# The Cheap Cost of Entertainment

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.