Mind the (DH) Gap! A Contrast in Risky Choices Between Reasoning and Conversational LLMs

Luise Ge; Yongyan Zhang; Yevgeniy Vorobeychik

cs.AIFeb 16, 2026

Mind the (DH) Gap! A Contrast in Risky Choices Between Reasoning and Conversational LLMs

Authors: Luise Ge, Yongyan Zhang, Yevgeniy Vorobeychik

Organizations: Washington University in St. Louis

Abstract

The use of large language models either as decision support systems, or in agentic workflows, is rapidly transforming the digital ecosystem. However, the understanding of LLM decision-making under uncertainty remains limited. We study LLM risky choices along two dimensions: (1) prospect representation (based on an explicit representation or outcome history) and (2) decision rationale (explanation). Our study, which involves 20 frontier and open LLMs, is complemented by a matched human subjects experiment, which provides one reference point, while an expected payoff maximizing rational agent model provides another. We find that LLMs cluster into two categories: reasoning models (RMs) and conversational models (CMs). RMs tend towards rational behavior, are insensitive to the order of prospects, gain/loss framing, and explanations, and behave similarly whether prospects are explicit or presented via a history of outcomes. CMs are significantly less rational, slightly more human-like, sensitive to prospect ordering, framing, and explanation, and exhibit a large description-history gap. Paired comparisons of open LLMs suggest that a key factor differentiating RMs and CMs is training for mathematical reasoning.

Figures & tables

Figure 1: Correlation matrix involving (1) frontier LLMs (GPT-4.1 and 5.1, Gemini-2.5-Flash and Pro, DeepSeek-R1 and Chat, and Claude-Haiku-4.5), (2) economicus , and (3) human responses.

Figure 2: Pairwise correlation between each frontier model and both the human and economicus references, shown as a 2D plot. Circles are CMs while x’s are RMs.

Figure 3: Consistency and decisiveness heatmap for frontier models and the human subjects.

Figure 4: HE representation of frontier LLMs (with human subjects as the reference). Change from explicit (blue) to implicit (red) prospects for each model is indicated by the arrows. RMs are x’s and CMs are circles.

Figure 5: HE representation of open LLMs (with human subjects as the reference). Change from explicit (blue) to implicit (red) prospects for each model is indicated by the arrows. RMs are x’s and CMs are circles.

Panel of Figure 6 — Figure 6: HE representation and the impact of explanations. Red: no explanation; Blue: one-sentence explanation; Green: math explanation.

Model	$\boldsymbol{\sigma}$	$\boldsymbol{\gamma}$	$\boldsymbol{\beta}_{\text{gain}}$	$\boldsymbol{\beta}_{\text{loss}}$	Corr	MSE
DeepSeek-R1	0.86	0.81	832	711	0.98	0.007
Gemini-Pro	0.81	0.84	815	857	0.96	0.014
GPT-5.1	0.87	0.81	1000	802	1.00	0.001
Claude Haiku	0.89	0.80	221	244	0.71	0.053
DeepSeek-Chat	0.86	0.82	181	149	0.77	0.040
Gemini-Flash	0.93	0.89	27	42	0.87	0.015

Table 1: Dual-Beta prospect theory parameters for decisions with explicit prospects.

Model	$\boldsymbol{\sigma}$	$\boldsymbol{\gamma}$	$\boldsymbol{\beta}_{\text{gain}}$	$\boldsymbol{\beta}_{\text{loss}}$	Corr	MSE
DeepSeek-R1	0.99	1.00	1000	346	0.98	0.009
Gemini-Pro	0.98	0.99	147	100	0.94	0.025
GPT-5.1	1.01	0.99	460	1000	0.98	0.010
Claude Haiku	1.07	0.98	4.81	23	0.55	0.078
DeepSeek-Chat	0.83	0.72	11	0.01	0.45	0.048
Gemini-Flash	1.57	0.82	2.61	14	0.58	0.047

Table 2: Dual-Beta prospect theory parameters for decisions with implicit prospects.

