DSchles said:
Yes, your thoughts are reasonably accurate. Your biggest problem in this thread is going to be sifting through the reams of unimportant drivel that will ensue. So, if you can avoid all the chaff, the wheat is as follows.
Suppose you are at a -2% edge 20% of the time; a -0.5% edge 60% of the time; and a +2% edge 20% of the time. How can you make money? Clearly, if you play all the hands (you don't have to!) and there are 100 per hour, you will make a one-unit bet (call it $1) on all the negative-edge hands, for a total of 80 such wagers. And you will lose, on average, $20 x (-.02) + $60 x (-0.005) = $0.70 on those 80 hands. How can you make that back and more, to show a profit?
On the 20 hands that you will have a 2% edge, you need to bet more than $1! Suppose you bet $5. Then you will have a 2% edge on a total of $100 wagered (20 hands x $5 per hand), for a $2 profit. When you subtract the $0.70 you lost on the losing hands, your overall profit for 100 hands is $1.30, which represents a global edge of 1.3% on all the 100 hands played.
The more you bet when you have the edge (you'll always bet one unit when you don't have the edge), the greater your overall profit will be.
Clear?
Don
Hello Don, I have gone through what you mentioned here and I think I grasp it so thank you very much for the expert breakdown. I would like to apply that logic to a different "system" pay off matrix per se. to understand some of the outputs that would flow from it. Let's say that I have a method that produces the following long term result "structure": During 66% of the hands dealt I have a - 1/2% edge against me, call it "X" type hands and for the remaining 33% of the hands I have a + 1/2% edge for me, call those "Y" type hands. Using the logic you provided I did the calculation with a $1.00 to $10.00 spread. On X types I bet $1.00, on Y types I bet $10.00.
So here it is 66 hands X $1.00 X -.005= minus 33 cents. & 33 hands X $10.00 X +.005= +$1.65 Agreed ?? If true, then my global edge as you call it is $1.65 - .33 = $1.32 over 100 hands, or also +1.32 %, (with the 1 to 10 unit ratio)
My questions are about the outputs: If what I stated above is really my global edge, is that the number I should use for risk of ruin calculations?? I mean when I ask what is my long term real "edge" should I count it as +1.32% with the above scenario??
My second question is what is my average earning rate at a certain dollar bet level? In this case I factored an example in the following way: Since there are no $1.00 min tables where I play, I assumed these values: $3.00 for the X type hands and $30.00 for the Y type hands which I think gives me this result in terms of average dollars earned per 100 hands. So here we go (math genius that I am) ::
66 X $3.00 X -.005 = minus 99 cents & then 33 X $30.00 X +.005 = +$4.95 so we see the per 100 hand average comes to + $3.96, I think. Is that right??
My last question is, should I factor my bankroll based on my average bet size Or should I factor it based on my large bet size of $30.00 in this example, because as you know, the framework is always If I have an edge of "A"% and I want a 90% chance of playing forever, I will need "B" units of capital, so which size unit?? the average unit or your max unit?? Again thank you very much for this wonderful forum, bklyn