RoR

[Red Green]

I revived an old poll.

Can’t seem to see it through the Taptalk app. Will check on desktop later. Thanks



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[hitthat16]

I play between half to full Kelly depending on the game. I’m willing to take slightly higher risk because i resize my bets when i win or lose a certain amount of money. My bankroll is also replenishable.

With all these factors I’d say my ROR is close to zero.

[Red Green]

With all these factors I’d say my ROR is close to zero.

Would you say close to zero because of resizing or replenishment (‘liferoll’ as it was coined in a old post I read earlier)


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[hitthat16]

Would you say close to zero because of resizing or replenishment (‘liferoll’ as it was coined in a old post I read earlier)


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Both. Computer perfect Kelly betting (resizing as your BR fluctuates) provides a ROR of 0. (In theory at least).

I have a job and am a pretty good saver so if i experience a significant enough loss i will put money back into the roll.

[Red Green]

If you are adequately funded you should play at most full kelly. Most would choose to play to a 5% RoR or less.

I have CVCX which doesn’t have the Kelly function. I think there sims default to full Kelly? If so, would doubling the bankroll in the sim yield 1/2 Kelly equivalent in RoR output on the bottom line?


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[weballinoutacontro]

I have CVCX which doesn’t have the Kelly function. I think there sims default to full Kelly? If so, would doubling the bankroll in the sim yield 1/2 Kelly equivalent in RoR output on the bottom line?


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The Kelly Criterion is a very straightforward formula. See: https://en.wikipedia.org/wiki/Kelly_criterion.

For simple bets with two outcomes, one involving losing the entire amount bet, and the other involving winning the bet amount multiplied by the payoff odds, the Kelly bet is:
where:

• f * is the fraction of the current bankroll to wager, i.e. how much to bet;
• b is the net odds received on the wager ("b to 1"); that is, you could win $b (on top of getting back your $1 wagered) for a $1 bet
• p is the probability of winning;
• q is the probability of losing, which is 1 ? p.

One common approximation of this for blackjack: your "Kelly bet" for a particular TC would be approximately your advantage for the TC times your bankroll. E.g., 0.5% advantage at TC X and $10k bankroll = kelly bet of appx. $50.

[Red Green]

Web (may I call you 'Web'?), I have read a number of entries on KC and all left me addled. Thanks for simplifying that. There is greatness in brevity. I will plug that into excel and see what I can do. Thanks!

I just plugged it in...is that second "=" maybe a * ?

[hitthat16]

One common approximation of this for blackjack: your "Kelly bet" for a particular TC would be approximately your advantage for the TC times your bankroll. E.g., 0.5% advantage at TC X and $10k bankroll = kelly bet of appx. $50.

Don’t forget to divide by the variance. About three quarters of what you get with the Kelly formula is a full Kelly bet in blackjack. E.g. with a 1% advantage and 10K bank you would get $100, then three quarters of that, $75, is the proper bet.

[weballinoutacontro]

Web (may I call you 'Web'?), I have read a number of entries on KC and all left me addled. Thanks for simplifying that. There is greatness in brevity. I will plug that into excel and see what I can do. Thanks!

I just plugged it in...is that second "=" maybe a * ?

No, it's an equals sign. Left side of the equation simplifies to equal the right because p+q=1 (in a game with only 2 results - this is why BJ players have simplified the equation to approximately edge*Bankroll).

For instance consider the simple case, 1% edge, f*=(p(b+1)-1)/b, f*=((0.505)(1+1)-1)/1=0.01=1%, which means bet 1% of your bankroll.

BJ obviously has a 3rd result (push), blackjacks, insurance, surrenders, doubles, and splits.

For games with k possible results ("horses"), the following equation applies:


where the total amount of bets placed on k-th horse is , and are the pay-off odds


This is why Kelly-betting BJ players have simplified the formula to simply Edge*Bankroll. Simply using your calculated "Edge" roughly accounts for all the idiosyncrasies in BJ. That is, Edge is roughly equivalent to p-q.

Don’t forget to divide by the variance. About three quarters of what you get with the Kelly formula is a full Kelly bet in blackjack. E.g. with a 1% advantage and 10K bank you would get $100, then three quarters of that, $75, is the proper bet.

