3 Hands

1357111317

Well-Known Member
#1
Lets say you are playing a full table where you can backline players as you play your own spot. Lets say that the 2 people beside you will heed your advice if you tell them how to play their hand. My understanding is that you would bet 50% of your 1 hand max on each of the spots? My question is that the general rule is that you bet 75% of your 1 hand max if you are playing 2 spots. When you work this out you end up bettting the same amount while keeping the varience the same. This doesn't make any sense, increasing the number of hands should decrease the variance should it not?
 
#2
1357111317 said:
Lets say you are playing a full table where you can backline players as you play your own spot. Lets say that the 2 people beside you will heed your advice if you tell them how to play their hand. My understanding is that you would bet 50% of your 1 hand max on each of the spots? My question is that the general rule is that you bet 75% of your 1 hand max if you are playing 2 spots. When you work this out you end up bettting the same amount while keeping the varience the same. This doesn't make any sense, increasing the number of hands should decrease the variance should it not?
Only IF you reduce the aggregate bet amount. zg
 

1357111317

Well-Known Member
#3
Lets say for maths sake my max bet is 100. On two hands I would bet 75 and on 3 hands I would bet 50. My total bet on one hand would be 100, 150 on two hands and 150 on 3 hands. Shouldnt my varience should be a lot lower on the 3 hands compared to 2 hands if the aggregate bet is the same?
 

rukus

Well-Known Member
#6
1357111317 said:
Lets say for maths sake my max bet is 100. On two hands I would bet 75 and on 3 hands I would bet 50. My total bet on one hand would be 100, 150 on two hands and 150 on 3 hands. Shouldnt my varience should be a lot lower on the 3 hands compared to 2 hands if the aggregate bet is the same?
youre variance of 1x100 and 2x75 are about equal. youre variance would be lower if you split your 100 bet into 50 and 50, but not if you split it into 75 and 75. the 75% "rule" was determined by setting the variance for the two scenarios (1 hand vs 2 hands) equal to each other. same thing for the 3 hands. but in your case of 2x75 vs 3x50, yes your variance would be lower in the 3 hand scenario.
 

Renzey

Well-Known Member
#7
1357111317 said:
Lets say you are playing a full table where you can backline players as you play your own spot. Lets say that the 2 people beside you will heed your advice if you tell them how to play their hand. My understanding is that you would bet 50% of your 1 hand max on each of the spots? My question is that the general rule is that you bet 75% of your 1 hand max if you are playing 2 spots. When you work this out you end up bettting the same amount while keeping the varience the same. This doesn't make any sense, increasing the number of hands should decrease the variance should it not?
The more accurate bet sizes are 1 x 100, 2 x 73 and 3 x 57
 
#9
1357111317 said:
Lets say for maths sake my max bet is 100. On two hands I would bet 75 and on 3 hands I would bet 50. My total bet on one hand would be 100, 150 on two hands and 150 on 3 hands. Shouldnt my varience should be a lot lower on the 3 hands compared to 2 hands if the aggregate bet is the same?
Yes. A little less. zg
 

Kasi

Well-Known Member
#11
rukus said:
youre variance of 1x100 and 2x75 are about equal. youre variance would be lower if you split your 100 bet into 50 and 50, but not if you split it into 75 and 75. the 75% "rule" was determined by setting the variance for the two scenarios (1 hand vs 2 hands) equal to each other. same thing for the 3 hands. but in your case of 2x75 vs 3x50, yes your variance would be lower in the 3 hand scenario.
Well, the way I understand it, your variance of 1*100 vs 2*75 would not be equal.

Assume, to keep it simple, an optimal bet defined by roll*%advantage divided by the sum of variance and co-variance if any.

Let's take Wong's benchmark numbers from Table 85. Variance=1.28 and co-variance=.47. 1/1.28=.78. 1/(1.28+.47)=.57. 1/(1.28+.47+.47)=.45. Which explains his factors in Table 86.

So now, let's assume a 1.28% adv with a $10K roll and determine an optimal bet for 1 hand. It's 78% of your edge * your roll or $100. For 2 hands it's 57% of your edge *$10K= $73 on each of 2 hands and a $146 bet in total. For 3 hands it's .0128*.45*$10K=$57 for each of 3 hands or $171 in total.

Hence Mr. Renzey's numbers of 2 * 73 or 3 times 57 if one chooses to express as a percent of your original optimal bet. The same %'s, btw, Don uses in Table 2.4 when analyzing the "eating up good cards" stuff.

