In fact, to calculate the growth of a bankroll over a time it issean1 said:If you start with 10,000$ and bet 1% per game and hit 60% at -110 and make 1000 bets/year, guess what you have in 10 years? $87,600,000,000 That's 87 billion.

i come up with $20.5 billion, but your point is correct.

1.0014545 raised to the 10,000th power on a $10k bankroll = $20.5b

**not**correct to simply raise 1 plus edge times bet size to the number of trials power. This should be clear when you consider the results obtained using this method when hitting 50% over 2 trials given payout odds of +99,900 (decimal: 1,000.0), and a 1% of bankroll bet, implying an expected return of 499% of bankroll per bet (obviously completely unrealistic, but I'm just trying to demonstrate a point).

By the methodology given above the resulting bankroll would be $10,000*(1+499%)<sup>2</sup> = $358,801.

However, the actual resulting bankroll would only be $108,801.<sup>*</sup>

In general after n bets, np of which were winners, a starting bankroll of B<sub>0</sub>, a wager per trial of X (as percentage of bankroll), and decimal odds of O, the resulting bankroll, B is given by:

B = B<sub>0</sub> * (1 + (O-1)*X)<sup>np</sup> * (1-X)<sup>n(1-p)</sup>

Hence, the actual resulting bankroll starting with $10,000 after hitting 60% across 10,000 bets, at payout odds of -110 (decimal: 1.9091) would be:

B = $10,000 * (1 + (1.9091-1)*1%)<sup>6,000</sup> * (1-1%)<sup>4,000</sup>

≈

I discuss this in my article on Kelly and expected growth.≈

**$13,259,897,312**

<hr>

<sup>*</sup> If you win the 1st bet and lose the 2nd:

Bankroll after winning 1st bet

= $10,000 + 1%*$10,000*999

= $109,900

Bankroll after losing 2nd bet

= $109,900 - 1%*$109,900

=

If, you were to lose the 1st bet and win the 2nd your results would of course be identical:= $10,000 + 1%*$10,000*999

= $109,900

Bankroll after losing 2nd bet

= $109,900 - 1%*$109,900

=

**$108,801**

Bankroll after losing 1st bet

= $10,000 - 1%*$10,000

= $9,900

Bankroll after losing 2nd bet

= $109,900 + 1%*$9,900*999

=

= $10,000 - 1%*$10,000

= $9,900

Bankroll after losing 2nd bet

= $109,900 + 1%*$9,900*999

=

**$108,801**