Video Poker Bankroll Thoughts

How Much of a Bankroll Do You Need?

There are hard and fast rules in regular poker about how big a bankroll you need in order to play professionally, and there are also similar rules and guidelines for blackjack and other games where a player might be able to get a long-term edge over the house. Basically, you need a big enough bankroll to avoid "risk of ruin", which is a math term for the chances that an unlucky streak will break you before your long term expectation kicks in.

Guidelines from Million Dollar Video Poker

Bob Dancer's book, Million Dollar Video Poker, includes a sidebar about calculating the necessary bankroll to play video poker professionally. He points out that calculating this number is reasonably complicated and takes into account things like volatility and aversion to risk of ruin. He uses something he calls the "3 to 5" rule instead.

This bankroll guideline works like this: You need 3 to 5 times the amount of the royal flush in order to play safely forever. So for a quarter machine, you would need between $3000 and $5000, and on a dollar machine, you would need between $60,000 and $100,000. Dancer warns that you need a higher bankroll amount for highly volatile games, and a lower bankroll amount for games that pay over 101%.

Perspectives on Bankroll from Video Poker - Optimum Play

8/5 Jacks or Better - Chances of Hitting a Royal Flush with $100

In Dan Paymar's book, he gives a calculation for how many plays $100 will last while playing 8/5 Jacks or Better then contrasts that with how long $100 will last playing 9/6 Jacks or Better instead.

You start by assuming you're playing a quarter machine with the max bet ($1.25). $100 divided by $1.25 per bet gives you a total of 80 bets. Since you'll only hit a royal flush once every 40,000 hands, this would appear to give you a 1 in 500 chance of hitting a jackpot.

But that doesn't take into account the little wins you get along the way. Paymar calculates that if you eliminate the 4 of a kind or better, the payback percentage for the 8/5 Jacks or Better game is 88.8%. This means that after feeding $100 through the machine, you'll have $88.80 in winnings that you can run through there again, which is enough for another 71 plays.

And of course, after those 71 plays, you would have $78.85 left over, or enough for 63 more plays, and so on.

The formula for calculating how many plays you'll get total before running out of money is actually not that complicated: 80 plays/(1 - 0.888), or 715 total plays.

But since a 4 of a kind is going to happen on average once every 424 hands, you can then add that back into the calculation of the payback and the number of hands possible. Adding that hand back in increases the payback percentage from 88.8% to 94.75%, which means you can recalculate how many hands you can play:

80 plays/(1 -0.9475) = 1520 plays

1520 plays gives you about a 1 in 26 chance of hitting the royal flush. (Here's my conclusion: you need a bankroll of 26 times $100 to feel pretty good about your chances of winning a royal flush, or $2600, on the 8/5 game.)

Chances of Hitting the Royal on a 9/6 Jacks or Better Game, with the Same $100 Bankroll

But, even more interesting is what happens to your bankroll considerations when you switch from 8/5 Jacks or Better to 9/6 Jacks or Better. The payback percentage, excluding the straight flushes and royals, is 97% instead of 94.75%, which gives us a new total number of plays we can get in:

80 plays/(1 -0.97) = 2665 plays

This isn't quite twice as many potential plays, but 2665 is a lot more than 1520 plays. But it changes your chances of getting a royal flush from 1 in 26 to 1 in 15. Seems pretty clear to me that you should look for the 9/6 Jacks or Better when you can, if you want to hit a jackpot.

It's much easier to come up with $1500 than it is to come up with $2600.

And of course, one of the best ways to play video poker without a bankroll at all is to play free video poker. These free games are even available in no download video poker versions. And you can learn more video poker strategy here.

This page was written on April 18, 2006 and was modified on September 18, 2007.

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