Model	$\boldsymbol{\sigma}$	$\boldsymbol{\gamma}$	$\boldsymbol{\beta}_{\text{gain}}$	$\boldsymbol{\beta}_{\text{loss}}$	Corr	MSE
Qwen2.5-7B-Instruct	0.84	0.75	57	0.01	0.64	0.030
Qwen2.5-Math-7B	0.85	0.82	1000	403	1.00	0.001
Qwen3-30B-Instruct	0.94	0.85	56	0.01	0.57	0.041
Qwen3-30B-Thinking	0.87	0.81	726	1000	0.99	0.004
Olmo-3-7B-Instruct	0.88	0.81	215	121	0.73	0.041
Olmo-3-7B-Think	1.33	1.16	1000	1000	1.00	0.001

Table 3: Dual-Beta prospect theory parameters comparing instruction-tuned and reasoning models with explicit prospects.

Model	$\boldsymbol{\sigma}$	$\boldsymbol{\gamma}$	$\boldsymbol{\beta}_{\text{gain}}$	$\boldsymbol{\beta}_{\text{loss}}$	Corr	MSE
Qwen2.5-7B-Instruct	48	0.66	0.01	2.45	0.46	0.070
Qwen2.5-Math-7B	0.55	0.88	7	0.82	0.54	0.027
Qwen3-30B-Instruct	1.10	0.83	17	2.84	0.50	0.047
Qwen3-30B-Thinking	1.00	0.88	668	585	0.94	0.025
Olmo-3-7B-Instruct	1.25	0.99	4.80	1.29	0.44	0.020
Olmo-3-7B-Think	0.73	0.71	1000	466	1.00	0.001

Table 4: Prospect theory model parameters comparing instruction-tuned and reasoning models with implicit prospects.

Appendix figures & tables21 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: Correlation matrix involving (1) LLMs, (2) economicus , and (3) human responses to all questions.

Figure 8: Correlation matrix involving (1) LLMs, (2) economicus , and (3) human responses to all questions with explicit prospects.

Figure 9: Correlation matrix involving (1) LLMs, (2) economicus , and (3) human responses to all questions with implicit prospects.

Figure 10: Consistency and decisiveness heatmap for all models and the human subjects.

Figure 11: Consistency and decisiveness heatmap for all models and the human subjects restricted to the explicit prospect setting.

Figure 12: Consistency and decisiveness heatmap for all models and the human subjects restricted to the implicit prospect setting.

Panel of Figure 13 — Figure 13: HE representation of the LLMs and the impact of sample size in implicit prospect. Blue: Explicit Prospect; Red: Sample size 100; Green: Sample size 20.

Model	$\boldsymbol{\sigma}$	$\boldsymbol{\gamma}$	$\boldsymbol{\beta}_{\text{gain}}$	$\boldsymbol{\beta}_{\text{loss}}$	Corr	MSE
Olmo-3-7B-Instruct-SFT	0.88	0.80	309	130	0.80	0.029
Olmo-3-7B-Instruct-DPO	0.88	0.81	320	142	0.82	0.030
Olmo-3-7B-Instruct	0.88	0.81	215	121	0.73	0.041
Olmo-3-7B-Think-SFT	1.27	1.13	1000	509	1.00	0.001
Olmo-3-7B-Think-DPO	1.33	1.16	1000	1000	1.00	0.000
Olmo-3-7B-Think	1.33	1.16	1000	1000	1.00	0.001

Appendix

Table 5: Dual-beta prospect theory model parameters for models over sequential training stages (explicit prospects).