In each case, one is betting more money in 2 hands than one hand and more in 3 hands than 2 hands. One is "getting more money on the table" to get a higher $win rate. At the same time, one is increasing variance. Since we're optimal betting here, giving rise, I think to a Kelly-risk, it's the ratio one's win rate has increased compared to the ratio one's variance has increased. When done right, the risk to one's bankroll remains unchanged in effect enjoying a higher win rate with the same overall risk to roll. The trade off for more money on the table is more risk.

So, in PrimeTime's case, if his orig $100 bet was an optimal one, betting 2 @75 might be a slight overbet but fine. Betting 3 @ $50 maybe makes little sense in a way since, yes, he has decreased variance but his win rate remains the same. In effect he is playing with a lower? risk to his roll than he was with his original $100 bet. Which is fine but then why not play with that risk all the time kind-of thing if you like it so much? It's probably not that big of a deal in reality lol.

Also, note how variance and co-variance will be different with different rules in place. Although that 2*73 and 3 * 57 always seems to be about right from what I can tell lol.

Also I'd guess co-variance would also change at different TC's and also change with use of indexes, just as variance does, and that his 0.47 (and 1.28) in this case is probably just an average over all hands? Any comments on this?

And, given the above, and since in real-life a fixed-spread guy can't always make the optimal bet, it's just one more reason to let a sim figure it out for you anyway lol.

Auto Monk - not sure I quite get your mnemonic lol. Something about it doesn't seem quite right to me but I'm not sure what lol. Not that that means anything anyway lol. Maybe something to do with stan dev? Like for $100 at three hands I'd go $100* square root of 3 times the stan dev for the 3 hands? Whatever, so what if it 2*71 may be a slight underbet or not lol.

There's alot more I don't get about spreading to multiple hands than I think I might get lol.
 

rukus

Well-Known Member
#12
Kasi said:
Well, the way I understand it, your variance of 1*100 vs 2*75 would not be equal.

Assume, to keep it simple, an optimal bet defined by roll*%advantage divided by the sum of variance and co-variance if any.

Let's take Wong's benchmark numbers from Table 85. Variance=1.28 and co-variance=.47. 1/1.28=.78. 1/(1.28+.47)=.57. 1/(1.28+.47+.47)=.45. Which explains his factors in Table 86.

So now, let's assume a 1.28% adv with a $10K roll and determine an optimal bet for 1 hand. It's 78% of your edge * your roll or $100. For 2 hands it's 57% of your edge *$10K= $73 on each of 2 hands and a $146 bet in total. For 3 hands it's .0128*.45*$10K=$57 for each of 3 hands or $171 in total.

Hence Mr. Renzey's numbers of 2 * 73 or 3 times 57 if one chooses to express as a percent of your original optimal bet. The same %'s, btw, Don uses in Table 2.4 when analyzing the "eating up good cards" stuff.

In each case, one is betting more money in 2 hands than one hand and more in 3 hands than 2 hands. One is "getting more money on the table" to get a higher $win rate. At the same time, one is increasing variance. Since we're optimal betting here, giving rise, I think to a Kelly-risk, it's the ratio one's win rate has increased compared to the ratio one's variance has increased. When done right, the risk to one's bankroll remains unchanged in effect enjoying a higher win rate with the same overall risk to roll. The trade off for more money on the table is more risk.

.....

There's alot more I don't get about spreading to multiple hands than I think I might get lol.
ha! kasi, you caught me red-handed, i admit it! :eek:. i indeed misspoke, and meant setting RoR (not variance) to be the same across the various betting options. anytime more money is on the table, there is definitely more variance :cool:. man, what an off-weekend im having...:cool:

you laid it out very well indeed, in effect proving to everyone where the 75% and ~60% "rules" come from. dont short-sell yourself with that last comment about not getting the issues of spread to multiple hands!
 

stophon

Well-Known Member
#13
Automatic Monkey said:
The mathematical mnemonic I use is the inverse of the nth root per hand, for n hands.

That would give you 2 x 71 for 2 hands and 3 x 58 for 3 hands.
Is that coincidence because that is clever
 
#14
It All Evens Out in the End

Kasi said:
Well, the way I understand it, your variance of 1*100 vs 2*75 would not be equal.

Assume, to keep it simple, an optimal bet defined by roll*%advantage divided by the sum of variance and co-variance if any.

Let's take Wong's benchmark numbers from Table 85. Variance=1.28 and co-variance=.47. 1/1.28=.78. 1/(1.28+.47)=.57. 1/(1.28+.47+.47)=.45. Which explains his factors in Table 86.

