While working on our Double Double Bonus Winner's Guide, Liam W. Daily ran some simulations. While we'll include much more of this information within the Winner's Guide itself, let me show you some highlights.

An unlucky day playing 5,000 hands of dollar DOUBLE DOUBLE BONUS

	FINAL LOSS					LOW POINT
	10%	5%	1%		10%	5%	1%
10/6 DDB	$2,570	$3,065	$3,890		$2,900	$3,325	$4,065
9/6 DDB	$2,810	$3,310	$4,125		$3,130	$3,560	$4,285
9/5 DDB	$3,085	$3,570	$4,400		$3,370	$3,795	$4,565

For each 0.1% of cash back, the final figures are $25 more positive

These figures were not calculated using a formula. They were simulated by having the computer play 5,000 hands of DDB 100,000 times. Why 5,000? That was arbitrary. Daily actually also ran them for 25,000 hands (and called it a week's worth of play) and 100,000 hands (and called it a month of play), among others. The columns on the right indicate three different pay schedules of DDB --- 10/6 (where the full house returns 10 for 1 and the flush returns 6 for 1 and the game is worth 100.07% when played well), 9/6 (where the game is worth 98.98%), and 9/5 (where the game is worth 97.87%).

The final results of these 100,000 different 5,000-hand scores were then sorted top to bottom. The ones at the top all hit royals and/or 4-aces-with-a-kicker. The ones who hit "not much of anything" were at the bottom. The score 10,000 places from bottom (i.e. 90,000 better scores, 9,999 worse scores, although some scores were tied) for the 10/6 DDB game was minus $2,570. The same position for the 9/6 game was minus $2,810 (a difference of $240), and the same position for the 9/5 game was minus $3,085 (a difference of an additional $265). The column above these figures is marked "10%" because 10,000 is 10% of 100,000.

Similar columns are found for 5% (indicating the score 5,000 from the bottom of the sorted list) and 1% (indicating the score 1,000 from the bottom). Predictably, the numbers get bigger (in a minus direction) as you go down the list because that's the way the list is sorted.

The final three columns represent the same 100,000 number list sorted in a different manner. Here, instead of the FINAL score of each of the 5,000-hand sessions, Daily looked at the LOW point of each sessions. On occasion a session ended at its low point, but usually the low point was LOWER than the final score because the "player" came back a little at the end. Again we have figures for the lowest 10%, 5%, and 1%.

When we compare the 10/6 scores with the 9/6 scores, the numbers differ in the $225 to $240 range each time. Since the only difference in the score is the $5 difference when you get a full house, this implies that there were 45 to 49 full houses in the 5,000 hands. Almost like clockwork. In our bad sessions and in our VERY bad sessions.

When we compare the 9/6 scores with the 9/5 scores, the numbers differ by $235 to $280, implying that the players received between 47 and 56 flushes in the 5,000 hands. The reason for the bigger range in the flushes than the full houses is that there are very few strategic differences between perfect 10/6 play and perfect 9/6 play and comparatively a lot more differences between perfect 9/6 play and 9/5 play. Since Daily's computer simulation assumed perfect play by the players, the difference in the scores also reflects the strategic differences rather than just keeping the same strategy and being paid less for flushes.

This actually surprised me. I'm used to players complaining "I haven't hit a full house all night", and even feeling that way myself. I KNOW I've gone on "half hour or longer dry spells" for these hands. Yet these numbers show that over 5,000 hands (which represents probably 7-10 hours, depending on how fast you play), the frequency of these hands is fairly constant.

There are other lessons from these numbers as well in addition to the constancy of full houses and flushes over 5,000 hands, but those will have to wait until next week or later. For now, know that if you play a machine with "less than the best" pay schedule, you WILL pay for it. The differences between DDB schedules always is in full houses and flushes, and you will get enough of these in virtually every session that it matters.