MJ: Global EV vs TC Bin EV: Question for Don or Norm

[MJ]

Why is it when bet spread increases, global EV% increases commensurately but the EV% for each particular TC bin remains fixed?

I understand that avg bet is equal to a weighted avg of the optimal bets for each particular TC bin. Basically it considers TC Freq for each TC x Optimal Bet at each TC and takes the aggregate.

Likewise, why shouldn't global EV simply be a weighted avg equal to the aggregate of TC Freq for each TC bin x EV% for each TC bin? I realize this is not how it works but I am interested in knowing why.

How exactly is global EV% calculated on CVCX?

Thanks,
MJ

[Don Schlesinger]

> Why is it when bet spread increases, global EV%
> increases commensurately but the EV% for each
> particular TC bin remains fixed?

How else should it be? The EVs for each bin are what they are. They don't know how much money you're betting at each count! For a given game and set of rules, including pen, they are what they are. You make more money by betting more at the good counts. The more you bet, the more you make.

> I understand that avg bet is equal to a weighted avg
> of the optimal bets for each particular TC bin.

Right.

> Basically it considers TC Freq for each TC x Optimal
> Bet at each TC and takes the aggregate.

The weighted average, not the aggregate.

> Likewise, why shouldn't global EV simply be a weighted
> avg equal to the aggregate of TC Freq for each TC bin
> x EV% for each TC bin?

Because you would then be ignoring the amount you bet at each true count. If you simply multiply each TC bin by its frequency, essentially for a flat bettor who is counting and using the I18 for play decisions, you will hardly get any edge at all, depending on the game in question. So, if you're interested in your global edge, with bet spreading, you had better factor in the varying bet sizes!

> I realize this is not how it
> works but I am interested in knowing why.

See above.

> How exactly is global EV% calculated on CVCX?

Calculate how much you win per hour. Calculate the average bet, as per your description above. Divide the first value by the second value and add a percent sign. :-)

Don

[MJ]

> How else should it be? The EVs for each bin are what
> they are. They don't know how much money you're
> betting at each count! For a given game and set of
> rules, including pen, they are what they are. You make
> more money by betting more at the good counts. The
> more you bet, the more you make.

Ok, so local EV%'s have nothing to do with bet spread.

> Because you would then be ignoring the amount you bet
> at each true count. If you simply multiply each TC bin
> by its frequency, essentially for a flat bettor who is
> counting and using the I18 for play decisions, you
> will hardly get any edge at all, depending on the game
> in question.

So simply multiplying local EV% by TC Freq would produce an erroneously high global EV% for a counter that flats bets using I-18 Fab4. I think you were trying to provide a simple example that demonstrates why it is important to factor in the amount bet.

> So, if you're interested in your global
> edge, with bet spreading, you had better factor in the
> varying bet sizes!

This is where I am still confused.

> Calculate how much you win per hour. Calculate the
> average bet, as per your description above. Divide the
> first value by the second value and add a percent
> sign. :-)

From what you stated, Global EV% = WR/Hr / Avg Bet

But this equation does not really make sense. WR/Hr is in part based upon how many hands are played per hour. Does this mean Global EV% is affected by how many rounds we play per hour? Take the following example.

WR/Hr = #Rounds/Hr x Avg Bet x Global EV%
WR/Hr = 100 rounds/Hr x $100 x 1% = $100

Now, if we only play 50 rounds/Hr then we earn $50/Hr given the aforementioned Avg Bet and Global EV%.

If we were to use Global EV% = WR/Hr / Avg Bet then in the first instance our Global EV% = $100/$100 = 1%. But if we only play 50 rounds/Hr, then Global EV% = $50/$100 = 0.5%.

Clearly, Global EV% is unrelated to # rounds per hour so I do not see how your definition can be correct. Perhaps you meant to write Global EV% = [WR/Hand / Avg Bet] x 100? This would probably make more sense.

This begs the question, how do we calculate WR/hand? This probably equals WR/Hr / #hands/Hr. The next logical question is how do we calculate WR/Hr?

Okay, correct me if I am wrong, but I would guess WR/Hr = a weighted avg of TC Freq x Local EV% x Optimal Bet.

So, as we increase our bet spread, we wager more at each TC Bin. Logic would indicate that the Avg Bet increases as a consequence. Fine. But wouldn't WR/Hand also increase in proportion to the avg bet? If this is the case, then Global EV% would remain fixed regardless of bet spread.

Then again, in order for Global EV% to increase as bet spread increases (which is the way it actually works), I suppose WR/Hand would have to increase disproportionately faster than the Avg bet. Hopefully you can point me in the right direction.

MJ

[Norm Wattenberger]

EV is winnings/initial bet.