The original Kelly Criterion (KC) doesn't include a factor based on standard deviation. Variance is built into the KC. Keep in mind the KC is purely an EV maximizing function. In particular, KC maximizes the expected value of the logarithm of your capital at each betting instance


edit to add: one article I thought that has a logical approach to adding a variance factor to reduce a Kelly-sized bet is here: http://www.elem.com/~btilly/kelly-criterion/

[Stealth]

Your question is a good one and can have a wide range of answers.

If I am playing on my bank and I have a replenish able bankroll, then playing to 5% is acceptable.

If it is a team bank, then less than .5% is the policy, however, bet sizes are more likely set by tolerance in preference for longevity than by bank size.

All new players should be taught how to evaluate their bank and set their playing levels (RoR) before they start play but I feel few do. I believe most new counters push this guidance (or ignore it) too far and many are subjected to the negative variance and severe or catastrophic bankroll damage. Bankroll management is as important a set of skills and decisions as a count selection, maybe more.

[Red Green]

For instance consider the simple case, 1% edge, f*=(p(b+1)-1)/b, f*=((0.505)(1+1)-1)/1=0.01=1%, which means bet 1% of your bankroll.

Why is p = .505 to represent a 1% edge? shouldn't it be .51?

[Red Green]

Your question is a good one and can have a wide range of answers.

If I am playing on my bank and I have a replenish able bankroll, then playing to 5% is acceptable.

If it is a team bank, then less than .5% is the policy, however, bet sizes are more likely set by tolerance in preference for longevity than by bank size.

All new players should be taught how to evaluate their bank and set their playing levels (RoR) before they start play but I feel few do. I believe most new counters push this guidance (or ignore it) too far and many are subjected to the negative variance and severe or catastrophic bankroll damage. Bankroll management is as important a set of skills and decisions as a count selection, maybe more.

Thanks Stealth. I've been around long enough to know its a good idea to know what you're getting yourself into when money is involved. Even though this a hobby, and I have a fine job, I'm pursuing this with a long term objective to make it a profitable hobby. To make it a fair challenge I know I can't be underrolled, nor am I willing to put in more than I'm willing to put in to test the waters (10K BR). I've been playing around with spreads, looking at RoR, Score, SD. For the game I've identified it will be 6D, 1-10, H17 DAS, Split to 4 hands. I've gone out a few times to play a bit and I can get 5/6 penetration, even 5.1/6 penetration from multiple dealers. There are some dealers still cutting off 1-1/2 decks, but I'm cataloging! The penetration makes the game playable. It's that darn RoR. The RoR can probably look a bit like a parabolic curve and as a newbie, I'm firmly on the flat bit. I can't find a way to get it under about 10.5% (5+ pen excepted). That still seems high. Growing the BR to $15+K makes a significant difference in BR longevity. That is the risk starting out. Many of you have described much higher (or unknown!) RoR so I'll be in good company but perhaps better prepared having had the benefit of your considerable, collective experience.

At the end of this thread, considering the excellent advice from you all, I think that my plan stays as is and I'll live with the 10.5% RoR. If I use a theoretical $15K BR my spread stays the same so it's a bit of a moot point. Likewise, if it falls but stays about $5K, I think I would keep the spread the same. If it falls below that, probably put the brakes on and examine the skill set for leaks.

I've really enjoyed the thread and your input.

RG

[weballinoutacontro]

Why is p = .505 to represent a 1% edge? shouldn't it be .51?

In this case:

edge=p-q and p+q=1...q=1-p
edge=p-(1-p)
edge=p-1+p
edge=2p-1


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Or, if you'd like a more lengthy explanation:

Edge is essentially the same as EV (edge is basically just EV-1).
p is Probability(win)
q is Probability(loss)

EV=payout_win*P(win)+payout_loss*P(loss)
EV=payout_win*p+payout_loss*q

And, p+q=1

Thus, via substitution...
EV=payout_win*p+payout_loss(1-p)
EV=payout_win*p+payout_loss-p*payout_loss

In blackjack, payout_loss=0, so..

EV=payout_win*p

Substituting numbers.. (1% edge=1.01 EV; payout_win=2 in an even money bet as in BJ)

(1.01)=(2)*p
0.505=p

QED