Model	$\boldsymbol{\sigma}$	$\boldsymbol{\gamma}$	$\boldsymbol{\beta}_{\text{gain}}$	$\boldsymbol{\beta}_{\text{loss}}$	Corr	MSE
Olmo-3-7B-Instruct-SFT	2.40	1.26	1.41	0.01	0.35	0.021
Olmo-3-7B-Instruct-DPO	1.50	1.05	2.86	0.07	0.37	0.020
Olmo-3-7B-Instruct	1.25	0.99	4.80	1.29	0.44	0.020
Olmo-3-7B-Think-SFT	0.78	1.04	21.7	10.6	0.61	0.097
Olmo-3-7B-Think-DPO	0.98	0.86	1000	824	0.96	0.015
Olmo-3-7B-Think	0.73	0.71	1000	466	1.00	0.001

Appendix

Table 6: Dual-beta prospect theory model parameters for models over sequential training stages (implicit prospects).

Model	$\boldsymbol{\sigma}$	$\boldsymbol{\gamma}$	$\boldsymbol{\beta}_{\text{gain}}$	$\boldsymbol{\beta}_{\text{loss}}$
DeepSeek-R1	[0.81, 0.96]	[0.80, 0.91]	[832, 832]	[711, 711]
Gemini-2.5-Pro	[0.76, 0.86]	[0.81, 0.88]	[951, 951]	[1000, 1000]
GPT-5.1	[1.28, 1.35]	[1.14, 1.22]	[1000, 1000]	[1000, 1000]
Claude-4.5-Haiku	[0.88, 0.91]	[0.79, 0.81]	[221, 221]	[244, 244]
DeepSeek-Chat	[0.84, 0.89]	[0.81, 0.84]	[181, 181]	[149, 149]
Gemini-2.5-Flash	[0.84, 3.27]	[0.81, 4.61]	[4.53, 303]	[15, 1000]

Appendix

Table 7: 95% Confidence Intervals for dual-beta prospect theory parameters of black-box models with explicit prospects.

Model	$\boldsymbol{\sigma}$	$\boldsymbol{\gamma}$	$\boldsymbol{\beta}_{\text{gain}}$	$\boldsymbol{\beta}_{\text{loss}}$
DeepSeek-R1	[0.97, 1.01]	[0.98, 1.04]	[1000, 1000]	[346, 346]
Gemini-2.5-Pro	[0.96, 0.99]	[0.97, 1.02]	[147, 147]	[100, 100]
GPT-5.1	[0.99, 1.03]	[0.96, 1.02]	[460, 460]	[1000, 1000]
Claude-4.5-Haiku	[1.01, 1.14]	[0.92, 1.10]	[3.27, 6.59]	[19.1, 28.1]
DeepSeek-Chat	[0.68, 0.96]	[0.68, 0.78]	[8.43, 14.0]	[0.01, 1.24]
Gemini-2.5-Flash	[1.46, 1.68]	[0.77, 0.89]	[1.29, 3.89]	[11.8, 17.2]

Appendix

Table 8: 95% Confidence Intervals for dual-beta prospect theory parameters of black-box models with implicit prospects.

Model	$\boldsymbol{\sigma}$	$\boldsymbol{\gamma}$	$\boldsymbol{\beta}_{\text{gain}}$	$\boldsymbol{\beta}_{\text{loss}}$
Qwen2.5-7B-Instruct	[0.30, 0.90]	[0.35, 0.78]	[4.86, 140]	[0.01, 16.2]
Qwen2.5-Math-7B	[0.80, 0.96]	[0.81, 0.98]	[1000, 1000]	[403, 403]
Qwen3-30B-Instruct	[0.88, 2.06]	[0.81, 3.40]	[15.9, 213]	[0.01, 17.2]
Qwen3-30B-Thinking	[0.82, 0.92]	[0.80, 0.90]	[726, 726]	[1000, 1000]
Olmo-3-7B-Instruct-SFT	[0.86, 0.89]	[0.80, 0.81]	[309, 309]	[130, 130]
Olmo-3-7B-Instruct-DPO	[0.87, 0.89]	[0.80, 0.82]	[320, 320]	[142, 142]

Appendix

Table 9: 95% Confidence Intervals for dual-beta prospect theory parameters of open-weight models with explicit prospects.

