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Risk of Ruin statistics for video poker

Last update: November 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

Deuces Wild

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.

Full Pay Deuces Wild Bankroll Requirement

Risk of Ruin 0.00% CB 0.25% CB 0.50% CB 0.75% CB 1.00% CB

50% 1061 771 596 480 397

40% 1402 1019 788 634 524

30% 1843 1339 1036 834 689

20% 2463 1790 1385 1114 921

10% 3524 2562 1981 1594 1318

7.5% 3964 2882 2229 1793 1482

5% 4585 3333 2578 2074 1714

2.5% 5646 4104 3174 2554 2111

1% 7048 5123 3963 3188 2635

0.5% 8109 5894 4559 3668 3032

0.25% 9170 6665 5156 4148 3429

0.1% 10572 7685 5944 4782 3953

0.05% 11633 8456 6541 5262 4350

0.025% 12694 9227 7137 5742 4746

0.01% 14096 10246 7926 6376 5271

Double Bonus

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.

10/7 Double Bonus Bankroll Requirement

Risk of Ruin 0.00% CB 0.25% CB 0.50% CB 0.75% CB 1.00% CB

50% 5579 2222 1361 967 742

40% 7376 2937 1799 1279 981

30% 9691 3859 2364 1680 1289

20% 12955 5159 3160 2246 1723

10% 18534 7380 4521 3213 2464

7.5% 20850 8303 5086 3615 2772

5% 24114 9602 5882 4181 3206

2.5% 29693 11824 7243 5148 3948

1% 37069 14761 9042 6426 4929

0.5% 42648 16983 10403 7394 5671

0.25% 48228 19204 11764 8361 6413

0.1% 55603 22141 13563 9640 7393

0.05% 61183 24363 14924 10607 8135

0.025% 66762 26585 16285 11574 8877

0.01% 74138 29522 18085 12853 9858

Jacks or Better

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.

9/6 Jacks or Better Bankroll Requirement

Risk of Ruin 0.5% CB 0.75% CB 1% CB 1.25% CB 1.5% CB

50% 15254 2150 1092 700 496

40% 20165 2843 1444 926 656

30% 26496 3735 1897 1216 862

20% 35419 4993 2536 1626 1152

10% 50674 7143 3628 2326 1648

7.5% 57005 8036 4081 2616 1854

5% 65928 9293 4720 3026 2144

2.5% 81182 11444 5812 3726 2640

1% 101347 14286 7256 4652 3296

0.5% 116602 16436 8348 5352 3792

0.25% 131856 18587 9440 6052 4288

0.1% 152021 21429 10883 6978 4944

0.05% 167275 23580 11975 7678 5440

0.025% 182529 25730 13067 8378 5936

0.01% 202694 28572 14511 9304 6591

Methodology

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 pr_i * p^r_i, where pr_i is the probability of hand i and r_i 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.

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Return tables:
Probability of Ruin for single-play video poker
Random simulations for multi-play video poker.
The standard deviation of n-play video poker.

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All about Double Pay Poker.
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My Strategies

Jacks or Better:

Simple Strategy (return of 99.46%)
Intermediate strategy (return of 99.52%)
Optimal Strategy (return of 99.54%)

Full Pay Deuces Wild:

Simple Strategy (return of 100.71%)
Optimal Strategy (return of 100.77%)
When to play two to a royal, king high, with no penalty cards
When to play two suited high cards, ace high, with a deuce
When to play two to a royal, king high, with a straight penalty card

Other Strategies:

Other Stuff

Jacks or better quiz.
Probability distribution for each hand by number of cards held in full pay Deuces Wild.
Programming video poker tips.

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