a proposition, where for a fee of whatever size you wish, he'll flip a coin - and if it comes up tails, you lose; but if it comes up heads, he'll pay you QUADRUPLE. Although you have a 100% advantage over him, if you were follow full Kelly and bet 100% of your BR, you would tap out exactly 50% of the time. With a certainty of virtually 100%, he would soon have ALL of your money; whereas someone who were to bet something like half - Kelly would soon have all of the money in the entire world.
(This IS a 2-outcome bet; perhaps I'm misunderstanding what Mango's trying to sa y?
Let me cite the Kelly bet from Wikpedia (I'm sure you will find reference to the original work in there):
The Kelly bet fraction is
where b=4 (your 4:1 payoff), p=q=0.5 from your 50% coin flip.
Hence the Full Kelly bet is (4*0.5 - 0.5)/4 = 37.5%.
As you can see from the formula, the Kelly bet is NEVER 100% of your bankroll (unless it is a sure win with p=1 and q=0). You already gave the reason.
I believe we're arguing the same thing. My original point was that when it comes to blackjack; if your advantage is x and you bet x% of your bankroll, you are overbetting according to Kelly. Your bet must be adjusted to adapt to the uneven betting and payoff schedules. Some people do NOT understand this, and the coin flip example that I gave was merely to help to make it clear WHY it must be adjusted.
I believe that the properly adjusted optimal betting strategy for blackjack is something like .6 Kelly, depending upon the rules. (Correct me if I'm wrong about the .6 figure)
I believe that the properly adjusted optimal betting strategy for blackjack is something like .6 Kelly, depending upon the rules. (Correct me if I'm wrong about the .6 figure)
London Colin
Well-Known Member
Kelly is Kelly. The adjustment to take account of uneven betting and payoffs is the division by the variance. And that is what gives you FULL Kelly (or at least an approximation thereof). It's not an adjustment to the Kelly bet; it is the Kelly bet.
Any other adjustments are for other, more practical, more subjective reasons.
You're getting it slightly wrong. You don't bet x% if your advantage is x%. Well you can, but that is not strict Kelly betting. The x%/x% bet is a Kelly bet ONLY IF the game is 2-outcome and pays even money. The real Kelly bet is written above.
You are however right, Blackjack is not a even-money game, but Kelly does not restrict to even-money games. Hence saying that Kelly betting fails because Blackjack is not an even-money game, is simply wrong.
You can Kelly-bet Roulette all your day long (well, if you are the house).
The reason Kelly-betting fails for Blackjack: Blackjack is not a 2-outcome game. For non-2-outcome games a Kelly bet isn't even defined.
What you CAN do (and I think you have that in mind), is to formulate a generalized Kelly bet applicable to Blackjack (and all other multi-outcome-games). If this is 0.6 * EV or something other is a different question, but I would agree it should be somewhere in the 0.4 - 0.8 range.
London Colin
Well-Known Member
Mango,
I hope you don't feel my comments have been getting in the way. I'm not a mathematician, and I'm sure you're more qualified to talk about this stuff than I am.
Just to clarify, I quoted the fraction as EV/Payoff, on the basis that (b*p - q) equals the EV if the possible outcomes are: lose one unit with probality q, or win b units with probability p. (And since Kelly is only defined for two outcomes, we can take it as read that p+q=1.)
Presumably though, if we were dealing with three possible outcomes, one of which was a push, then we would have to adjust p and q so that they again add up to 1. (i.e. the probability of winning or losing the next resolved bet.) And then we would have a valid formula.
So my description of Kelly as EV/Payoff would only hold if we were talking about the EV in those terms. i.e. ignore pushes.
Does that all make sense?