So now, let's assume a 1.28% adv with a $10K roll and determine an optimal bet for 1 hand. It's 78% of your edge * your roll or $100. For 2 hands it's 57% of your edge *$10K= $73 on each of 2 hands and a $146 bet in total. For 3 hands it's .0128*.45*$10K=$57 for each of 3 hands or $171 in total.

Hence Mr. Renzey's numbers of 2 * 73 or 3 times 57 if one chooses to express as a percent of your original optimal bet. The same %'s, btw, Don uses in Table 2.4 when analyzing the "eating up good cards" stuff.

In each case, one is betting more money in 2 hands than one hand and more in 3 hands than 2 hands. One is "getting more money on the table" to get a higher $win rate. At the same time, one is increasing variance. Since we're optimal betting here, giving rise, I think to a Kelly-risk, it's the ratio one's win rate has increased compared to the ratio one's variance has increased. When done right, the risk to one's bankroll remains unchanged in effect enjoying a higher win rate with the same overall risk to roll. The trade off for more money on the table is more risk.

So, in PrimeTime's case, if his orig $100 bet was an optimal one, betting 2 @75 might be a slight overbet but fine. Betting 3 @ $50 maybe makes little sense in a way since, yes, he has decreased variance but his win rate remains the same. In effect he is playing with a lower? risk to his roll than he was with his original $100 bet. Which is fine but then why not play with that risk all the time kind-of thing if you like it so much? It's probably not that big of a deal in reality lol.

Also, note how variance and co-variance will be different with different rules in place. Although that 2*73 and 3 * 57 always seems to be about right from what I can tell lol.

Also I'd guess co-variance would also change at different TC's and also change with use of indexes, just as variance does, and that his 0.47 (and 1.28) in this case is probably just an average over all hands? Any comments on this?

And, given the above, and since in real-life a fixed-spread guy can't always make the optimal bet, it's just one more reason to let a sim figure it out for you anyway lol.

Auto Monk - not sure I quite get your mnemonic lol. Something about it doesn't seem quite right to me but I'm not sure what lol. Not that that means anything anyway lol. Maybe something to do with stan dev? Like for $100 at three hands I'd go $100* square root of 3 times the stan dev for the 3 hands? Whatever, so what if it 2*71 may be a slight underbet or not lol.

There's alot more I don't get about spreading to multiple hands than I think I might get lol.
In the short run the variance for multiple hands is higher. In the short run instead of losing one hand of $100 you can lose 2 hands of $73. This can be an issue for a weekend trip.

In the medium to long run the variance evens out. It must in order to have the same ror given the various bets.:joker::whip:
 

Kasi

Well-Known Member
#15
rukus said:
. i indeed misspoke, and meant setting RoR (not variance) to be the same across the various betting options. ..
Embarrassing you in any way was my last intent. Please accept my apologies for making you feel that way. I already knew it was a simple brain fart, basically a typo, on your part as soon as I read it anyway lol.

Everything you say makes so much sense to me that when something doesn't I go into this uncomfortable mode of questioning my own reality so I thank you mucho for corroborating my reality lol.

Mostly I just wanted to show how and why I think that 73-57 rule is what it is so I'm glad you saw that lol.

Oh no - even if I got what I said right lol - there's way more I don't understand than I do about this question.

Can co-variance be calced without a sim? Why does Norm's stuff, apparently, it seems to me, the few "multiple-hands" sims I've seen, not change the SD in the SD column to reflect the co-variance, if that indeed is even the case?
Does co-variance change with each TC, maybe even more than variance does? Etc lol.

I guess I really liked how Katrina Walker actually listed co-variance at each TC in her book on SP21. So simple. So direct.

Expressing stuff per "round" vs "per hand", expressing spread per 1 hand bet or including 2-hand amounts. Etc.

I'm a mostly voodoo flat-betting $min guy anyway so spreading is generally not in my vocabulary lol. So blame Multi-Action BJ for ever making me even deal with the question lol.

Keep doing what you do. Can't do it but I like it.
 

Kasi

Well-Known Member
#16
stophon said:
Is that coincidence because that is clever
If it was right, it might be coincidence.

Anyway, I've always thought of mnemonics as making life easier. Stuff like LEOGER - loss of electrons oxidation, gain of electrons reduction. Or "Will A Jolly Man Make A Jolly Visitor" to help me remember the first letter equates to the first 8 presidents. Or "Every Good Boy Does Fine" or "FACE" to help understand the notes on the lines and spaces of a sheet of music.

Taking the inverse of the square root of 2 or 3 or 5, is not my idea of a mnemonic anyway lol.
 
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