EV% by TC is fixed. If you double the bet, the winnings are doubled and the answer is the same.

win per hand is average bet * overall EV

win per hour is win per hand * hands per hour

Changing the bet ramp has no effect on TC EVs. The effect on average bet and win rate is very complex since doubling the spread does NOT double the bet at each count. The entire betting ramp must be recalculated to hit the desired risk. There is no simple correlation between spread, EV, average bet or win rate.

[MJ]

> EV is winnings/initial bet.

It seems like you, Don, and I are using different definitions for global EV. Just to clarify, when you write "winnings" do you mean WR/Hand or WR/Hour? Does it make a difference? I presume that "initial bet" is the same thing as avg bet.

Would the equation, global EV = [WR Hr / Avg Bet] still hold up if the # rounds played were any number other than 100? Suppose you only play 50 rounds per hour, now WR/Hr is reduced by 50% yet the denominator (avg bet) remains unchanged. Thus, the global EV is reduced by half!

Isn't overall EV suppose to remain constant, regardless of how many rounds are played? If you use my equation, EV% = [WR/Hand / Avg Bet] then global EV remains unaffected by # rounds per hour. Please clarify.

MJ

> win per hand is average bet * overall EV

> win per hour is win per hand * hands per hour

[Norm Wattenberger]

EV is all of the amount won divided by all of the money bet at the start of the rounds.

Win rate per hour is win rate per hand times the number of rounds per hour.

Average bet is a number I throw in for fun. The number is not used in any calculations.

> It seems like you, Don, and I are using different
> definitions for global EV. Just to clarify, when you
> write "winnings" do you mean WR/Hand or
> WR/Hour? Does it make a difference? I presume that
> "initial bet" is the same thing as avg bet.

> Would the equation, global EV = [WR Hr / Avg Bet]
> still hold up if the # rounds played were any number
> other than 100? Suppose you only play 50 rounds per
> hour, now WR/Hr is reduced by 50% yet the denominator
> (avg bet) remains unchanged. Thus, the global EV is
> reduced by half!

> Isn't overall EV suppose to remain constant,
> regardless of how many rounds are played? If you use
> my equation, EV% = [WR/Hand / Avg Bet] then global EV
> remains unaffected by # rounds per hour. Please
> clarify.

> MJ

[Don Schlesinger]

> Average bet is a number I throw in for fun. The number
> is not used in any calculations.

But, if you multiply average bet by WR%, you will get $Win/Hr.

Don

[Norm Wattenberger]

[Don Schlesinger]

Right. But I actually meant to write WR% x 100.

Same thing, if we figure 100 hands per hour.

Don

[Brett Harris]

This may be a bit technical, but there are three sets of figures that you need from a simulation to mathematically define the 'game' you are playing. These are the count distribution c(i) and the unit expected value ev(i) and the unit variance var(i). These numbers are fixed although in monetary terms, your dollar EV(i) = B(i)* ev(i) can be anything you want. However to bet optimally and to control your risk your actual spread at each count value depends on all the others. If you go to the Optimal Spread link all is explained. Right at the end of Section 2, there is a simple method which can be used in Excel once your have your values of c(i), ev(i) and var(i). There are numbers in a table further along which can be cut and pasted.

Cheers,
Brett.

Theory of Optimal Betting Spreads

[MJ]

Thanks Brett!

Getting back to the matter which prompted this thread, why should increasing the bet spread increase overall EV%?

If EV% = WR/Hr / Avg Bet, then in order for EV% to increase by enhancing the spread, WR/Hr would have to increase at a faster rate than the avg bet. But why do they not increase in proportion to one another?

MJ

[Brett Harris]

MJ,

I think the confusing factor here is the notion of 'average bet'. Things become clearer if you think in terms of unit bet $B which multiplies a spread which goes from 1 to M. There are really two degrees of freedom here, one is simply how much your unit bet is, the other is the 'ramp' which is how quickly you go from your min bet to your max bet. Anyone can increase their expectation 'EV' per hour by simply betting more at every count - its the ramp that controls the variance and risk involved. It turns out that if you play all hands, with all those nasty negative counts, the optimal spread ramp is very sharp, you go from 1 to M units real quick. If you are a Wonger, and jump in and out in positive expectation rounds only, the optimal spread becomes very flat. But this flat spread would have a higher unit bet for the same risk as the play-all player. So you would have two players, one maybe going $10-$100 playing all hands and another jumping in and out going $25-$100 in positive counts, both having the same win rate per hour. But the difference is that the play-all player has a much higher standard deviation (SD) and will take much longer to get into the 'long run'. Thats where N0=(SD/EV)^2 comes in..

Brett.

[MJ]