Model	$\boldsymbol{\sigma}$	$\boldsymbol{\gamma}$	$\boldsymbol{\beta}_{\text{gain}}$	$\boldsymbol{\beta}_{\text{loss}}$
Qwen2.5-7B-Instruct	[23.4, 198]	[0.47, 0.90]	[0.01, 0.29]	[2.07, 3.28]
Qwen2.5-Math-7B	[0.20, 0.77]	[0.76, 1.48]	[4.77, 9.88]	[0.01, 2.02]
Qwen3-30B-Instruct	[1.02, 1.18]	[0.78, 0.89]	[13.8, 20.2]	[1.04, 4.84]
Qwen3-30B-Thinking	[0.99, 1.00]	[0.87, 0.88]	[668, 668]	[585, 585]
Olmo-3-7B-Instruct-SFT	[1.45, 54.5]	[0.63, 5.88]	[0.62, 3.47]	[0.01, 0.76]
Olmo-3-7B-Instruct-DPO	[1.19, 4.52]	[0.75, 3.52]	[1.40, 4.91]	[0.01, 1.26]

Appendix

Table 10: 95% Confidence Intervals for dual-beta prospect theory parameters of open-weight models with implicit prospects.

	Model 1	Model 2 (Shape-Only)
Model	$\boldsymbol{\beta}$	$\boldsymbol{\sigma}$	$\boldsymbol{\lambda}$	$\boldsymbol{\gamma}$
DeepSeek-R1	1000	391	3.19	1.35
Gemini-Pro	745	0.74	1000	0.86
GPT-5.1	1000	338	4.13	1.34
Claude Haiku	14	277	1.26	1.21
DeepSeek-Chat	95	294	1.41	1.49

Appendix

Table 11: Restricted prospect theory parameters of black-box models for decisions with explicit prospects.

	Model 1	Model 2 (Shape-Only)
Model	$\boldsymbol{\beta}$	$\boldsymbol{\sigma}$	$\boldsymbol{\lambda}$	$\boldsymbol{\gamma}$
DeepSeek-R1	407	1.24	506	1.32
Gemini-Pro	127	1.29	132	1.39
GPT-5.1	1000	1.32	1000	1.35
Claude Haiku	11	0.38	13	12
DeepSeek-Chat	6	0.21	10	25

Appendix

Table 12: Restricted prospect theory parameters of black-box models for decisions with implicit prospects.

Model	$\boldsymbol{\lambda_{reg}}$	$\boldsymbol{\kappa}$	$\boldsymbol{\alpha}$	Corr	MSE
DeepSeek-R1	0.01	108	0	0.53	0.14
Gemini-Pro	0.01	87	0	0.45	0.15
GPT-5.1	0.01	144	0	0.61	0.15
Claude Haiku	0.01	82	0	0.58	0.07
DeepSeek-Chat	0.01	61	0	0.48	0.08
Gemini-Flash	0.01	127	0.31	0.77	0.03

Appendix

Table 13: Regret aversion parameters of black-box models for decisions with explicit prospects.

Model	$\boldsymbol{\lambda_{reg}}$	$\boldsymbol{\kappa}$	$\boldsymbol{\alpha}$	Corr	MSE
DeepSeek-R1	0.01	51	0	0.30	0.19
Gemini-Pro	0.01	46	0	0.30	0.17
GPT-5.1	0.01	59	0	0.33	0.21
Claude Haiku	0.02	780	181	0.00	0.11
DeepSeek-Chat	0.01	0	2.25	-0.11	0.07
Gemini-Flash	0.81	0	1.32	0.25	0.07

Appendix

Table 14: Regret aversion parameters of black-box models for decisions with implicit prospects.

Model	$\boldsymbol{\sigma}$	$\boldsymbol{\lambda}$	$\boldsymbol{\gamma}$	$\boldsymbol{\beta}$	Corr	MSE
DeepSeek-R1	0.79	1000	0.86	1000	0.98	0.012
Gemini-Pro	0.82	0.57	0.83	1000	0.95	0.019
GPT-5.1	1.33	1000	1.16	1000	1.00	0.002
Claude Haiku	0.92	3.89	0.83	89	0.72	0.063
DeepSeek-Chat	0.84	0.43	0.84	159	0.75	0.042
Gemini-Flash	0.95	1.58	0.94	20	0.87	0.015

Appendix

Table 15: Standard prospect theory parameters for frontier models with explicit prospects.

