Simple Math!

[Nathanael]

These formulas have nothing to do with unit amounts of bets, just number of bets.

T = Total bets
W = Total Wins
L = Total Losses

T = W + L

W = (L+1)/1  This is the formula if you flat bet.  Our next bet will always be the sum of our last bet.  Our last bet is always 1 since we are flat betting.  (It doesn't have to be our last bet, it can be any previous lost bet.)

W = L/1 + 1
L/1 = W - 1
L = 1W -1

Substitute 1W-1 for L in our equation T = W + L and we get T = W + 1W-1

Or T =  2W - 1
Or 2W  = T + 1
or W = (T+1)/2

If the total bets = 100 then W = (100+1)/2 or W = 101/2  or  W = 50.5  Round up to 51 because we can't have a half bet.  This means that if we bet the sum of any 1 of our lost bets and we win 51 bets out of 100 we will come out ahead.

If we bet the sum of 2 of our lost bets, our formula becomes:

W = (L+2)/2
or L = 2W-2
So  T or 100 = W + 2W-2
Or 100 = 3W-2
Or  3W = 100 +2
Or  W = 102/3
So W = 34  which means that if we bet the sum of any 2 of our lost bets each time and we win 34 bets out of 100 we will come out ahead.

If we bet the sum of any 4 of our lost bets, our formula becomes:

100 = W + 4W-4
100 = 5W-4
5W = 100 + 4
W = 104/5
W = 20.8  which means that if we bet the sum of any 4 of our lost bets each time and we win 21 bets out of 100 we will come out ahead.

Last one:

100 = W + 6W-6
7W = 100+6
W = 106/7 = 15.16  which means that if we bet the sum of any 6 of our lost bets each time and we win 16 times out of 100 bets we will come out ahead.

If my math is correct, with a large enough bank, can't we create a winning system with this information?

What do you think Fripper?

Can we use this with a labby somehow?

Table limits and bankroll size are our enemies. 

That's always the problem, isn't it?  Still???

Nate

[GLC]

Nate,


Interesting post. 


Tomla021 just turned me on to a blog re: target betting.  It too is very interesting.


Target betting is done by betting 1 unit after every loss and after a Win we bet the total of all previous losses.


This means that all we have to do is Win twice in a row to fully recover. 


Example: LLLLLWLLLLWW


1 1 1 1 1  This is after our 1st 5 Ls
1 1 1 1    After our 1st W since we won a unit
1 1 1 1 4  After our attempt to recover all previous losses.
1 1 1 1 1 1 1 1 4  Our line after losing 4 more 1 unit bets.  We always keep our units in ascending order.
1 1 1 1 1 1 1 4  Our line after winning a 1 unit bet
We bet 11 units which is the number of units lost up to this bet.  Since we win our line is fully recovered. 




If you want some profit, you just add it on to the recovery bet.  Add all you want, just remember if you lose it becomes part of the losses that have to be recovered with larger bets.


Here's another recovery line example:  LLLLLWLLLLWLLLLLLLLLLWLWW


1 1 1 1 4 This is our line after our 1st recovery attempt and loss.
1 1 1 1 1 1 1 4 11  This is our line after our 2nd recovery attempt and loss.
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 11 31  This is our line after our 3rd recovery attempt and loss.
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 11 31  Next win of 1 unit.
0 =  Won the bet of 61 units, the sum of all previous losse.


As you can see, our bets can climb very quickly.  But remember, 2 in a row is all we need to resolve our line.  This line represents 20 wins out of 100 bets or 20% win ratio.


If we use Nate's formula and say, "I think I can win 16 times out of 100 bets pretty regularly, then we can temper the escalation of bet sizes quite a bit by only betting 6 of the previous losses instead of all of them.


If we use our above W vs L example we have the exact numbers since we didn't lose more than 6 bets, but what if we had this W vs L line? LLLLLWLLLLWLLLLLLLLLLLWL


1 1 1 1 4  This is our line after our 1st recovery attempt and loss.
1 1 1 1 1 1 1 4 6  this is our line after our 2nd recovery attempt and loss.  Notice that we only bet the 1st 6 lost bets.
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 6 6  This is our line after our 3rd recovery attempt and loss.  Once again we only bet the 1st 6 lost bets. 


Let's assume the line continues with 3 wins in a row. LLLLLWLLLLWLLLLLLLLLLLWLWWW


1 1 1 1 1 1 1 1 1 1 4 6 6 We bet the next win of 1 unit and then the 2nd win of the 1st 6 lost bets and won.


1 1 1 4 6 6  We bet the next W of 6 each 1 unit lost bets and won.


1 more win of 19 units clears the recovery line.


This idea may have some legs.


I just don't know if it's any better than our 2 step parlay method.  Since we still only have to win 2 times in a row to clear all previous losses.  I think the big advantage with the target method is if you have a lot of losses in a row, all you are losing after the 1st recovery attempt is 1 unit per loss. That's probably a really big difference.


GLC

[Nathanael]

GLC,

I see your point about the 2 step parlay.  I think the target betting is better.

Here's an idea.  Why not sum up the total units lost and divide that number by the total number of bets lost?

24 units lost in 12 bets would be 12 bets of 2 units each.  Then the 1st bet to recover 6 losses would be for 12 units instead of 6.

This would have the result of equalizing the bet sizes so we don't go from small to very large as quickly.

Since we are eliminating 6 bets with each second win, we will recover in the exact same number of recovery bets.

1 1 1 1  1 1 1 1 4 6  Here we have 18 units to recover representing 10 bets.  We can have 8 bets of 2 units each and 2 bets of 1 unit each.

1 1 2 2 2 2 2 2 2 2  Recovery bets would be 10 and then  8 instead of 6 and then 12.

The larger the numbers and the more lost bets to recover the more advantageous this idea would be.

Nate

[Nathanael]

Just tested a quick game to +60.

About 110 spins.

Highest bet was 36 units.

More wins than losses, so an easy session.

16 bets was the longest series before recovery.



Nate

[catalyst]

dear George
i am looking for a slow progression for even chances. probably your tweak on Nate's idea is the answer.
thanks to Nate and George.
catalyst

[GLC]

dear George
i am looking for a slow progression for even chances. probably your tweak on Nate's idea is the answer.
thanks to Nate and George.
catalyst

I have tested this tweak a couple of times. 

I played Horror session #3 using the original Target betting and won the session, but at one point I had to bet just over 1000 units.  That would be hard to do for real.


I will test the same session using the 6 loss tweak to see how it performs.


Let you know soon.


G