I speak French, maybe there is inconsistencies in formulas description, i hope i was be enough exact in each description. If someone want give suggestions to improve anything, he is welcome. don't hesitate to request other calculations or post your own formulas and of course don't hesitate report any errors .

payout = (100-casino)/chance -- casino = house edge (1% often)

chance = (100-casino)/payout -- casino = house edge (1% often)

Minimum multiplier on loss (Martingale), to be profitable for each win = 1+(1/(payout-1))

Minimum increase on loss in % = (1/(payout-1))*100

Minimum bet amount depending on payout to recover amount lost (amount lost = perte): nextbet = -perte/(payout-1)

Minimum value of payout to recover loss amount depending on the wager (amount lost = perte): payout = (-perte/nextbet)+1

Calculation of maximum lose streak possible in a martingale:

n = math.floor(math.log((balance/bb)*(-1+q)+1)/math.log(q)) --(q = multiplier on loss // bb = base bet)

Calculation of maximum base bet amount, to be able to resist to this number "n" of losses:

bb = balance/((1-q^n)/(1-q))

Average payout calculation of a random chance included in an interval [chanceMIN; chanceMAX]:

Average payout = ((100-casino)*(math.log(chanceMAX)-math.log(chanceMIN)))/(chanceMAX-chanceMIN)