In this 1Win Id Guide, Let's Explore Money's Value Over Time
The Kelly Criterion Is Being Reconsidered.
Remember that the exponential rate of expansion of the gambler's capital is expressed as follows in
Part 2 of 1Win Id:
(1/n) *log (Wn/W0) = log [(1 + f*(d-1)) k (1 – f)
(n-k)]1/n
Bet Present Value: Discounting Future Returns
The blue text reflects a win's gross return, whereas the red text represents a loss's gross
return. Let $x represent the monetary value of a bet you place. A losing bet might be viewed as
occurring instantly in terms of cash flow time. You bet $x, which is deducted from your account balance
today and never repaid. If you win a bet, $x is deducted from your account balance today and $x(d-1) is
restored to your account balance later, where d is the decimal odds of your wager. This can be viewed as
an investment. You deposit $x now and will receive $x(d-1) later. To calculate our PV, we must discount
this future payment (FV) using the formula PV = FV/(1+r).
When the time value of money is considered, the gross return for winning becomes (1 + f*(d-1)/(1+r)t)k,
whereas the gross return for losing remains unchanged. When you plug this equation into the Part 2
workings and solve for f, you get:
The given formula is for the decimal odds system, which is prevalent in Australia. The related formula
for people who are more familiar with the “b to 1” betting odds used in other literature is:
Take note of how the value of f lowers as r and t grow.
The Arsenal Vs. Chelsea Game Has Been Reconsidered.
Remember the imaginary Arsenal vs. Chelsea matchup from Part 1? To summarize, the odds are as follows,
with your perceived probabilities displayed in brackets:
Full-Time Outcome:
Arsenal: 2.60 (pA = 20% chance of occurring)
Chelsea: 2.65 (pC = 50% chance of occurring)
Draw: 3.25 (pD = 30% chance of occurring)
You Should Gamble Based on The Kelly Criterion.
f = [0.5(2.65 – 1) – 0.50]/ (2.65 – 1) = 0.197 = 19.7% of your Chelsea account balance.
Now, assuming that the fixture will take place, we will compute the best bet amount: in (A) three days,
(B) thirty days, (C) one year, and (D) three years. Assume you can earn 5% per year on a savings
account. Using the given formula, we get:
(A): t = 3/365 = 0.008219
(B): t = 30/365 = 0.08219
(C): t = 1
(D): t = 3
f(A) = 0.5 – 0.5(1.050.008219)/1.65 = 0.197
f(B) = 0.5 – 0.5(1.050.08219)/1.65 = 0.196
f(C) = 0.5 – 0.5(1.051)/1.65 = 0.182
f(D) = 0.5 – 0.5(1.050.008219)/1.65 = 0.149
As a result, unless you are making extremely huge bets, you may overlook the temporal impact of money
for fixtures within the next month or two. However, the time value of money becomes an essential factor
for activities that take place more than a year from today.
Optimal Bet Size Analysis: Assessing Ideal Bets and Time Value Impact
You may discover that your optimal bet size is less than zero, implying that you should not gamble at
all. Consider the FIFA World Cup in 2014. Brazil has odds of 4.50 to win the event, according to 1Win
Id. Assume you feel Brazil has a one-in-four chance of winning. Leaving aside the time value of money,
your ideal bet would be as follows:
f = [(0.25) (4.50 – 1) – 0.75]/ (4.50 – 1) = 0.036
This translates to betting 3.6% of your account amount on Brazil to win the tournament.
However, when the time value of money is considered, where t = 3.98 and r = 5%, your ideal bet size
becomes:
f = 0.25 – 0.75*1.053.98/3.5 = -0.01
As a result, if you consider the time value of money, you would pass on betting on Brazil.
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