# The Cheap Cost of Entertainment

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I received an e-mail this week from a loyal reader who
was questioning some of the numbers from my recent column. The column was discussing the definition of
payback and had the amount of the buy-in is irrelevant to the discussion of the
payback. The example I cited was
discussing someone who sat down to play 100 hands of $5 blackjack. With a payback of 99.5%, a Player can expect
to lose $2.80. The point of the column
was to discuss how this $2.80 will not change no matter how much the Player
buys in for. If he buys in for $20 or
$100 he will still lose the same $2.80.
All that changes is the percent of the Player's bankroll that he will
lose. The $2.80 is a fixed amount.

My reader questioned this calculation. Not so much for its pure math, but because I
'ignored' the situation where the Player might lose his first 4 hands be
'bankrupt.' My reader is quite correct. The situation I described ignored the
numerous circumstances in which the Player will actually lose his entire buy-in
before reaching 100 hands. With a buy-in
of only $20, this is fairly likely to occur.
Roughly 1 in 16 times, he will lose the first 4 hands and be done right
then and there. This doesn't even
include the times he may double or split in the first couple of hands and go
broke before even 4 hands.

That said, this was not really the purpose behind my
calculation. Since the point was to show
how the expected loss rate does not change based on the buy-in, I could have
just as easily used a $100 and $500 buy-in in my examples. With a $100 buy-in, it is far less likely
that the Player will go broke before 100 hands.
However, my reader does bring up a very, very important point about the
importance of being properly bankrolled for any game. The amount will vary greatly from game to
game, mostly dependent on the volatility of the game. Blackjack is a relatively low volatility game
so $100 would be good enough most of the time.

The second part that the reader questioned was my math
regarding the anticipated loss while playing 1000 hands of full-pay jacks or
better video poker at max-coin quarters.
I said that it would be $6.25. My
reader wished that his expected loss was only $6.25 and that this would make it
'cheap entertainment'. Well, I stand by
this number. On a max-coin machine, the
Player will wager $1.25 per hand. Over
1000 hands, he will wager $1250. A
full-pay jacks or better machine pays about 99.5%. Losing just 0.5% of his total wager brings us
back to $6.25.

Of course, this is the long term average. Unlike blackjack, video poker has a much
higher volatility. Blackjack is a lot
like a coin toss. You win about half the
hands. You lose about half the
hands. Except for actual blackjacks,
splits and double downs, all payouts are
even money to the original wager. There
tends not to be huge swings in how you will do.
After 1000 hands, you'd probably be very close to the theoretical 99.5%
for blackjack.

Video poker is quite different. You 'win' about 45% of your hands, but an
overwhelming majority of these are really pushes (High Pair). The rest of the payouts range from even money
all the way up to 800 for 1 for a Royal Flush.
That Royal accounts for about 2% of the total payback. This means that until you hit the Royal,
you're only playing a 97.5% game which means the loss rate over 1000 hands
would be closer to $20. Eventually, you
will hit that Royal and for that 1000 hands, you will have a significant
win. When you add up the TOTAL amount
you wager and multiply it by 0.5% (the loss rate), the total amount you've lost
should be very close to this number. At
the same time, if you hit more Royals than 'average', you'll probably be up
significantly. If you hit less than
average, your loss rate is likely to be quite a bit more.

When we tie together the two thoughts that my reader
brought to me, we realize the importance of being properly bankrolled when playing
video poker. Given the volatility of the
game, it becomes even more important to make sure you are in the game until you
get to one of the big hands. In jacks or
better, this mostly means the Royal. In
double double bonus video poker, you have the luxury of a few of the Quad
payouts AND the Royal.

I had an opportunity to experience this first hand twice
this past week. I ventured out on 2
separate occasions to play video poker.
In one case, I was down about $40-$50 when I hit two solid hands and
came all the way back and left even. In
the other case, I hung around even most of the night. I was down about $5 when I hit I was dealt 3
Aces on a five-play double double machines.
Short of being dealt quads, this is about all you can hope for. Now all you have to do is hit the Quads. On the fifth hand, I was dealt an Ace and a
3. Not only did I hit the 4 Aces, I hit
the bonus 4 Aces. About 5 hands later, I
left up with a nice victory. In the case
of my first night, if I had brought only $40 with me, my bankroll would've been
gone and I never would've made it to the big hands. Also, if I weren't using proper strategy, my
losses up to that point would have been that much larger, and even a $60 or $80
bankroll might not have lasted as long as it needed to.

Proper strategy and proper bankrolling are keys to
achieving the theoretical paybacks of a casino game. In turn, this is what can lead you have
'only' that much of an expected loss rate and get a cheap night of entertainment.