Progressive Average Bet

Is there a formula out there to calculate what my average bet in a given game will be with a progressive (increase after win) system with a given table (or personal) limit?

e.g.
If I'm playing $5 Craps (PASS line) and increase to $10, $15, $20, $25 etc. after a win (decrease to $5 after a loss), what will my average bet be at a $500 maximum table?
If I'm playing $10 Blackjack (perfect basic strategy) and increase to $20, $30, etc. after a net win (don't change after split that is W/L, or push), what will my average bet be at a $1,000 maximum table?

Yes, I know that progressive systems won't give me an edge, but I want to know this for expected comps, disguise, etc.

Quote: nvr55xx

Is there a formula out there to calculate what my average bet in a given game will be with a progressive (increase after win) system with a given table (or personal) limit?

e.g.
If I'm playing $5 Craps (PASS line) and increase to $10, $15, $20, $25 etc. after a win (decrease to $5 after a loss), what will my average bet be at a $500 maximum table?
If I'm playing $10 Blackjack (perfect basic strategy) and increase to $20, $30, etc. after a net win (don't change after split that is W/L, or push), what will my average bet be at a $1,000 maximum table?

Yes, I know that progressive systems won't give me an edge, but I want to know this for expected comps, disguise, etc.

Wincraps

For a back of an envelope estimate, you will be betting 2 units per hand on average if you use a linear progression as you outlined.

Quote: endermike

For a back of an envelope estimate, you will be betting 2 units per hand on average if you use a linear progression as you outlined.

Quoted for truth. Slightly less because of the house edge, but 2x is a solid estimate.

Quote: nvr55xx

Is there a formula out there to calculate what my average bet in a given game will be with a progressive (increase after win) system with a given table (or personal) limit?

yes there is

Quote: nvr55xx

e.g.
If I'm playing $5 Craps (PASS line) and increase to $10, $15, $20, $25 etc. after a win (decrease to $5 after a loss), what will my average bet be at a $500 maximum table?

Summing a Geometric Series
info on this subject can be found here:
https://www.mathsisfun.com/algebra/sequences-sums-geometric.html

formula
sum=a*(1-r^n) / (1-r)
(when r=1 one should simply use a*n as (1-r) becomes 0 in the denominator)

where
a = 5 (the first term)
r = 244/495 (the "common ratio") for craps pass line
n = 100
sum=9.860557769 (rounds to 10 I say)

when a=1 we get 1.972111554 (so now we can think 'units')

for r = 1/2
sum=2

handy calculator found here:
https://sites.google.com/view/krapstuff/formulas

Sally