Model	$\boldsymbol{\sigma}$	$\boldsymbol{\lambda}$	$\boldsymbol{\gamma}$	$\boldsymbol{\beta}$	Corr	MSE
DeepSeek-R1	1.05	1.20	0.92	1000	0.99	0.005
Gemini-Pro	0.84	1.05	1.24	128	0.95	0.021
GPT-5.1	1.04	1000	0.94	1000	1.00	0.001
Claude Haiku	0.70	0.90	2.10	12	0.66	0.059
DeepSeek-Chat	0.80	0.48	2.51	9	0.59	0.039
Gemini-Flash	1.31	0.91	0.67	17	0.69	0.037

Appendix

Table 16: Standard prospect theory parameters for frontier models with implicit prospects.

Model	$\boldsymbol{\sigma}$	$\boldsymbol{\lambda}$	$\boldsymbol{\gamma}$	$\boldsymbol{\beta}$	Corr	MSE
Qwen2.5-7B-Instruct	0.58	0.80	3.59	8	0.83	0.017
Qwen2.5-Math-7B	1.11	0.34	1.03	1000	0.99	0.004
Qwen3-30B-Instruct	0.94	0.01	0.86	48	0.57	0.041
Qwen3-30B-Thinking	0.87	1000	0.81	1000	0.99	0.003
Olmo-3-7B-Instruct	0.87	0.20	0.82	220	0.73	0.042
Olmo-3-7B-Think	1.33	1000	1.15	1000	1.00	0.001

Appendix

Table 17: Standard prospect theory parameters for open models with explicit prospects.

Model	$\boldsymbol{\sigma}$	$\boldsymbol{\lambda}$	$\boldsymbol{\gamma}$	$\boldsymbol{\beta}$	Corr	MSE
Qwen2.5-7B-Instruct	1.60	0.21	3.17	19	0.58	0.056
Qwen2.5-Math-7B	0.55	0.12	0.88	7	0.54	0.027
Qwen3-30B-Instruct	1.11	0.19	0.81	17	0.50	0.047
Qwen3-30B-Thinking	0.98	1.67	0.85	913	0.95	0.024
Olmo-3-7B-Instruct	1.25	0.27	1.00	4.80	0.44	0.020
Olmo-3-7B-Think	0.82	0.69	0.78	702	1.00	0.001

Appendix

Table 18: Standard prospect theory parameters for open models with implicit prospects.

LLM Decision-Making

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As large language models (LLMs) are increasingly used in decision support, it is important to understand whether their choices under uncertainty exhibit stable and interpretable behavioural regularities. Human decision-making combines relatively persistent risk preferences with context-dependent adjustment, yet it remains unclear whether analogous behavioural structure can be observed in LLM-based decision systems. Here we examine this question using a controlled multi-model framework based on no-limit Texas Hold'em, where behaviour is quantified by Participation, measuring voluntary engagement in uncertain opportunities, and Proactiveness, measuring pre-flop risk escalation. Across homogeneous self-play and heterogeneous mixed-model interactions, frontier LLMs exhibit stable, model-specific risk profiles, forming a spectrum from conservative to aggressive decision styles. These profiles remain largely robust under changing opponent composition, while the most conservative and most aggressive models diverge further in mixed settings. Under global risk pressure and personal resource constraint, models adapt in structured but heterogeneous ways, ranging from broad behavioural contraction to selective de-escalation and near-invariant behaviour. These findings suggest that LLMs differ not only in baseline risk disposition, but also in the risk signals they respond to and the flexibility with which they adjust, providing a behavioural basis for auditing risk-sensitive decision-making in interactive settings. Our code is publicly available at: https://github.com/XuankunRong/AgentTexasPoker.

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