1. folklore knows if you are in a winning streak you have to keep betting while if you are losing is better to retire

ill prove this is mathematically true and logic:

lets analize the odds of following this startegy in a single game

my startegy is bet in pairs, on draw(one win one lose) i keep gambling, on losing i retire (one lose one lose), i only keep gambling on win(one win one win) or on draw

in this universe the first two posible outcomes are:

00=win or 11=lose

01 or 10 doesnt exist in this universe cause if this was the case i would keep gambling, i bet 0.5 euro in ech game

so the first two posible games that exist in the universe of this staregy are:

win or lose 00 or 11 for this two theres a chance of 1/4 each profit=0

the next posible outcomes in this universe are:

ww or wl with a chance 1/16 profit 1 euro

then www or wwl chance 1/64 profit 2 euro

then wwww or wwwl chance 1/256 profit 3 euro

then wwwww or wwwwl chance 1/1024 profit 4 euro

...

these are the only posible outcomes of a single game with this strategy the rest just dont exist

so now its just a matter of adding the odds:

1/16+ 2/64 +3/256 +4/ 1024 ...=0.109375

so following the staregy of keeping in a lucky strike and retiring on a bad one gives you a 10% edge

popular folklore is right on this one

2.

3. with this like with quantum entanglement is imposible to know whats gonna be a randon number

still nonlocality as with quantum entanglement is big enough as to can have a winning startegy

4. there is no difference when you bet, the odds do not change

5. actually i got it reversed lets start all over with the simetric strategy:

i gamble 3 couples of games then stop playing unless my startegy makes me stop before

if i draw getting 01 or 10 i keep gambling if i win i stop if i lose i keep at it untill i win or the 3 couple of games are over

this is the universe of posible end games:

w i retire
lw i retire
llw or lll or ll draw or ll draw

there are no other elements in this universe

for w the chance is 1 / 4 so theres a chance 1 /4 i win one
lw doesnt count is a draw 0 chance 1/(4*4)
for llw or lll or lldraw or lldraw theres a chance 1/(4*4*4) each

for llw i lose -1 with lll i lose -3 with lldraw i lose -2 with ll draw i lose -2

win chance 1* 1/4=16/64
lose chance -8* 1/64= -8/64

edit

i neglected ldl and ld"l so actually i can lose - 12/64 but win 16/64

dll doesnt exist in this universe because if i draw on first i stop

6. the key is im applying a tetravvalent value w,l,d or d" to a binary tree

imagine i follow the startegy of completly ignore draw just dont count them an i applied this system

the universe of this startegy would be only composed of

w +1 chance 1/2(now its 1/2 not 1/4)
lw 0 chance 1/(2*2)
llw -1 chance 1/(2*2*2)
lll -3 chance 1/(2*2*2)
now with this startegy i win 1*4/8

and lose -4 * 1/8

0 gain 0 lose chance

but if you apply a tetravalent tree to a binary one locality of randomness is broken still you cant know the future but you can have an strategy to have future to be favorable

7. i realized of my mistake:

i neglected ldd", ld"d , ldd and ld"d" with with the 4/64 edge is lost

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