Video Poker: Bankroll size vs. Risk of Ruin
Last Update: Nov 11, 2005
This appendix addresses the question of bankroll size Vs. risk of ruin in video poker. For those who don't know, the risk of ruin is the probability of losing an entire bankroll. The following tables show the number of betting units required according to the desired risk of ruin, the game, and cash back. A "betting unit" is five coins, for example a betting unit would be $1.25 for a 25 cent machine player.
As an example the full play deuces wild player, with 0.25% cash back, would need a bankroll of 3333 units to have a probability of ruin of 5%. See the following chart to find this number. These numbers may seem high compared to other sources based on ruin before some other event is achieved. The tables below are for ruin at any time over an infinite period of time and thus have no successful terminating event, other than reaching an infinite bankroll. Consequently these tables are best used by the player considering establishing a bankroll for an indefinite period of play
The following table applies to "full pay" deuces wild. This pay table can be found in my video poker tables but is generally marked by paying 5 for a four of a kind. The expected return on this game is 100.76% and the standard deviation is 5.08.
The following table applies to "10/7" double bonus. This pay table can be found in my video poker tables but is generally marked by paying 7 for a flush and 10 for a full house. The expected return on this game is 100.17% and the standard deviation is 5.32.
The following table applies to "full pay" jacks or better. This pay table can be found in my video poker tables but is generally marked by paying 6 for a flush and 9 for a full house. The expected return on this game is 99.54% and the standard deviation is 4.42.
Jacks or Better
An entirely mathematical approach was used to create the above tables. The theory was similar to that of the solution of problem 72 in my site of math problems. Briefly if p is the probability of ruin with 1 unit then p2 is the probability of ruin with 2 units, p3 is the probability of ruin with 3 units, and so on. With the known probabilities for the outcome of each hand an equation could be set up to solve: p=sum over all possible outcomes of pri * pri, where pri is the probability of hand i and ri is the return for hand i. Using an iterative process I solved for p. The cash back was given to the player at every hand. For example if the cash back rate was 1% than one penny was added to each win, including no win at all, for each $1 bet.
Go to video poker appendix 6 for risk of ruin in multi-play video poker.
Reason #1 why the Wizard likes Bovada:
Excellent customer support
The thing that separates Bovada from the rest is its customer support. Many other online gaming companies outsource their support. It can be difficult getting a response from them, and if you do it is often slow and handled by somebody with little understanding of gambling or even of English. But Bovada’s support is handled by Bovada, and their support staff is actually knowledgeable and helpful.
I’m so confident that you’ll have a good experience with Bovada that if you have a problem getting paid and you can’t resolve it with them on your own, I’ll talk to them myself. I personally have known the Bovada management for about three years and always found them to be professional, friendly, and knowledgeable. I have also personally visited one of their call centers so I could see first-hand how they handle customer issues. (More on my mediation service.)
If you have a problem with any other casino besides Bovada, I can’t help you. I get complaints from players of other online casinos every day who have difficulty getting paid. However that isn’t my job nor my problem. If you play at Bovada after clicking through my site I’ll stand behind you 100%. Any place else and you’re on your own.